Researchers from our department showcased their work at NeurIPS 2024, a leading conference that brings together experts in machine learning and related sciences to exchange ideas, foster collaboration, and advance interdisciplinary innovation.
Below are the abstracts of the accepted papers:
Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making
Drago Plecko Columbia University, Elias Bareinboim Columbia University
Abstract:
As society increasingly relies on AI-based tools for decision-making in socially sensitive domains, investigating fairness and equity of such automated systems has become a critical field of inquiry. Most of the literature in fair machine learning focuses on defining and achieving fairness criteria in the context of prediction, while not explicitly focusing on how these predictions may be used later on in the pipeline. For instance, if commonly used criteria, such as independence or sufficiency, are satisfied for a prediction score S used for binary classification, they need not be satisfied after an application of a simple thresholding operation on S (as commonly used in practice). In this paper, we take an important step to address this issue in numerous statistical and causal notions of fairness. We introduce the notion of a margin complement, which measures how much a prediction score S changes due to a thresholding operation. We then demonstrate that the marginal difference in the optimal 0/1 predictor Yb between groups, written P(ˆy | x1) − P(ˆy | x0), can be causally decomposed into the influences of X on the L2-optimal prediction score S and the influences of X on the margin complement M, along different causal pathways (direct, indirect, spurious). We then show that under suitable causal assumptions, the influences of X on the prediction score S are equal to the influences of X on the true outcome Y . This yields a new decomposition of the disparity in the predictor Yb that allows us to disentangle causal differences inherited from the true outcome Y that exists in the real world vs. those coming from the optimization procedure itself. This observation highlights the need for more regulatory oversight due to the potential for bias amplification, and to address this issue we introduce new notions of weak and strong business necessity, together with an algorithm for assessing whether these notions are satisfied. We apply our method to three real-world datasets and derive new insights on bias amplification in prediction and decision-making.
Causal Imitation for Markov Decision Processes: a Partial Identification Approach
Kangrui Ruan Columbia University, Junzhe Zhang Columbia University, Xuan Di Columbia University, Elias Bareinboim Columbia University
Abstract:
Imitation learning enables an agent to learn from expert demonstrations when the performance measure is unknown and the reward signal is not specified. Standard imitation methods do not generally apply when the learner and the expert’s sensory capabilities mismatch and demonstrations are contaminated with unobserved confounding bias. To address these challenges, recent advancements in causal imitation learning have been pursued. However, these methods often require access to underlying causal structures that might not always be available, posing practical challenges.In this paper, we investigate robust imitation learning within the framework of canonical Markov Decision Processes (MDPs) using partial identification, allowing the agent to achieve expert performance even when the system dynamics are not uniquely determined from the confounded expert demonstrations. Specifically, first, we theoretically demonstrate that when unobserved confounders (UCs) exist in an MDP, the learner is generally unable to imitate expert performance. We then explore imitation learning in partially identifiable settings — either transition distribution or reward function is non-identifiable from the available data and knowledge. Augmenting the celebrated GAIL method (Ho \& Ermon, 2016), our analysis leads to two novel causal imitation algorithms that can obtain effective policies guaranteed to achieve expert performance.
Partial Transportability for Domain Generalization
Kasra Jalaldoust Columbia University, Alexis Bellot Columbia University, Elias Bareinboim Columbia University
Abstract:
A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of existing predictors. Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution, such as the generalization error of a classifiers, given data from source domains and assumptions about the data generating mechanisms, encoded in causal diagrams. Our contribution is to provide the first general estimation technique for transportability problems, adapting existing parameterization schemes such Neural Causal Models to encode the structural constraints necessary for cross-population inference. We demonstrate the expressiveness and consistency of this procedure and further propose a gradient-based optimization scheme for making scalable inferences in practice. Our results are corroborated with experiments.
Unified Covariate Adjustment for Causal Inference
Yonghan Jung Purdue University, Jin Tian Iowa State University, Elias Bareinboim Columbia University
Abstract:
Causal effect identification and estimation are two crucial tasks in causal inference. Although causal effect identification has been theoretically resolved, many existing estimators only address a subset of scenarios, known as the sequential back-door adjustment (SBD) (Pearl and Robins, 1995) or g-formula (Robins, 1986). Recent efforts for developing general-purpose estimators with broader coverage, incorporating the front-door adjustment (FD) (Pearl, 2000) and more, lack scalability due to the high computational cost of summing over high-dimensional variables. In this paper, we introduce a novel approach that achieves broad coverage of causal estimands beyond the SBD, incorporating various sum-product functionals like the FD, while maintaining scalability — estimated in polynomial time relative to the number of variables and samples. Specifically, we present the class of UCA for which a scalable and doubly robust estimator is developed. In particular, we illustrate the expressiveness of UCA for a wide spectrum of causal estimands (e.g., SBD, FD, and more) in causal inference. We then develop an estimator that exhibits computational efficiency and doubly robustness. The scalability and robustness of the proposed framework are verified through simulations.
Disentangled Representation Learning in Non-Markovian Causal Systems
Adam Li Columbia University, Yushu Pan Columbia University, Elias Bareinboim Columbia University
Abstract:
Considering various data modalities, such as images, videos, and text, humans perform causal reasoning using high-level causal variables, as opposed to operating at the low, pixel level from which the data comes. In practice, most causal reasoning methods assume that the data is described as granular as the underlying causal generative factors, which is often violated in various AI tasks. This mismatch translates into a lack of guarantees in various tasks such as generative modeling, decision-making, fairness, and generalizability, to cite a few. In this paper, we acknowledge this issue and study the problem of causal disentangled representation learning from a combination of data gathered from various heterogeneous domains and assumptions in the form of a latent causal graph. To the best of our knowledge, the proposed work is the first to consider i) non-Markovian causal settings, where there may be unobserved confounding, ii) arbitrary distributions that arise from multiple domains, and iii) a relaxed version of disentanglement. Specifically, we introduce graphical criteria that allow for disentanglement under various conditions. Building on these results, we develop an algorithm that returns a causal disentanglement map, highlighting which latent variables can be disentangled given the combination of data and assumptions. The theory is corroborated by experiments.
The Fine-Grained Complexity of Gradient Computation for Training Large Language Models
Josh Alman Columbia University, Zhao Song Adobe Research
Abstract:
Large language models (LLMs) have made fundamental contributions over the last a few years. To train an LLM, one needs to alternatingly run ‘forward’ computations and ‘backward’ computations. The forward computation can be viewed as attention function evaluation, and the backward computation can be viewed as a gradient computation. In previous work by [Alman and Song, NeurIPS 2023], it was proved that the forward step can be performed in almost-linear time in certain parameter regimes, but that there is no truly sub-quadratic time algorithm in the remaining parameter regimes unless the popular hypothesis SETH is false. In this work, we show nearly identical results for the harder-seeming problem of computing the gradient of loss function of one layer attention network, and thus for the entire process of LLM training. This completely characterizes the fine-grained complexity of every step of LLM training.
Metric Transforms and Low Rank Representations of Kernels for Fast Attention
Timothy Chu Independent Researcher, Josh Alman Columbia University, Gary L. Miller Carnegie Mellon University, Shyam Narayanan Citadel Securities, Mark Sellke Harvard University, Zhao Song Simons Institute for the Theory of Computing, UC Berkeley
Abstract:
We introduce a new linear-algebraic tool based on group representation theory, and use it to address three key problems in machine learning.
- Past researchers have proposed fast attention algorithms for LLMs by approximating or replace softmax attention with other functions, such as low-degree polynomials. The key property of these functions is that, when applied entrywise to the matrix QK>, the result is a low rank matrix when Q and K are n × d matrices and n d. This suggests a natural question: what are all functions f with this property? If other f exist and are quickly computable, they can be used in place of softmax for fast subquadratic attention algorithms. It was previously known that low-degree polynomials have this property. We prove that low-degree polynomials are the only piecewise continuous functions with this property. This suggests that the low-rank fast attention only works for functions approximable by polynomials. Our work gives a converse to the polynomial method in algorithm design.
- We prove the first full classification of all positive definite kernels that are functions of Manhattan or `1 distance. Our work generalizes, and also gives a new proof for, an existing theorem at the heart of kernel methods in machine learning: the classification of all positive definite kernels that are functions of Euclidean distance.
- The key problem in metric transforms, a mathematical theory used in geometry and machine learning, asks what functions transform pairwise distances in metric space M to metric space N for specified M and N. We prove the first full classification of functions that transform Manhattan distances to Manhattan distances. Our work generalizes the foundational work of Schoenberg, which fully classifies functions that transform Euclidean to Euclidean distances.
We additionally prove results about stable-rank preserving functions that are potentially useful in algorithmic design, and more. Our core tool for all our results is a new technique called the representation theory of the hyperrectangle.
Statistical-Computational Trade-offs for Density Estimation
Anders Aamand University of Copenhagen, Alexandr Andoni Columbia University, Justin Chen hen MIT, Piotr Indyk hen MIT, Shyam Narayanan Citadel Securities, Sandeep Silwal UW-Madison, Haike Xu MIT
Abstract:
We study the density estimation problem defined as follows: given k distributions p1, . . . , pk over a discrete domain [n], as well as a collection of samples chosen from a “query” distribution q over [n], output pi that is “close” to q. Recently [1] gave the first and only known result that achieves sublinear bounds in both the sampling complexity and the query time while preserving polynomial data structure space. However, their improvement over linear samples and time is only by subpolynomial factors. Our main result is a lower bound showing that, for a broad class of data structures, their bounds cannot be significantly improved. In particular, if an algorithm uses O(n/ logc k) samples for some constant c > 0 and polynomial space, then the query time of the data structure must be at least k 1−O(1)/ log log k , i.e., close to linear in the number of distributions k. This is a novel statistical-computational trade-off for density estimation, demonstrating that any data structure must use close to a linear number of samples or take close to linear query time. The lower bound holds even in the realizable case where q = pi for some i, and when the distributions are flat (specifically, all distributions are uniform over half of the domain [n]). We also give a simple data structure for our lower bound instance with asymptotically matching upper bounds. Experiments show that the data structure is quite efficient in practice.
Hypothesis Testing the Circuit Hypothesis in LLMs
Claudia Shi Columbia University, Nicolas Beltran Velez Columbia University, Achille Nazaret Columbia University, Carolina Zheng Columbia University, Adrià Garriga-Alonso FAR AI, Andrew Jesson Columbia University, Maggie Makar University of Michigan, Ann Arbor, David Blei Columbia University
Abstract:
Large language models (LLMs) demonstrate surprising capabilities, but we do not understand how they are implemented. One hypothesis suggests that these capabilities are primarily executed by small subnetworks within the LLM, known as circuits. But how can we evaluate this hypothesis?In this paper, we formalize a set of criteria that a circuit is hypothesized to meet and develop a suite of hypothesis tests to evaluate how well circuits satisfy them. The criteria focus on the extent to which the LLM’s behavior is preserved, the degree of localization of this behavior, and whether the circuit is minimal.We apply these tests to six circuits described in the research literature. We find that synthetic circuits — circuits that are hard-coded in the model — align with the idealized properties. Circuits discovered in Transformer models satisfy the criteria to varying degrees.To facilitate future empirical studies of circuits, we created the \textit{circuitry} package, a wrapper around the \textit{TransformerLens} library, which abstracts away lower-level manipulations of hooks and activations. The software is available at \url{https://github.com/blei-lab/circuitry}.
Treeffuser: probabilistic prediction via conditional diffusions with gradient-boosted trees
Nicolas Beltran Velez Columbia University, Alessandro A Grande Columbia University, Achille Nazaret Columbia University, Alp Kucukelbir Columbia University, David Blei Columbia University
Abstract:
Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods assume parametric responses, such as Gaussian or Poisson distributions. When these assumptions fail, such models lead to bad predictions and poorly calibrated uncertainty. In this paper, we propose Treeffuser, an easy-to-use method for probabilistic prediction on tabular data. The idea is to learn a conditional diffusion model where the score function is estimated using gradient-boosted trees. The conditional diffusion model makes Treeffuser flexible and non-parametric, while the gradient-boosted trees make it robust and easy to train on CPUs. Treeffuser learns well-calibrated predictive distributions and can handle a wide range of regression tasks—including those with multivariate, multimodal, and skewed responses. We study Treeffuser on synthetic and real data and show that it outperforms existing methods, providing better calibrated probabilistic predictions. We further demonstrate its versatility with an application to inventory allocation under uncertainty using sales data from Walmart. We implement Treeffuser in https://github.com/blei-lab/treeffuser.
Estimating the Hallucination Rate of Generative AI
Andrew Jesson Columbia University, Nicolas Beltran Velez Columbia University, Quentin Chu Columbia University, Sweta Karlekar Columbia University, Jannik Kossen University of Oxford, Yarin Gal University of Oxford, John Cunningham Columbia University, David Blei Columbia University
Abstract:
This paper presents a method for estimating the hallucination rate for in-context learning (ICL) with generative AI. In ICL, a conditional generative model (CGM) is prompted with a dataset and a prediction question and asked to generate a response. One interpretation of ICL assumes that the CGM computes the posterior predictive of an unknown Bayesian model, which implicitly defines a joint distribution over observable datasets and latent mechanisms. This joint distribution factorizes into two components: the model prior over mechanisms and the model likelihood of datasets given a mechanism. With this perspective, we define a \textit{hallucination} as a generated response to the prediction question with low model likelihood given the mechanism. We develop a new method that takes an ICL problem and estimates the probability that a CGM will generate a hallucination. Our method only requires generating prediction questions and responses from the CGM and evaluating its response log probability. We empirically evaluate our method using large language models for synthetic regression and natural language ICL tasks.
EigenVI: score-based variational inference with orthogonal function expansions
Diana Cai Flatiron Institute, Chirag Modi Flatiron Institute, Charles Margossian Flatiron Institute, Robert Gower Flatiron Institute, David Blei Columbia University, Lawrence Saul Flatiron Institute
Abstract
We develop EigenVI, an eigenvalue-based approach for black-box variational inference (BBVI). EigenVI constructs its variational approximations from orthogonal function expansions. For distributions over R D, the lowest order term in these expansions provides a Gaussian variational approximation, while higher-order terms provide a systematic way to model non-Gaussianity. These approximations are flexible enough to model complex distributions (multimodal, asymmetric), but they are simple enough that one can calculate their low-order moments and draw samples from them. EigenVI can also model other types of random variables (e.g., nonnegative, bounded) by constructing variational approximations from different families of orthogonal functions. Within these families, EigenVI computes the variational approximation that best matches the score function of the target distribution by minimizing a stochastic estimate of the Fisher divergence. Notably, this optimization reduces to solving a minimum eigenvalue problem, so that EigenVI effectively sidesteps the iterative gradient-based optimizations that are required for many other BBVI algorithms. (Gradient-based methods can be sensitive to learning rates, termination criteria, and other tunable hyperparameters.) We use EigenVI to approximate a variety of target distributions, including a benchmark suite of Bayesian models from posteriordb. On these distributions, we find that EigenVI is more accurate than existing methods for Gaussian BBVI.
Optimization-based Causal Estimation from Heterogeneous Environments
Mingzhang Yin University of Florida, Yixin Wang University of Michigan, David Blei Columbia University
Abstract:
This paper presents a new optimization approach to causal estimation. Given data that contains covariates and an outcome, which covariates are causes of the outcome, and what is the strength of the causality? In classical machine learning (ML), the goal of optimization is to maximize predictive accuracy. However, some covariates might exhibit a non-causal association with the outcome. Such spurious associations provide predictive power for classical ML, but they prevent us from causally interpreting the result. This paper proposes CoCo, an optimization algorithm that bridges the gap between pure prediction and causal inference. CoCo leverages the recently-proposed idea of environments, datasets of covariates/response where the causal relationships remain invariant but where the distribution of the covariates changes from environment to environment. Given datasets from multiple environments—and ones that exhibit sufficient heterogeneity—CoCo maximizes an objective for which the only solution is the causal solution. We describe the theoretical foundations of this approach and demonstrate its effectiveness on simulated and real datasets. Compared to classical ML and existing methods, CoCo provides more accurate estimates of the causal model and more accurate predictions under interventions.
Understanding Transformer Reasoning Capabilities via Graph Algorithms
Clayton Sanford Columbia University, Bahare Fatemi Google Research, Ethan Hall Google, Anton Tsitsulin Google Research, Mehran Kazemi Google DeepMind, Jonathan Halcrow Google Research, Bryan Perozzi Google Research, Vahab Mirrokni Google Research
Abstract:
Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network’s depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.
Researchers from the department presented machine learning and artificial intelligence research at the thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2023).
Outstanding Dataset Paper
ClimSim: An Open Large-Scale Dataset For Training High-Resolution Physics Emulators In Hybrid Multi-Scale Climate Models
Sungduk Yu, Walter Hannah, Liran Peng, Jerry Lin, Mohamed Aziz Bhouri, Ritwik Gupta, Björn Lütjens, Justus C. Will, Gunnar Behrens, Nora Loose, Charles Stern, Tom Beucler, Bryce Harrop, Benjamin Hillman, Andrea Jenney, Savannah L. Ferretti, Nana Liu, Animashree Anandkumar, Noah Brenowitz, Veronika Eyring, Nicholas Geneva, Pierre Gentine, Stephan Mandt, Jaideep Pathak, Akshay Subramaniam, Carl Vondrick, Rose Yu, Laure Zanna, Ryan Abernathey, Fiaz Ahmed, David Bader, Pierre Baldi, Elizabeth Barnes, Christopher Bretherton, Julius Busecke, Peter Caldwell, Wayne Chuang, Yilun Han, YU HUANG, Fernando Iglesias-Suarez, Sanket Jantre, Karthik Kashinath, Marat Khairoutdinov, Thorsten Kurth, Nicholas Lutsko, Po-Lun Ma, Griffin Mooers, J. David Neelin, David Randall, Sara Shamekh, Mark Taylor, Nathan Urban, Janni Yuval, Guang Zhang, Tian Zheng, Mike Pritchard
Abstract:
Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore’s Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator’s macro-scale physical state. The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring. The data (https://huggingface.co/datasets/LEAP/ClimSim_high-res) and code (https://leap-stc.github.io/ClimSim) are released openly to support the development of hybrid ML-physics and high-fidelity climate simulations for the benefit of science and society.
Objaverse-XL: A Colossal Universe of 3D Objects
Matt Deitke, Ruoshi Liu, Matthew Wallingford, Huong Ngo, Oscar Michel, Aditya Kusupati, Alan Fan, Christian Laforte, Vikram Voleti, Samir Yitzhak Gadre, Eli VanderBilt, Aniruddha Kembhavi, Carl Vondrick, Georgia Gkioxari, Kiana Ehsani, Ludwig Schmidt, Ali Farhadi
Abstract:
Natural language processing and 2D vision models have attained remarkable proficiency on many tasks primarily by escalating the scale of training data. However, 3D vision tasks have not seen the same progress, in part due to the challenges of acquiring high-quality 3D data. In this work, we present Objaverse-XL, a dataset of over 10 million 3D objects. Our dataset comprises deduplicated 3D objects from a diverse set of sources, including manually designed objects, photogrammetry scans of landmarks and everyday items, and professional scans of historic and antique artifacts. Representing the largest scale and diversity in the realm of 3D datasets, Objaverse-XL enables significant new possibilities for 3D vision. Our experiments demonstrate the improvements enabled with the scale provided by Objaverse-XL. We show that by training Zero123 on novel view synthesis, utilizing over 100 million multi-view rendered images, we achieve strong zero-shot generalization abilities. We hope that releasing Objaverse-XL will enable further innovations in the field of 3D vision at scale.
Causal discovery from observational and interventional data across multiple environments
Adam Li, Amin Jaber, Elias Bareinboim
Abstract:
A fundamental problem in many sciences is the learning of causal structure underlying a system, typically through observation and experimentation. Commonly, one even collects data across multiple domains, such as gene sequencing from different labs, or neural recordings from different species. Although there exist methods for learning the equivalence class of causal diagrams from observational and experimental data, they are meant to operate in a single domain. In this paper, we develop a fundamental approach to structure learning in non-Markovian systems (i.e. when there exist latent confounders) leveraging observational and interventional data collected from multiple domains. Specifically, we start by showing that learning from observational data in multiple domains is equivalent to learning from interventional data with unknown targets in a single domain. But there are also subtleties when considering observational and experimental data. Using causal invariances derived from do-calculus, we define a property called S-Markov that connects interventional distributions from multiple-domains to graphical criterion on a selection diagram. Leveraging the S-Markov property, we introduce a new constraint-based causal discovery algorithm, S-FCI, that can learn from observational and interventional data from different domains. We prove that the algorithm is sound and subsumes existing constraint-based causal discovery algorithms.
A Causal Framework for Decomposing Spurious Variations
Drago Plecko, Elias Bareinboim
Abstract:
One of the fundamental challenges found throughout the data sciences is to explain why things happen in specific ways, or through which mechanisms a certain variable X exerts influences over another variable Y. In statistics and machine learning, significant efforts have been put into developing machinery to estimate correlations across variables efficiently. In causal inference, a large body of literature is concerned with the decomposition of causal effects under the rubric of mediation analysis. However, many variations are spurious in nature, including different phenomena throughout the applied sciences. Despite the statistical power to estimate correlations and the identification power to decompose causal effects, there is still little understanding of the properties of spurious associations and how they can be decomposed in terms of the underlying causal mechanisms. In this manuscript, we develop formal tools for decomposing spurious variations in both Markovian and Semi-Markovian models. We prove the first results that allow a non-parametric decomposition of spurious effects and provide sufficient conditions for the identification of such decompositions. The described approach has several applications, ranging from explainable and fair AI to questions in epidemiology and medicine, and we empirically demonstrate its use on a real-world dataset.
Nonparametric Identifiability of Causal Representations from Unknown Interventions
Julius von Kügelgen, Michel Besserve, Liang Wendong, Luigi Gresele, Armin Kekić, Elias Bareinboim, David Blei, Bernhard Schölkopf
Abstract:
We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional mixtures of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that at least one pair of distinct perfect interventional domains per node guarantees identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.
Estimating Causal Effects Identifiable from Combination of Observations and Experiments
Yonghan Jung, Ivan Diaz, Jin Tian, Elias Bareinboim
Abstract:
Learning cause and effect relations is arguably one of the central challenges found throughout the data sciences. Formally, determining whether a collection of observational and interventional distributions can be combined to learn a target causal relation is known as the problem of generalized identification (or g-identification) [Lee et al., 2019]. Although g-identification has been well understood and solved in theory, it turns out to be challenging to apply these results in practice, in particular when considering the estimation of the target distribution from finite samples. In this paper, we develop a new, general estimator that exhibits multiply robustness properties for g-identifiable causal functionals. Specifically, we show that any g-identifiable causal effect can be expressed as a function of generalized multioutcome sequential back-door adjustments that are amenable to estimation. We then construct a corresponding estimator for the g-identification expression that exhibits robustness properties to bias. We analyze the asymptotic convergence properties of the estimator. Finally, we illustrate the use of the proposed estimator in experimental studies. Simulation results corroborate the theory.
Causal Fairness for Outcome Control
Drago Plecko, Elias Bareinboim
Abstract:
As society transitions towards an AI-based decision-making infrastructure, an ever-increasing number of decisions once under control of humans are now delegated to automated systems. Even though such developments make various parts of society more efficient, a large body of evidence suggests that a great deal of care needs to be taken to make such automated decision-making systems fair and equitable, namely, taking into account sensitive attributes such as gender, race, and religion. In this paper, we study a specific decision-making task called outcome control in which an automated system aims to optimize an outcome variable Y while being fair and equitable. The interest in such a setting ranges from interventions related to criminal justice and welfare, all the way to clinical decision-making and public health. In this paper, we first analyze through causal lenses the notion of benefit, which captures how much a specific individual would benefit from a positive decision, counterfactually speaking, when contrasted with an alternative, negative one. We introduce the notion of benefit fairness, which can be seen as the minimal fairness requirement in decision-making, and develop an algorithm for satisfying it. We then note that the benefit itself may be influenced by the protected attribute, and propose causal tools which can be used to analyze this. Finally, if some of the variations of the protected attribute in the benefit are considered as discriminatory, the notion of benefit fairness may need to be strengthened, which leads us to articulating a notion of causal benefit fairness. Using this notion, we develop a new optimization procedure capable of maximizing Y while ascertaining causal fairness in the decision process.
Distribution-Free Statistical Dispersion Control for Societal Applications
Zhun Deng, Thomas Zollo, Jake Snell, Toniann Pitassi, Richard Zemel
Abstract:
Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an individual prediction will incur a loss value in a specified range. However, for many high-stakes applications, it is crucial to understand and control the dispersion of a loss distribution, or the extent to which different members of a population experience unequal effects of algorithmic decisions. We initiate the study of distribution-free control of statistical dispersion measures with societal implications and propose a simple yet flexible framework that allows us to handle a much richer class of statistical functionals beyond previous work. Our methods are verified through experiments in toxic comment detection, medical imaging, and film recommendation.
Representational Strengths and Limitations of Transformers
Clayton Sanford, Daniel Hsu, Matus Telgarsky
Abstract:
Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.
Fast Attention Requires Bounded Entries
Josh Alman, Zhao Song
Abstract:
In modern machine learning, inner product attention computation is a fundamental task for training large language models such as Transformer, GPT-1, BERT, GPT-2, GPT-3 and ChatGPT. Formally, in this problem, one is given as input three matrices Q,K,V∈[−B,B]n×d, and the goal is to construct the matrix Att(Q,K,V):=diag(A1n)−1AV∈ℝn×d, where A=exp(QK⊤/d) is the `attention matrix’, and exp is applied entry-wise. Straightforward methods for this problem explicitly compute the n×n attention matrix A, and hence require time Ω(n2) even when d=no(1) is small.
In this paper, we investigate whether faster algorithms are possible by implicitly making use of the matrix A. We present two results, showing that there is a sharp transition at B=Θ(logn‾‾‾‾‾√).
∙ If d=O(logn) and B=o(logn‾‾‾‾‾√), there is an n1+o(1) time algorithm to approximate Att(Q,K,V) up to 1/poly(n) additive error.
∙ If d=O(logn) and B=Θ(logn‾‾‾‾‾√), assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory, it is impossible to approximate Att(Q,K,V) up to 1/poly(n) additive error in truly subquadratic time n2−Ω(1).
This gives a theoretical explanation for the phenomenon observed in practice that attention computation is much more efficient when the input matrices have smaller entries.
Bypass Exponential Time Preprocessing: Fast Neural Network Training via Weight-Data Correlation Preprocessing
Josh Alman, Jiehao Liang, Zhao Song, Ruizhe Zhang, Danyang Zhuo
Abstract:
Over the last decade, deep neural networks have transformed our society, and they are already widely applied in various machine learning applications. State-of-art deep neural networks are becoming larger in size every year to deliver increasing model accuracy, and as a result, model training consumes substantial computing resources and will only consume more in the future. Using current training methods, in each iteration, to process a data point x∈ℝd in a layer, we need to spend Θ(md) time to evaluate all the m neurons in the layer. This means processing the entire layer takes Θ(nmd) time for n data points. Recent work [Song, Yang and Zhang, NeurIPS 2021] reduces this time per iteration to o(nmd), but requires exponential time to preprocess either the data or the neural network weights, making it unlikely to have practical usage.
In this work, we present a new preprocessing method that simply stores the weight-data correlation in a tree data structure in order to quickly, dynamically detect which neurons fire at each iteration. Our method requires only O(nmd) time in preprocessing and still achieves o(nmd) time per iteration. We complement our new algorithm with a lower bound, proving that assuming a popular conjecture from complexity theory, one could not substantially speed up our algorithm for dynamic detection of firing neurons.
Differentially Private Approximate Near Neighbor Counting in High Dimensions
Alexandr Andoni, Piotr Indyk, Sepideh Mahabadi, Shyam Narayanan
Abstract:
Range counting (e.g., counting the number of data points falling into a given query ball) under differential privacy has been studied extensively. However, the current algorithms for this problem are subject to the following dichotomy. One class of algorithms suffers from an additive error that is a fixed polynomial in the number of points. Another class of algorithms allows for polylogarithmic additive error, but the error grows exponentially in the dimension. To achieve the latter, the problem is relaxed to allow a “fuzzy” definition of the range boundary, e.g., a count of the points in a ball of radius r might also include points in a ball of radius cr for some c > 1.
In this paper, we present an efficient algorithm that offers a sweet spot between these two classes. The algorithm has an additive error that is an arbitrary small power of the data set size, depending on how fuzzy the range boundary is, as well as a small (1 + o(1)) multiplicative error. Crucially, the amount of noise added has no dependence on the dimension. Our algorithm introduces a variant of Locality-Sensitive Hashing, utilizing it in a novel manner.
Variational Inference with Gaussian Score Matching
Chirag Modi, Robert Gower, Charles Margossian, Yuling Yao, David Blei, Lawrence Saul
Abstract:
Variational inference (VI) is a method to approximate the computationally intractable posterior distributions that arise in Bayesian statistics. Typically, VI fits a simple parametric distribution to the target posterior by minimizing an appropriate objective such as the evidence lower bound (ELBO). In this work, we present a new approach to VI based on the principle of score matching, that if two distributions are equal then their score functions (i.e., gradients of the log density) are equal at every point on their support. With this, we develop score matching VI, an iterative algorithm that seeks to match the scores between the variational approximation and the exact posterior. At each iteration, score matching VI solves an inner optimization, one that minimally adjusts the current variational estimate to match the scores at a newly sampled value of the latent variables.
We show that when the variational family is a Gaussian, this inner optimization enjoys a closed form solution, which we call Gaussian score matching VI (GSM-VI). GSM-VI is also a “black box” variational algorithm in that it only requires a differentiable joint distribution, and as such it can be applied to a wide class of models. We compare GSM-VI to black box variational inference (BBVI), which has similar requirements but instead optimizes the ELBO. We study how GSM-VI behaves as a function of the problem dimensionality, the condition number of the target covariance matrix (when the target is Gaussian), and the degree of mismatch between the approximating and exact posterior distribution. We also study GSM-VI on a collection of real-world Bayesian inference problems from the posteriorDB database of datasets and models. In all of our studies we find that GSM-VI is faster than BBVI, but without sacrificing accuracy. It requires 10-100x fewer gradient evaluations to obtain a comparable quality of approximation.
Practical and Asymptotically Exact Conditional Sampling in Diffusion Models
Luhuan Wu, Brian Trippe, Christian Naesseth, David Blei, John Cunningham
Abstract:
Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and on MNIST image inpainting and class-conditional generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state-of-the-art.
Causal-structure Driven Augmentations for Text OOD Generalization
Amir Feder, Yoav Wald, Claudia Shi, Suchi Saria, David Blei
Abstract:
The reliance of text classifiers on spurious correlations can lead to poor generalization at deployment, raising concerns about their use in safety-critical domains such as healthcare. In this work, we propose to use counterfactual data augmentation, guided by knowledge of the causal structure of the data, to simulate interventions on spurious features and to learn more robust text classifiers. We show that this strategy is appropriate in prediction problems where the label is spuriously correlated with an attribute. Under the assumptions of such problems, we discuss the favorable sample complexity of counterfactual data augmentation, compared to importance re-weighting. Pragmatically, we match examples using auxiliary data, based on diff-in-diff methodology, and use a large language model (LLM) to represent a conditional probability of text. Through extensive experimentation on learning caregiver-invariant predictors of clinical diagnoses from medical narratives and on semi-synthetic data, we demonstrate that our method for simulating interventions improves out-of-distribution (OOD) accuracy compared to baseline invariant learning algorithms.
Evaluating the Moral Beliefs Encoded in LLMs
Nino Scherrer, Claudia Shi, Amir Feder, David Blei
Abstract:
This paper presents a case study on the design, administration, post-processing, and evaluation of surveys on large language models (LLMs). It comprises two components: (1) A statistical method for eliciting beliefs encoded in LLMs. We introduce statistical measures and evaluation metrics that quantify the probability of an LLM “making a choice”, the associated uncertainty, and the consistency of that choice. (2) We apply this method to study what moral beliefs are encoded in different LLMs, especially in ambiguous cases where the right choice is not obvious. We design a large-scale survey comprising 680 high-ambiguity moral scenarios (e.g., “Should I tell a white lie?”) and 687 low-ambiguity moral scenarios (e.g., “Should I stop for a pedestrian on the road?”). Each scenario includes a description, two possible actions, and auxiliary labels indicating violated rules (e.g., “do not kill”). We administer the survey to 28 open- and closed-source LLMs. We find that (a) in unambiguous scenarios, most models “choose” actions that align with commonsense. In ambiguous cases, most models express uncertainty. (b) Some models are uncertain about choosing the commonsense action because their responses are sensitive to the question-wording. (c) Some models reflect clear preferences in ambiguous scenarios. Specifically, closed-source models tend to agree with each other.
Researchers from the department presented machine learning and artificial intelligence research at the thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2022).
Finding and Listing Front-door Adjustment Sets
Hyunchai Jeong Purdue University, Jin Tian Iowa State University, Elias Bareinboim Columbia University
Abstract:
Identifying the effects of new interventions from data is a significant challenge found across a wide range of the empirical sciences. A well-known strategy for identifying such effects is Pearl’s front-door (FD) criterion. The definition of the FD criterion is declarative, only allowing one to decide whether a specific set satisfies the criterion. In this paper, we present algorithms for finding and enumerating possible sets satisfying the FD criterion in a given causal diagram. These results are useful in facilitating the practical applications of the FD criterion for causal effects estimation and helping scientists to select estimands with desired properties, e.g., based on cost, feasibility of measurement, or statistical power.
Causal Identification under Markov equivalence: Calculus, Algorithm, and Completeness
Amin Jaber Purdue University, Adele Ribeiro Columbia University, Jiji Zhang Hong Kong Baptist University, Elias Bareinboim Columbia University
Abstract:
One common task in many data sciences applications is to answer questions about the effect of new interventions, like: `what would happen to Y if we make X equal to x while observing covariates Z=z?’. Formally, this is known as conditional effect identification, where the goal is to determine whether a post-interventional distribution is computable from the combination of an observational distribution and assumptions about the underlying domain represented by a causal diagram. A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available. In this paper, we assume as the input of the task a less informative structure known as a partial ancestral graph (PAG), which represents a Markov equivalence class of causal diagrams, learnable from observational data. We make the following contributions under this relaxed setting. First, we introduce a new causal calculus, which subsumes the current state-of-the-art, PAG-calculus. Second, we develop an algorithm for conditional effect identification given a PAG and prove it to be both sound and complete. In words, failure of the algorithm to identify a certain effect implies that this effect is not identifiable by any method. Third, we prove the proposed calculus to be complete for the same task.
Online Reinforcement Learning for Mixed Policy Scopes
Junzhe Zhang Columbia University, Elias Bareinboim Columbia University
Abstract:
Combination therapy refers to the use of multiple treatments — such as surgery, medication, and behavioral therapy – to cure a single disease, and has become a cornerstone for treating various conditions including cancer, HIV, and depression. All possible combinations of treatments lead to a collection of treatment regimens (i.e., policies) with mixed scopes, or what physicians could observe and which actions they should take depending on the context. In this paper, we investigate the online reinforcement learning setting for optimizing the policy space with mixed scopes. In particular, we develop novel online algorithms that achieve sublinear regret compared to an optimal agent deployed in the environment. The regret bound has a dependency on the maximal cardinality of the induced state-action space associated with mixed scopes. We further introduce a canonical representation for an arbitrary subset of interventional distributions given a causal diagram, which leads to a non-trivial, minimal representation of the model parameters.
Masked Prediction: A Parameter Identifiability View
Bingbin Liu Carnegie Mellon University, Daniel Hsu Columbia University, Pradeep Ravikumar Carnegie Mellon University, Andrej Risteski Carnegie Mellon University
Abstract:
The vast majority of work in self-supervised learning have focused on assessing recovered features by a chosen set of downstream tasks. While there are several commonly used benchmark datasets, this lens of feature learning requires assumptions on the downstream tasks which are not inherent to the data distribution itself. In this paper, we present an alternative lens, one of parameter identifiability: assuming data comes from a parametric probabilistic model, we train a self-supervised learning predictor with a suitable parametric form, and ask whether the parameters of the optimal predictor can be used to extract the parameters of the ground truth generative model.Specifically, we focus on latent-variable models capturing sequential structures, namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We focus on masked prediction as the self-supervised learning task and study the optimal masked predictor. We show that parameter identifiability is governed by the task difficulty, which is determined by the choice of data model and the amount of tokens to predict. Technique-wise, we uncover close connections with the uniqueness of tensor rank decompositions, a widely used tool in studying identifiability through the lens of the method of moments.
Learning single-index models with shallow neural networks
Alberto Bietti Meta AI/New York University, Joan Bruna New York University, Clayton Sanford Columbia University, Min Jae Song New York University
Abstract:
Single-index models are a class of functions given by an unknown univariate link” function applied to an unknown one-dimensional projection of the input. These models are particularly relevant in high dimension, when the data might present low-dimensional structure that learning algorithms should adapt to. While several statistical aspects of this model, such as the sample complexity of recovering the relevant (one-dimensional) subspace, are well-understood, they rely on tailored algorithms that exploit the specific structure of the target function. In this work, we introduce a natural class of shallow neural networks and study its ability to learn single-index models via gradient flow. More precisely, we consider shallow networks in which biases of the neurons are frozen at random initialization. We show that the corresponding optimization landscape is benign, which in turn leads to generalization guarantees that match the near-optimal sample complexity of dedicated semi-parametric methods.
On Scrambling Phenomena for Randomly Initialized Recurrent Networks
Evangelos Chatziafratis University of California Santa Cruz, Ioannis Panageas University of California Irvine, Clayton Sanford Columbia University, Stelios Stavroulakis University of California Irvine
Abstract:
Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train. Recent works have shed light on such phenomena analyzing when exploding or vanishing gradients may occur, either of which is detrimental for training dynamics. In this paper, we point to a formal connection between RNNs and chaotic dynamical systems and prove a qualitatively stronger phenomenon about RNNs than what exploding gradients seem to suggest. Our main result proves that under standard initialization (e.g., He, Xavier etc.), RNNs will exhibit \textit{Li-Yorke chaos} with \textit{constant} probability \textit{independent} of the network’s width. This explains the experimentally observed phenomenon of \textit{scrambling}, under which trajectories of nearby points may appear to be arbitrarily close during some timesteps, yet will be far away in future timesteps. In stark contrast to their feedforward counterparts, we show that chaotic behavior in RNNs is preserved under small perturbations and that their expressive power remains exponential in the number of feedback iterations. Our technical arguments rely on viewing RNNs as random walks under non-linear activations, and studying the existence of certain types of higher-order fixed points called \textit{periodic points} in order to establish phase transitions from order to chaos.
Patching open-vocabulary models by interpolating weights
Gabriel Ilharco University of Washington, Mitchell Wortsman University of Washington, Samir Yitzhak Gadre Columbia University, Shuran Song Columbia University, Hannaneh Hajishirzi University of Washington, Simon Kornblith Google Brain, Ali Farhadi University of Washington, Ludwig Schmidt University of Washington
Abstract:
Open-vocabulary models like CLIP achieve high accuracy across many image classification tasks. However, there are still settings where their zero-shot performance is far from optimal. We study model patching, where the goal is to improve accuracy on specific tasks without degrading accuracy on tasks where performance is already adequate. Towards this goal, we introduce PAINT, a patching method that uses interpolations between the weights of a model before fine-tuning and the weights after fine-tuning on a task to be patched. On nine tasks where zero-shot CLIP performs poorly, PAINT increases accuracy by 15 to 60 percentage points while preserving accuracy on ImageNet within one percentage point of the zero-shot model. PAINT also allows a single model to be patched on multiple tasks and improves with model scale. Furthermore, we identify cases of broad transfer, where patching on one task increases accuracy on other tasks even when the tasks have disjoint classes. Finally, we investigate applications beyond common benchmarks such as counting or reducing the impact of typographic attacks on CLIP. Our findings demonstrate that it is possible to expand the set of tasks on which open-vocabulary models achieve high accuracy without re-training them from scratch.
ASPiRe: Adaptive Skill Priors for Reinforcement Learning
Mengda Xu Columbia University, Manuela Veloso JP Morgan/Carnegie Mellon University, Shuran Song Columbia University
Abstract:
We introduce ASPiRe (Adaptive Skill Prior for RL), a new approach that leverages prior experience to accelerate reinforcement learning. Unlike existing methods that learn a single skill prior from a large and diverse dataset, our framework learns a library of different distinction skill priors (i.e., behavior priors) from a collection of specialized datasets, and learns how to combine them to solve a new task. This formulation allows the algorithm to acquire a set of specialized skill priors that are more reusable for downstream tasks; however, it also brings up additional challenges of how to effectively combine these unstructured sets of skill priors to form a new prior for new tasks. Specifically, it requires the agent not only to identify which skill prior(s) to use but also how to combine them (either sequentially or concurrently) to form a new prior. To achieve this goal, ASPiRe includes Adaptive Weight Module (AWM) that learns to infer an adaptive weight assignment between different skill priors and uses them to guide policy learning for downstream tasks via weighted Kullback-Leibler divergences. Our experiments demonstrate that ASPiRe can significantly accelerate the learning of new downstream tasks in the presence of multiple priors and show improvement on competitive baselines.
Language Models with Image Descriptors are Strong Few-Shot Video-Language Learners
Zhenhailong Wang Columbia University, Manling Li Columbia University, Ruochen Xu Microsoft, Luowei Zhou Meta, Jie Lei Meta, Xudong Lin Columbia University, Shuohang Wang Microsoft, Ziyi Yang Stanford University, Chenguang Zhu Stanford University, Derek Hoiem University of Illinois, Shih-Fu Chang Columbia University, Mohit Bansal University of North Carolina Chapel Hill, Heng Ji University of Illinois
Abstract:
The goal of this work is to build flexible video-language models that can generalize to various video-to-text tasks from few examples. Existing few-shot video-language learners focus exclusively on the encoder, resulting in the absence of a video-to-text decoder to handle generative tasks. Video captioners have been pretrained on large-scale video-language datasets, but they rely heavily on finetuning and lack the ability to generate text for unseen tasks in a few-shot setting. We propose VidIL, a few-shot Video-language Learner via Image and Language models, which demonstrates strong performance on few-shot video-to-text tasks without the necessity of pretraining or finetuning on any video datasets. We use image-language models to translate the video content into frame captions, object, attribute, and event phrases, and compose them into a temporal-aware template. We then instruct a language model, with a prompt containing a few in-context examples, to generate a target output from the composed content. The flexibility of prompting allows the model to capture any form of text input, such as automatic speech recognition (ASR) transcripts. Our experiments demonstrate the power of language models in understanding videos on a wide variety of video-language tasks, including video captioning, video question answering, video caption retrieval, and video future event prediction. Especially, on video future event prediction, our few-shot model significantly outperforms state-of-the-art supervised models trained on large-scale video datasets.Code and processed data are publicly available for research purposes at https://github.com/MikeWangWZHL/VidIL.
Implications of Model Indeterminacy for Explanations of Automated Decisions
Marc-Etienne Brunet University of Toronto, Ashton Anderson University of Toronto, Richard Zemel Columbia University
Abstract:
There has been a significant research effort focused on explaining predictive models, for example through post-hoc explainability and recourse methods. Most of the proposed techniques operate upon a single, fixed, predictive model. However, it is well-known that given a dataset and a predictive task, there may be a multiplicity of models that solve the problem (nearly) equally well. In this work, we investigate the implications of this kind of model indeterminacy on the post-hoc explanations of predictive models. We show how it can lead to explanatory multiplicity, and we explore the underlying drivers. We show how predictive multiplicity, and the related concept of epistemic uncertainty, are not reliable indicators of explanatory multiplicity. We further illustrate how a set of models showing very similar aggregate performance on a test dataset may show large variations in their local explanations, i.e., for a specific input. We explore these effects for Shapley value based explanations on three risk assessment datasets. Our results indicate that model indeterminacy may have a substantial impact on explanations in practice, leading to inconsistent and even contradicting explanations.
Reconsidering Deep Ensembles
Taiga Abe Columbia University, Estefany Kelly Buchanan Columbia University, Geoff Pleiss Columbia University, Richard Zemel Columbia University, John Cunningham Columbia University
Abstract:
Ensembling neural networks is an effective way to increase accuracy, and can often match the performance of individual larger models. This observation poses a natural question: given the choice between a deep ensemble and a single neural network with similar accuracy, is one preferable over the other? Recent work suggests that deep ensembles may offer distinct benefits beyond predictive power: namely, uncertainty quantification and robustness to dataset shift. In this work, we demonstrate limitations to these purported benefits, and show that a single (but larger) neural network can replicate these qualities. First, we show that ensemble diversity, by any metric, does not meaningfully contribute to an ensemble’s ability to detect out-of-distribution (OOD) data, but is instead highly correlated with the relative improvement of a single larger model. Second, we show that the OOD performance afforded by ensembles is strongly determined by their in-distribution (InD) performance, and – in this sense – is not indicative of any “effective robustness.” While deep ensembles are a practical way to achieve improvements to predictive power, uncertainty quantification, and robustness, our results show that these improvements can be replicated by a (larger) single model
Professor David Blei, with co-authors Matthew Hoffman and Francis Bach, is recognized with a Test of Time Award at NeurIPS, the world’s top machine learning conference, for scaling his topic modeling algorithm to billions of documents.
Team leader David Watkins discusses how playing computer games can give roboticists real-world insights.
The 33rd Conference on Neural Information Processing Systems (NeurIPS 2019) fosters the exchange of research on neural information processing systems in their biological, technological, mathematical, and theoretical aspects.
The annual meeting is one of the premier gatherings in artificial intelligence and machine learning that featured talks, demos from industry partners as well as tutorials. Professor Vishal Misra, with colleagues from the Massachusetts Institute of Technology (MIT), held a tutorial on synthetic control.
At this year’s NeurIPS, 21 papers from the department were accepted to the conference. Computer science professors and students worked with researchers from the statistics department and the Data Science Institute.
Noise-tolerant Fair Classification
Alex Lamy Columbia University, Ziyuan Zhong Columbia University, Aditya Menon Google, Nakul Verma Columbia University
Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender) and is usually done under the assumption that the sensitive feature available in a training sample is perfectly reliable.
This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. In the paper, the researchers show that fair classifiers can still be used given noisy sensitive features by simply changing the desired fairness-tolerance. Their procedure is empirically effective on two relevant real-world case-studies involving sensitive feature censoring.
Poisson-randomized Gamma Dynamical Systems
Aaron Schein UMass Amherst, Scott Linderman Columbia University, Mingyuan Zhou University of Texas at Austin, David Blei Columbia University, Hanna Wallach MSR NYC
This paper presents a new class of state space models for count data. It derives new properties of the Poisson-randomized gamma distribution for efficient posterior inference.
Using Embeddings to Correct for Unobserved Confounding in Networks
Victor Veitch Columbia University, Yixin Wang Columbia University, David Blei Columbia University
This paper address causal inference in the presence of unobserved confounder when proxy is available for the confounders in the form of a network connecting the units. For example, the link structure of friendships in a social network reveals information about the latent preferences of people in that network. The researchers show how modern network embedding methods can be exploited to harness the network estimation for efficient causal adjustment.
Variational Bayes Under Model Misspecification
Yixin Wang Columbia University, David Blei Columbia University
The paper characterizes the theoretical properties of a popular machine learning algorithm, variational Bayes (VB). The researchers studied the VB under model misspecification, which is the setting that is most aligned with the practice, and show that the VB posterior is asymptotically normal and centers at the value that minimizes the Kullback-Leibler (KL) divergence to the true data-generating distribution.
As a consequence, they found that the model misspecification error dominates the variational approximation error in VB posterior predictive distributions. In other words, VB pays a negligible price in producing posterior predictive distributions. It explains the widely observed phenomenon that VB achieves comparable predictive accuracy with MCMC even though VB uses an approximating family.
Poincaré Recurrence, Cycles and Spurious Equilibria in Gradient-Descent-Ascent for Non-Convex Non-Concave Zero-Sum Games
Emmanouil-Vasileios Vlatakis-Gkaragkounis Columbia University, Lampros Flokas Columbia University, Georgios Piliouras Singapore University of Technology and Design
The paper introduces a model that captures a min-max competition over complex error landscapes and shows that even a simplified model can provably replicate some of the most commonly reported failure modes of GANs (non-convergence, deadlock in suboptimal states, etc).
Moreover, the researchers were able to understand the hidden structure in these systems — the min-max competition can lead to system behavior that is similar to that of energy preserving systems in physics (e.g. connected pendulums, many-body problems, etc). This makes it easier to understand why these systems can fail and gives new tools in the design of algorithms for training GANs.
Near-Optimal Reinforcement Learning in Dynamic Treatment Regimes
Junzhe Zhang Columbia University, Elias Bareinboim Columbia University
Dynamic Treatment Regimes (DTRs) are particularly effective for managing chronic disorders and is arguably one of the key aspects towards more personalized decision-making. The researchers developed the first adaptive algorithm that achieves near-optimal regret in DTRs in online settings, while leveraging the abundant, yet imperfect confounded observations. Applications are given to personalized medicine and treatment recommendation in clinical decision support.
Paraphrase Generation with Latent Bag of Words
Yao Fu Columbia University, Yansong Feng Peking University, John Cunningham University of Columbia
The paper proposes a latent bag of words model for differentiable content planning and surface realization in text generation. This model generates paraphrases with clear steps, adding interpretability and controllability of existing neural text generation models.
Adapting Neural Networks for the Estimation of Treatment Effects
Claudia Shi Columbia University, David Blei Columbia University, Victor Veitch Columbia University
This paper addresses how to design neural networks to get very accurate estimates of causal effects from observational data. The researchers propose two methods based on insights from the statistical literature on the estimation of treatment effects.
The first is a new architecture, the Dragonnet, that exploits the sufficiency of the propensity score for estimation adjustment. The second is a regularization procedure, targeted regularization, that induces a bias towards models that have non-parametrically optimal asymptotic properties “out-of-the-box”. Studies on benchmark datasets for causal inference show these adaptations outperform existing methods.
Efficiently Avoiding Saddle Points with Zero Order Methods: No Gradients Required
Emmanouil-Vasileios Vlatakis-Gkaragkounis Columbia University, Lampros Flokas Columbia University, Georgios Piliouras Singapore University of Technology and Design
The researchers prove that properly tailored zero-order methods are as effective as their first-order counterparts. This analysis requires a combination of tools from optimization theory, probability theory and dynamical systems to show that even without perfect knowledge of the shape of the error landscape, effective optimization is possible.
Metric Learning for Adversarial Robustness
Chengzhi Mao Columbia University, Ziyuan Zhong Columbia University, Junfeng Yang Columbia University, Carl Vondrick Columbia University, Baishakhi Ray Columbia University
Deep networks are well-known to be fragile to adversarial attacks. The paper introduces a novel Triplet Loss Adversarial (TLA) regulation that is the first method that leverages metric learning to improve the robustness of deep networks. This method is inspired by the evidence that deep networks suffer from distorted feature space under adversarial attacks. The method increases the model robustness and efficiency for the detection of adversarial attacks significantly.
Efficient Symmetric Norm Regression via Linear Sketching
Zhao Song University of Washington, Ruosong Wang Carnegie Mellon University, Lin Yang Johns Hopkins University, Hongyang Zhang TTIC, Peilin Zhong Columbia University
The paper studies linear regression problems with general symmetric norm loss and gives efficient algorithms for solving such linear regression problems via sketching techniques.
Rethinking Generative Coverage: A Pointwise Guaranteed Approach
Peilin Zhong Columbia University, Yuchen Mo Columbia University, Chang Xiao Columbia University, Pengyu Chen Columbia University, Changxi Zheng Columbia University
The paper presents a novel and formal definition of mode coverage for generative models. It also gives a boosting algorithm to achieve this mode coverage guarantee.
How Many Variables Should Be Entered in a Principal Component Regression Equation?
Ji Xu Columbia University, Daniel Hsu Columbia University
The researchers studied the least-squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance with the number of selected features $p$ can be either smaller or greater than the sample size $n$. And give an average-case analysis of the out-of-sample prediction error as $p,n,N \to \infty$ with $p/N \to \alpha$ and $n/N \to \beta$, for some constants $\alpha \in [0,1]$ and $\beta \in (0,1)$. In this average-case setting, the prediction error exhibits a “double descent” shape as a function of $p$. This also establishes conditions under which the minimum risk is achieved in the interpolating ($p>n$) regime.
Adaptive Influence Maximization with Myopic Feedback
Binghui Peng Columbia University, Wei Chen Microsoft Research
The paper investigates the adaptive influence maximization problem and provides upper and lower bounds for the adaptivity gaps under myopic feedback model. The results confirm a long standing open conjecture by Golovin and Krause (2011).
Towards a Zero-One Law for Column Subset Selection
Zhao Song University of Washington, David Woodruff Carnegie Mellon University, Peilin Zhong Columbia University
The researchers studied low-rank matrix approximation with general loss function and showed that if the loss function has several good properties, then there is an efficient way to compute a good low-rank approximation. Otherwise, it could be hard to compute a good low-rank approximation efficiently.
Average Case Column Subset Selection for Entrywise l1-Norm Loss
Zhao Song University of Washington, David Woodruff Carnegie Mellon University, Peilin Zhong Columbia University
The researchers studied how to compute an l1-norm loss low-rank matrix approximation to a given matrix. And showed that if the given matrix can be decomposed into a low-rank matrix and a noise matrix with a mild distributional assumption, we can obtain a (1+eps) approximation to the optimal solution.
A New Distribution on the Simplex with Auto-Encoding Applications
Andrew Stirn Columbia University, Tony Jebara Spotify, David Knowles Columbia University
The researchers developed a surrogate distribution for the Dirichlet that offers explicit, tractable reparameterization, the ability to capture sparsity, and has barycentric symmetry properties (i.e. exchangeability) equivalent to the Dirichlet. Previous works have used the Kumaraswamy distribution in a stick-breaking process to create a non-exchangeable distribution on the simplex. The method was improved by restoring exchangeability and demonstrating that approximate exchangeability is efficiently achievable. Lastly, the method was showcased in a variety of VAE semi-supervised learning tasks.
Discrete Flows: Invertible Generative Models of Discrete Data
Dustin Tran Google Brain, Keyon Vafa Columbia University, Kumar Agrawal Google AI Resident, Laurent Dinh Google Brain, Ben Poole Google Brain
While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. The researchers extend normalizing flows to discrete events, using a simple change-of-variables formula not requiring log-determinant-Jacobian computations. Empirically, they find that discrete flows obtain competitive performance with or outperform autoregressive baselines on various tasks, including addition, Potts models, and language models.
Characterization and Learning of Causal Graphs with Latent Variables from Soft Interventions
Murat Kocaoglu MIT-IBM Watson AI Lab IBM Research, Amin Jaber Purdue University, Karthikeyan Shanmugam MIT-IBM Watson AI Lab IBM Research NY, Elias Bareinboim Columbia University
This work is all about learning causal relationships – the classic aim of which is to characterize all possible sets that could produce the observed data. In the paper, the researchers provide a complete characterization of all possible causal graphs with observational and interventional data involving so-called ‘soft interventions’ on variables when the targets of soft interventions are known.
This work potentially could lead to discovery of other novel learning algorithms that are both sound and complete.
Identification of Conditional Causal Effects Under Markov Equivalence
Amin Jaber Purdue University, Jiji Zhang Lingnan University, Elias Bareinboim Columbia University
Causal identification is the problem of deciding whether a causal distribution is computable from a combination of qualitative knowledge about the underlying data-generating process, which is usually encoded in the form of a causal graph, and an observational distribution. Despite the obvious need for identifying causal effects throughout the data-driven sciences, in practice, finding the causal graph is a notoriously challenging task.
In this work, the researchers provide a relaxation of the requirement of having to specify the causal graph (based on substantive knowledge) and allow the input of the inference to be an equivalence class of causal graphs, which can be inferred from data. Specifically, they propose the first general algorithm to learn conditional causal effects entirely from data. This result is particularly useful for evaluating the impact of conditional plans and stochastic policies, which appear both in AI (in the context of reinforcement learning) and in the data-driven sciences.
Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets
Daniel Kumor Purdue University, Bryant Chen Brex Inc., Elias Bareinboim Columbia University
Regression analysis is one of the most common tools used in modern data science. While there is a great understanding and powerful technology to perform regression analysis in high dimensional spaces, the output of such a method is purely associational and devoid of any causal interpretation.
The researchers studied the problem of identification of structural (causal) coefficients in linear systems (deciding whether regression coefficients are amenable to causal interpretation, etc). Building on a technique called instrumental variables, they developed a new method called Instrumental Cutset, which partitions the systems into tractable components such that identification can be decided more efficiently. The resulting algorithm was efficient and strictly more powerful than the current state-of-the-art methods.
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