NeurIPS 2020 Papers

Interpretability of machine learning models is critical to scientific understanding, AI safety, as well as debugging. Attribution is one approach to interpretability, which highlights input dimensions that are influential to a neural network’s prediction. Evaluation of these methods is largely qualitative for image and text models, because acquiring ground truth attributions requires expensive and unreliable human judgment. Attribution has been little studied for graph neural networks (GNNs), a model class of growing importance that makes predictions on arbitrarily-sized graphs. In this work we adapt commonly-used attribution methods for GNNs and quantitatively evaluate them using computable ground-truths that are objective and challenging to learn. We make concrete recommendations for which attribution methods to use, and provide the data and code for our benchmarking suite. Rigorous and open source benchmarking of attribution methods in graphs could enable new methods development and broader use of attribution in real-world ML tasks.

Missing Not At Random (MNAR) values where the probability of having missing data may depend on the missing value itself, are notoriously difficult to account for in analyses, although very frequent in the data. One solution to handle MNAR data is to specify a model for the missing data mechanism, which makes inference or imputation tasks more complex. Furthermore, this implies a strong \textit{a priori} on the parametric form of the distribution. However, some works have obtained guarantees on the estimation of parameters in the presence of MNAR data, without specifying the distribution of missing data \citep{mohan2018estimation, tang2003analysis}. This is very useful in practice, but is limited to simple cases such as few self-masked MNAR variables in data generated according to linear regression models. We continue this line of research, but extend it to a more general MNAR mechanism, in a more general model of the probabilistic principal component analysis (PPCA), \textit{i.e.}, a low-rank model with random effects. We prove identifiability of the PPCA parameters. We then propose an estimation of the loading coefficients and a data imputation method. They are based on estimators of means, variances and covariances of missing variables, for which consistency is discussed. These estimators have the great advantage of being calculated using only the observed information, leveraging the underlying low-rank structure of the data. We illustrate the relevance of the method with numerical experiments on synthetic data and also on two datasets, one collected from a medical register and the other one from a recommendation system.

Exponential bounds on the estimation error are given for the plug-in estimator of weighted areas under the ROC curve. The bounds hold for single score functions and uniformly over classes of functions, whose complexity can be controlled by Gaussian or Rademacher averages. The results justify learning algorithms which select score functions to maximize the empirical partial area under the curve (pAUC). They also illustrate the use of some recent advances in the theory of nonlinear empirical processes.

While much attention has been given to the problem of estimating the effect of discrete interventions from observational data, relatively little work has been done in the setting of continuous-valued interventions, such as treatments associated with a dosage parameter. In this paper, we tackle this problem by building on a modification of the generative adversarial networks (GANs) framework. Our model, SCIGAN, is flexible and capable of simultaneously estimating counterfactual outcomes for several different continuous interventions. The key idea is to use a significantly modified GAN model to learn to generate counterfactual outcomes, which can then be used to learn an inference model, using standard supervised methods, capable of estimating these counterfactuals for a new sample. To address the challenges presented by shifting to continuous interventions, we propose a novel architecture for our discriminator - we build a hierarchical discriminator that leverages the structure of the continuous intervention setting. Moreover, we provide theoretical results to support our use of the GAN framework and of the hierarchical discriminator. In the experiments section, we introduce a new semi-synthetic data simulation for use in the continuous intervention setting and demonstrate improvements over the existing benchmark models.

We show that top-down decision tree learning heuristics (such as ID3, C4.5, and CART) are amenable to highly efficient {\sl learnability estimation}: for monotone target functions, the error of the decision tree hypothesis constructed by these heuristics can be estimated with {\sl polylogarithmically} many labeled examples, exponentially smaller than the number necessary to run these heuristics, and indeed, exponentially smaller than information-theoretic minimum required to learn a good decision tree. This adds to a small but growing list of fundamental learning algorithms that have been shown to be amenable to learnability estimation. En route to this result, we design and analyze sample-efficient {\sl minibatch} versions of top-down decision tree learning heuristics and show that they achieve the same provable guarantees as the full-batch versions. We further give ``active local'' versions of these heuristics: given a test point $x^\star$, we show how the label $T(x^\star)$ of the decision tree hypothesis $T$ can be computed with polylogarithmically many labeled examples, exponentially smaller than the number necessary to learn~$T$.

Neural Coding analyses often reflect an assumption that neural populations respond uniquely and consistently to particular stimuli. For example, analyses of spatial remapping in hippocampal populations often assume that each environment has one unique representation and that remapping occurs over long time scales as an animal traverses between distinct environments. However, as neuroscience experiments begin to explore more naturalistic tasks and stimuli, and reflect more ambiguity in neural representations, methods for analyzing population neural codes must adapt to reflect these features. In this paper, we develop a new state-space modeling framework to address two important issues related to remapping. First, neurons may exhibit significant trial-to-trial or moment-to-moment variability in the firing patterns used to represent a particular environment or stimulus. Second, in ambiguous environments and tasks that involve cognitive uncertainty, neural populations may rapidly fluctuate between multiple representations. The state-space model addresses these two issues by integrating an observation model, which allows for multiple representations of the same stimulus or environment, with a state model, which characterizes the moment-by-moment probability of a shift in the neural representation. These models allow us to compute instantaneous estimates of the stimulus or environment currently represented by the population. We demonstrate the application of this approach to the analysis of population activity in the CA1 region of hippocampus of a mouse moving through ambiguous virtual environments. Our analyses demonstrate that many hippocampal cells express significant trial-to-trial variability in their representations and that the population representation can fluctuate rapidly between environments within a single trial when spatial cues are most ambiguous.

In this paper, we show that under over-parametrization several standard stochastic optimization algorithms escape saddle-points and converge to local-minimizers much faster. One of the fundamental aspects of over-parametrized models is that they are capable of interpolating the training data. We show that, under interpolation-like assumptions satisfied by the stochastic gradients in an over-parametrization setting, the first-order oracle complexity of Perturbed Stochastic Gradient Descent (PSGD) algorithm to reach an $\epsilon$-local-minimizer, matches the corresponding deterministic rate of $O(1/\epsilon^{2})$. We next analyze Stochastic Cubic-Regularized Newton (SCRN) algorithm under interpolation-like conditions, and show that the oracle complexity to reach an $\epsilon$-local-minimizer under interpolation-like conditions, is $O(1/\epsilon^{2.5})$. While this obtained complexity is better than the corresponding complexity of either PSGD, or SCRN without interpolation-like assumptions, it does not match the rate of $O(1/\epsilon^{1.5})$ corresponding to deterministic Cubic-Regularized Newton method. It seems further Hessian-based interpolation-like assumptions are necessary to bridge this gap. We also discuss the corresponding improved complexities in the zeroth-order settings.

Imitation learning trains a policy by mimicking expert demonstrations. Various imitation methods were proposed and empirically evaluated, meanwhile, their theoretical understanding needs further studies. In this paper, we firstly analyze the value gap between the expert policy and imitated policies by two imitation methods, behavioral cloning and generative adversarial imitation. The results support that generative adversarial imitation can reduce the compounding errors compared to behavioral cloning, and thus has a better sample complexity. Noticed that by considering the environment transition model as a dual agent, imitation learning can also be used to learn the environment model. Therefore, based on the bounds of imitating policies, we further analyze the performance of imitating environments. The results show that environment models can be more effectively imitated by generative adversarial imitation than behavioral cloning, suggesting a novel application of adversarial imitation for model-based reinforcement learning. We hope these results could inspire future advances in imitation learning and model-based reinforcement learning.

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or Krylov methods. While there is classical and comprehensive analysis for subspace convergence guarantees with respect to the spectral norm, in many modern applications other notions of subspace distance are more appropriate. Recent theoretical work has focused on perturbations of subspaces measured in the ℓ2→∞ norm, but does not consider the actual computation of eigenvectors. Here we address the convergence of subspace iteration when distances are measured in the ℓ2→∞ norm and provide deterministic bounds. We complement our analysis with a practical stopping criterion and demonstrate its applicability via numerical experiments. Our results show that one can get comparable performance on downstream tasks while requiring fewer iterations, thereby saving substantial computational time.

Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture. Namely, we show that for almost all causal models where the exogenous variable has entropy that does not scale with the number of states of the observed variables, the causal direction is identifiable from observational data. We also consider the minimum entropy coupling-based algorithmic approach presented by Kocaoglu et al., and for the first time demonstrate algorithmic identifiability guarantees using a finite number of samples. We conduct extensive experiments to evaluate the robustness of the method to relaxing some of the assumptions in our theory and demonstrate that both the constant-entropy exogenous variable and the no latent confounder assumptions can be relaxed in practice. We also empirically characterize the number of observational samples needed for causal identification. Finally, we apply the algorithm on Tuebingen cause-effect pairs dataset.

We initiate the study of fair classifiers that are robust to perturbations in the training distribution. Despite recent progress, the literature on fairness has largely ignored the design of fair and robust classifiers. In this work, we develop classifiers that are fair not only with respect to the training distribution but also for a class of distributions that are weighted perturbations of the training samples. We formulate a min-max objective function whose goal is to minimize a distributionally robust training loss, and at the same time, find a classifier that is fair with respect to a class of distributions. We first reduce this problem to finding a fair classifier that is robust with respect to the class of distributions. Based on an online learning algorithm, we develop an iterative algorithm that provably converges to such a fair and robust solution. Experiments on standard machine learning fairness datasets suggest that, compared to the state-of-the-art fair classifiers, our classifier retains fairness guarantees and test accuracy for a large class of perturbations on the test set. Furthermore, our experiments show that there is an inherent trade-off between fairness robustness and accuracy of such classifiers.

Ensembles of geophysical models improve projection accuracy and express uncertainties. We develop a novel data-driven ensembling strategy for combining geophysical models using Bayesian Neural Networks, which infers spatiotemporally varying model weights and bias while accounting for heteroscedastic uncertainties in the observations. This produces more accurate and uncertainty-aware projections without sacrificing interpretability. Applied to the prediction of total column ozone from an ensemble of 15 chemistry-climate models, we find that the Bayesian neural network ensemble (BayNNE) outperforms existing ensembling methods, achieving a 49.4% reduction in RMSE for temporal extrapolation, and a 67.4% reduction in RMSE for polar data voids, compared to a weighted mean. Uncertainty is also well-characterized, with 90.6% of the data points in our extrapolation validation dataset lying within 2 standard deviations and 98.5% within 3 standard deviations.

Federated Learning (FL) is a machine learning setting where many devices collaboratively train a machine learning model while keeping the training data decentralized. In most of the current training schemes the central model is refined by averaging the parameters of the server model and the updated parameters from the client side. However, directly averaging model parameters is only possible if all models have the same structure and size, which could be a restrictive constraint in many scenarios.

Determining whether inputs are out-of-distribution (OOD) is an essential building block for safely deploying machine learning models in the open world. However, previous methods relying on the softmax confidence score suffer from overconfident posterior distributions for OOD data. We propose a unified framework for OOD detection that uses an energy score. We show that energy scores better distinguish in- and out-of-distribution samples than the traditional approach using the softmax scores. Unlike softmax confidence scores, energy scores are theoretically aligned with the probability density of the inputs and are less susceptible to the overconfidence issue. Within this framework, energy can be flexibly used as a scoring function for any pre-trained neural classifier as well as a trainable cost function to shape the energy surface explicitly for OOD detection. On a CIFAR-10 pre-trained WideResNet, using the energy score reduces the average FPR (at TPR 95%) by 18.03% compared to the softmax confidence score. With energy-based training, our method outperforms the state-of-the-art on common benchmarks.

In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework. To enable the backward propagation through the equilibria of games, we propose two approaches, respectively based on explicit and implicit differentiation. Specifically, we cast the equilibria as the solutions to variational inequalities (VIs). The explicit approach unrolls the projection method for solving VIs, while the implicit approach exploits the sensitivity of the solutions to VIs. At the core of both approaches is the differentiation through a projection operator. Moreover, we establish the correctness of both approaches and identify the conditions under which one approach is more desirable than the other. The analytical results are validated using several real-world problems.

Convex relaxations have emerged as a promising approach for verifying properties of neural networks, but widely used using Linear Programming (LP) relaxations only provide meaningful certificates when networks are specifically trained to facilitate verification. This precludes many important applications which involve \emph{verification-agnostic} networks that are not trained specifically to promote verifiability. On the other hand, semidefinite programming (SDP) relaxations have shown success on verification-agnostic networks, such as adversarially trained image classifiers without additional regularization, but do not currently scale beyond small networks due to poor time and space asymptotics. In this work, we propose a first-order dual SDP algorithm that provides (1) any-time bounds (2) requires memory only linear in the total number of network activations and (3) has per-iteration complexity that scales linearly with the complexity of a forward/backward pass through the network. By exploiting iterative eigenvector methods, we express all solver operations in terms of forward and backward passes through the network, enabling efficient use of hardware optimized for deep learning. This allows us to dramatically improve the magnitude of $\ell_\infty$ perturbations for which we can verify robustness verification-agnostic networks ($1\% \to 88\%$ on MNIST, $6\%\to 40\%$ on CIFAR-10). We also demonstrate tight verification for a quadratic stability specification for the decoder of a variational autoencoder.

We propose an estimator and confidence interval for computing the value of a policy from off-policy data in the contextual bandit setting. To this end we apply empirical likelihood techniques to formulate our estimator and confidence interval as simple convex optimization problems. Using the lower bound of our confidence interval, we then propose an off-policy policy optimization algorithm that searches for policies with large reward lower bound. We empirically find that both our estimator and confidence interval improve over previous proposals in finite sample regimes. Finally, the policy optimization algorithm we propose outperforms a strong baseline system for learning from off-policy data.

Multi-agent reinforcement learning (MARL) has shown recent success in increasingly complex fixed-team zero-sum environments. However, the real world is not zero-sum nor does it have fixed teams; humans face numerous social dilemmas and must learn when to cooperate and when to compete. To successfully deploy agents into the human world, it may be important that they be able to understand and help in our conflicts. Unfortunately, selfish MARL agents typically fail when faced with social dilemmas. In this work, we show evidence of emergent direct reciprocity, indirect reciprocity and reputation, and team formation when training agents with randomized uncertain social preferences (RUSP), a novel environment augmentation that expands the distribution of environments agents play in. RUSP is generic and scalable; it can be applied to any multi-agent environment without changing the original underlying game dynamics or objectives. In particular, we show that with RUSP these behaviors can emerge and lead to higher social welfare equilibria in both classic abstract social dilemmas like Iterated Prisoner's Dilemma as well in more complex intertemporal environments.

Current distributed learning systems suffer from serious performance degradation under Byzantine attacks. This paper proposes Election Coding, a coding-theoretic framework to guarantee Byzantine-robustness for distributed learning algorithms based on signed stochastic gradient descent (SignSGD) that minimizes the worker-master communication load. The suggested framework explores new information-theoretic limits of finding the majority opinion when some workers could be attacked by adversary, and paves the road to implement robust and communication-efficient distributed learning algorithms. Under this framework, we construct two types of codes, random Bernoulli codes and deterministic algebraic codes, that tolerate Byzantine attacks with a controlled amount of computational redundancy and guarantee convergence in general non-convex scenarios. For the Bernoulli codes, we provide an upper bound on the error probability in estimating the signs of the true gradients, which gives useful insights into code design for Byzantine tolerance. The proposed deterministic codes are proven to perfectly tolerate arbitrary Byzantine attacks. Experiments on real datasets confirm that the suggested codes provide substantial improvement in Byzantine tolerance of distributed learning systems employing SignSGD.