ICML 2020 Papers

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions — this is crucial in high-stakes applications that involve critical decision-making. Bayesian neural networks (BNNs) aim at solving this problem by placing a prior distribution over the network’s parameters, thereby inducing a posterior distribution that encapsulates predictive uncertainty. While existing variants of BNNs based on Monte Carlo dropout produce reliable (albeit approximate) uncertainty estimates over in-distribution data, they tend to exhibit over-confidence in predictions made on target data whose feature distribution differs from the training data, i.e., the covariate shift setup. In this paper, we develop an approximate Bayesian inference scheme based on posterior regularisation, wherein unlabelled target data are used as “pseudo-labels” of model confidence that are used to regularise the model’s loss on labelled source data. We show that this approach significantly improves the accuracy of uncertainty quantification on covariate-shifted data sets, with minimal modification to the underlying model architecture. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.

Group invariant and equivariant Multilayer Perceptrons (MLP), also known as Equivariant Networks and Group Group Convolutional Neural Networks (G-CNN) have achieved remarkable success in learning on a variety of data structures, such as sequences, images, sets, and graphs. This paper proves the universality of a broad class of equivariant MLPs with a single hidden layer. In particular, it is shown that having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance). For example, some types of steerable-CNN’s become universal. Another corollary is the unconditional universality of equivariant MLPs for all Abelian groups. A third corollary is the universality of equivariant MLPs with a high-order hidden layer, where we give both group-agnostic bounds and group-specific bounds on the order of the hidden layer that guarantees universal equivariance.

Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives. However, its remarkable empirical success is not fully explained by this optimality, as the worst-case analysis –contrary to the average-case– is not representative of the expected complexity of an algorithm. In this work we establish a novel link between PM and the average-case analysis. Our main contribution is to prove that any optimal average-case method converges in the number of iterations to PM, under mild assumptions. This brings a new perspective on this classical method, showing that PM is asymptotically both worst-case and average-case optimal.

It is well known that (stochastic) gradient descent has an implicit bias towards flat minima. In deep neural network training, this mechanism serves to screen out minima. However, the precise effect that this has on the trained network is not yet fully understood. In this paper, we characterize the flat minima in linear neural networks trained with a quadratic loss. First, we show that linear ResNets with zero initialization necessarily converge to the flattest of all minima. We then prove that these minima correspond to nearly balanced networks whereby the gain from the input to any intermediate representation does not change drastically from one layer to the next. Finally, we show that consecutive layers in flat minima solutions are coupled. That is, one of the left singular vectors of each weight matrix, equals one of the right singular vectors of the next matrix. This forms a distinct path from input to output, that, as we show, is dedicated to the signal that experiences the largest gain end-to-end. Experiments indicate that these properties are characteristic of both linear and nonlinear models trained in practice.

The decision-theoretic foundations of classical machine learning models have largely focused on estimating model parameters that minimize the expectation of a given loss function. However, as machine learning models are deployed in varied contexts, such as in high-stakes decision-making and societal settings, it is clear that these models are not just evaluated by their average performances. In this work, we study a novel notion of L-Risk based on the classical idea of rank-weighted learning. These L-Risks, induced by rank-dependent weighting functions with bounded variation, is a unification of popular risk measures such as conditional value-at-risk and those defined by cumulative prospect theory. We give uniform convergence bounds of this broad class of risk measures and study their consequences on a logistic regression example.

We propose to pre-train a unified language model for both autoencoding and partially autoregressive language modeling tasks using a novel training procedure, referred to as a pseudo-masked language model (PMLM). Given an input text with masked tokens, we rely on conventional masks to learn inter-relations between corrupted tokens and context via autoencoding, and pseudo masks to learn intra-relations between masked spans via partially autoregressive modeling. With well-designed position embeddings and self-attention masks, the context encodings are reused to avoid redundant computation. Moreover, conventional masks used for autoencoding provide global masking information, so that all the position embeddings are accessible in partially autoregressive language modeling. In addition, the two tasks pre-train a unified language model as a bidirectional encoder and a sequence-to-sequence decoder, respectively. Our experiments show that the unified language models pre-trained using PMLM achieve new state-of-the-art results on a wide range of language understanding and generation tasks across several widely used benchmarks. The code and pre-trained models are available at https://github.com/microsoft/unilm.

The representation of the approximate posterior is a critical aspect of effective variational autoencoders (VAEs). Poor choices for the approximate posterior have a detrimental impact on the generative performance of VAEs due to the mismatch with the true posterior. We extend the class of posterior models that may be learned by using undirected graphical models. We develop an efficient method to train undirected approximate posteriors by showing that the gradient of the training objective with respect to the parameters of the undirected posterior can be computed by backpropagation through Markov chain Monte Carlo updates. We apply these gradient estimators for training discrete VAEs with Boltzmann machines as approximate posteriors and demonstrate that undirected models outperform previous results obtained using directed graphical models. Our implementation is publicly available.

Although SGD with random reshuffle has been widely-used in machine learning applications, there is a limited understanding of how model characteristics affect the convergence of the algorithm. In this work, we introduce model incoherence to characterize the diversity of model characteristics and study its impact on convergence of SGD with random reshuffle under weak strong convexity. Specifically, minimizer incoherence measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle. In particular, we show that the variable sequence generated by SGD with random reshuffle converges to a certain global minimizer of the total loss under full minimizer coherence. The other curvature incoherence measures the quality of condition numbers of the sample losses and determines the convergence rate of SGD. With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to the superior practical performance of SGD with random reshuffle.

Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of conditional Monte Carlo. Surprisingly, we find that in finite horizon MDPs there is no strict variance reduction of per-decision importance sampling or marginalized importance sampling, comparing with vanilla importance sampling. We then provide sufficient conditions under which the per-decision or marginalized estimators will provably reduce the variance over importance sampling with finite horizons. For the asymptotic (in terms of horizon $T$) case, we develop upper and lower bounds on the variance of those estimators which yields sufficient conditions under which there exists an exponential v.s. polynomial gap between the variance of importance sampling and that of the per-decision or stationary/marginalized estimators. These results help advance our understanding of if and when new types of IS estimators will improve the accuracy of off-policy estimation.

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the frequency domain and provide simple yet effective methods to stabilize GAN’s training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, which can be implemented as an L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.

Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class has low standard and robust error. In this work, we precisely characterize the effect of augmentation on the standard error in linear regression when the optimal linear predictor has zero standard and robust error. In particular, we show that the standard error could increase even when the augmented perturbations have noiseless observations from the optimal linear predictor. We then prove that the recently proposed robust self-training (RST) estimator improves robust error without sacrificing standard error for noiseless linear regression. Empirically, for neural networks, we find that RST with different adversarial training methods improves both standard and robust error for random and adversarial rotations and adversarial l_infty perturbations in CIFAR-10.

Machine learning systems must adapt to data distributions that evolve over time, in applications ranging from sensor networks and self-driving car perception modules to brain-machine interfaces. Traditional domain adaptation is only guaranteed to work when the distribution shift is small; empirical methods combine several heuristics for larger shifts but can be dataset specific. To adapt to larger shifts we consider gradual domain adaptation, where the goal is to adapt an initial classifier trained on a source domain given only unlabeled data that shifts gradually in distribution towards a target domain. We prove the first non-vacuous upper bound on the error of self-training with gradual shifts, under settings where directly adapting to the target domain can result in unbounded error. The theoretical analysis leads to algorithmic insights, highlighting that regularization and label sharpening are essential even when we have infinite data. Leveraging the gradual shift structure leads to higher accuracies on a rotating MNIST dataset, a forest Cover Type dataset, and a realistic Portraits dataset.

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity of the induced distribution of the (normalized) features on the hypersphere. We prove that, asymptotically, the contrastive loss optimizes these properties, and analyze their positive effects on downstream tasks. Empirically, we introduce an optimizable metric to quantify each property. Extensive experiments on standard vision and language datasets confirm the strong agreement between both metrics and downstream task performance. Directly optimizing for these two metrics leads to representations with comparable or better performance at downstream tasks than contrastive learning.

On a periodic basis, publicly traded companies report fundamentals, financial data including revenue, earnings, debt, among others. Quantitative finance research has identified several factors, functions of the reported data that historically correlate with stock market performance. In this paper, we first show through simulation that if we could select stocks via factors calculated on future fundamentals (via oracle), that our portfolios would far outperform standard factor models. Motivated by this insight, we train deep nets to forecast future fundamentals from a trailing 5-year history. We propose lookahead factor models which plug these predicted future fundamentals into traditional factors. Finally, we incorporate uncertainty estimates from both neural heteroscedastic regression and a dropout-based heuristic, improving performance by adjusting our portfolios to avert risk. In retrospective analysis, we leverage an industry-grade portfolio simulator (backtester) to show simultaneous improvement in annualized return and Sharpe ratio. Specifically, the simulated annualized return for the uncertainty-aware model is 17.7% (vs 14.0% for a standard factor model) and the Sharpe ratio is 0.84 (vs 0.52).

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion — the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage nonconvex estimation algorithm proposed by (Cai et al., 2019), we characterize the distribution of this estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and its underlying tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and adapts automatically to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable estimation accuracy — including both the rates and the pre-constants — under i.i.d. Gaussian noise.

We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme and match the accuracy of softmax models. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model, we improve upon or match Deep Ensembles in out of distribution detection on notable difficult dataset pairs such as FashionMNIST vs. MNIST, and CIFAR-10 vs. SVHN.

In weakly supervised learning, unbiased risk estimator(URE) is a powerful tool for training classifiers when training and test data are drawn from different distributions. Nevertheless, UREs lead to overfitting in many problem settings when the models are complex like deep networks. In this paper, we investigate reasons for such overfitting by studying a weakly supervised problem called learning with complementary labels. We argue the quality of gradient estimation matters more in risk minimization. Theoretically, we show that a URE gives an unbiased gradient estimator(UGE). Practically, however, UGEs may suffer from huge variance, which causes empirical gradients to be usually far away from true gradients during minimization. To this end, we propose a novel surrogate complementary loss(SCL) framework that trades zero bias with reduced variance and makes empirical gradients more aligned with true gradients in the direction. Thanks to this characteristic, SCL successfully mitigates the overfitting issue and improves URE-based methods.

Individual fairness is an intuitive definition of algorithmic fairness that addresses some of the drawbacks of group fairness. Despite its benefits, it depends on a task specific fair metric that encodes our intuition of what is fair and unfair for the ML task at hand, and the lack of a widely accepted fair metric for many ML tasks is the main barrier to broader adoption of individual fairness. In this paper, we present two simple ways to learn fair metrics from a variety of data types. We show empirically that fair training with the learned metrics leads to improved fairness on three machine learning tasks susceptible to gender and racial biases. We also provide theoretical guarantees on the statistical performance of both approaches.

The neural plausibility of backpropagation has long been disputed, primarily for its use of non-local weight transport — the biologically dubious requirement that one neuron instantaneously measure the synaptic weights of another. Until recently, attempts to create local learning rules that avoid weight transport have typically failed in the large-scale learning scenarios where backpropagation shines, e.g. ImageNet categorization with deep convolutional networks. Here, we investigate a recently proposed local learning rule that yields competitive performance with backpropagation and find that it is highly sensitive to metaparameter choices, requiring laborious tuning that does not transfer across network architecture. Our analysis indicates the underlying mathematical reason for this instability, allowing us to identify a more robust local learning rule that better transfers without metaparameter tuning. Nonetheless, we find a performance and stability gap between this local rule and backpropagation that widens with increasing model depth. We then investigate several non-local learning rules that relax the need for instantaneous weight transport into a more biologically-plausible "weight estimation" process, showing that these rules match state-of-the-art performance on deep networks and operate effectively in the presence of noisy updates. Taken together, our results suggest two routes towards the discovery of neural implementations for credit assignment without weight symmetry: further improvement of local rules so that they perform consistently across architectures and the identification of biological implementations for non-local learning mechanisms.