AISTATS 2021 论文列表

Given only data generated by a standard confounding graph with unobserved confounder, the Average Treatment Effect (ATE) is not identifiable. To estimate the ATE, a practitioner must then either (a) collect deconfounded data; (b) run a clinical trial; or (c) elucidate further properties of the causal graph that might render the ATE identifiable. In this paper, we consider the benefit of incorporating a large confounded observational dataset (confounder unobserved) alongside a small deconfounded observational dataset (confounder revealed) when estimating the ATE. Our theoretical results suggest that the inclusion of confounded data can significantly reduce the quantity of deconfounded data required to estimate the ATE to within a desired accuracy level. Moreover, in some cases—say, genetics—we could imagine retrospectively selecting samples to deconfound. We demonstrate that by actively selecting these samples based upon the (already observed) treatment and outcome, we can reduce sample complexity further. Our theoretical and empirical results establish that the worst-case relative performance of our approach (vs. a natural benchmark) is bounded while our best-case gains are unbounded. Finally, we demonstrate the benefits of selective deconfounding using a large real-world dataset related to genetic mutation in cancer.

Estimating individual treatment effects from data of randomized experiments is a critical task in causal inference. The Stable Unit Treatment Value Assumption (SUTVA) is usually made in causal inference. However, interference can introduce bias when the assigned treatment on one unit affects the potential outcomes of the neighboring units. This interference phenomenon is known as spillover effect in economics or peer effect in social science. Usually, in randomized experiments or observational studies with interconnected units, one can only observe treatment responses under interference. Hence, the issue of how to estimate the superimposed causal effect and recover the individual treatment effect in the presence of interference becomes a challenging task in causal inference. In this work, we study causal effect estimation under general network interference using Graph Neural Networks, which are powerful tools for capturing node and link dependencies in graphs. After deriving causal effect estimators, we further study intervention policy improvement on the graph under capacity constraint. We give policy regret bounds under network interference and treatment capacity constraint. Furthermore, a heuristic graph structure-dependent error bound for Graph Neural Network-based causal estimators is provided.

Two apparently unrelated fields — normalizing flows and causality — have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of autoregressive normalizing flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks, ranging from causal discovery to making interventional and counterfactual predictions. First, we show that causal models derived from both affine and additive autoregressive flows with fixed orderings over variables are identifiable, i.e. the true direction of causal influence can be recovered. This provides a generalization of the additive noise model well-known in causal discovery. Second, we derive a bivariate measure of causal direction based on likelihood ratios, leveraging the fact that flow models can estimate normalized log-densities of data. Third, we demonstrate that flows naturally allow for direct evaluation of both interventional and counterfactual queries, the latter case being possible due to the invertible nature of flows. Finally, throughout a series of experiments on synthetic and real data, the proposed method is shown to outperform current approaches for causal discovery as well as making accurate interventional and counterfactual predictions.

Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The contraction rate of this error estimate as a function of the solver’s step-size identifies it as a well-calibrated worst-case error, but its explicit numerical value for a certain step size is not automatically a good estimate of the explicit error. Addressing this issue, we introduce, discuss, and assess several probabilistically motivated ways to calibrate the uncertainty estimate. Numerical experiments demonstrate that these calibration methods interact efficiently with adaptive step-size selection, resulting in descriptive, and efficiently computable posteriors. We demonstrate the efficiency of the methodology by benchmarking against the classic, widely used Dormand-Prince 4/5 Runge-Kutta method.

We introduce an efficient approach for optimization over orthogonal groups on highly parallel computation units such as GPUs or TPUs. As in earlier work, we parametrize an orthogonal matrix as a product of Householder reflections. However, to overcome low parallelization capabilities of computing Householder reflections sequentially, we propose employing an accumulation scheme called the compact WY (or CWY) transform – a compact parallelization-friendly matrix representation for the series of Householder reflections. We further develop a novel Truncated CWY (or T-CWY) approach for Stiefel manifold parametrization which has a competitive complexity and, again, yields benefits when computed on GPUs and TPUs. We prove that our CWY and T-CWY methods lead to convergence to a stationary point of the training objective when coupled with stochastic gradient descent. We apply our methods to train recurrent neural network architectures in the tasks of neural machine translation and video prediction.

The holdout randomization test (HRT) discovers a set of covariates most predictive of a response. Given the covariate distribution, HRTs can explicitly control the false discovery rate (FDR). However, if this distribution is unknown and must be estimated from data, HRTs can inflate the FDR. To alleviate the inflation of FDR, we propose the contrarian randomization test (CONTRA), which is designed explicitly for scenarios where the covariate distribution must be estimated from data and may even be misspecified. Our key insight is to use an equal mixture of two “contrarian” probabilistic models in determining the importance of a covariate. One model is fit with the real data, while the other is fit using the same data, but with the covariate being tested replaced with samples from an estimate of the covariate distribution. CONTRA is flexible enough to achieve a power of 1 asymptotically, can reduce the FDR compared to state-of-the-art CVS methods when the covariate distribution is misspecified, and is computationally efficient in high dimensions and large sample sizes. We further demonstrate the effectiveness of CONTRA on numerous synthetic benchmarks, and highlight its capabilities on a genetic dataset.

Learning rich visual representations using contrastive self-supervised learning has been extremely successful. However, it is still a major question whether we could use a similar approach to learn superior auditory representations. In this paper, we expand on prior work (SimCLR) to learn better auditory representations. We (1) introduce various data augmentations suitable for auditory data and evaluate their impact on predictive performance, (2) show that training with time-frequency audio features substantially improves the quality of the learned representations compared to raw signals, and (3) demonstrate that training with both supervised and contrastive losses simultaneously improves the learned representations compared to self-supervised pre-training followed by supervised fine-tuning. We illustrate that by combining all these methods and with substantially less labeled data, our framework (CLAR) achieves significant improvement on prediction performance compared to supervised approach. Moreover, compared to self-supervised approach, our framework converges faster with significantly better representations.

Stochastic gradient descent (SGD) has taken the stage as the primary workhorse for largescale machine learning. It is often used with its adaptive variants such as AdaGrad, Adam, and AMSGrad. This paper proposes an adaptive stochastic gradient descent method for distributed machine learning, which can be viewed as the communicationadaptive counterpart of the celebrated Adam method — justifying its name CADA. The key components of CADA are a set of new rules tailored for adaptive stochastic gradients that can be implemented to save communication upload. The new algorithms adaptively reuse the stale Adam gradients, thus saving communication, and still have convergence rates comparable to original Adam. In numerical experiments, CADA achieves impressive empirical performance in terms of total communication round reduction.

Learning good interventions in a causal graph can be modelled as a stochastic multi-armed bandit problem with side-information. First, we study this problem when interventions are more expensive than observations and a budget is specified. If there are no backdoor paths from the intervenable nodes to the reward node then we propose an algorithm to minimize simple regret that optimally trades-off observations and interventions based on the cost of intervention. We also propose an algorithm that accounts for the cost of interventions, utilizes causal side-information, and minimizes the expected cumulative regret without exceeding the budget. Our algorithm performs better than standard algorithms that do not take side-information into account. Finally, we study the problem of learning best interventions without budget constraint in general graphs and give an algorithm that achieves constant expected cumulative regret in terms of the instance parameters when the parent distribution of the reward variable for each intervention is known. Our results are experimentally validated and compared to the best-known bounds in the current literature.

Several works have shown that perturbation stable instances of the MAP inference problem can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for the LP solutions on instances that do not satisfy the relatively strict perturbation stability definitions. In this work, we go beyond these stability results by showing that the LP approximately recovers the MAP solution of a stable instance even after the instance is corrupted by noise. This "noisy stable" model realistically fits with practical MAP inference problems: we design an algorithm for finding "close" stable instances, and show that several real-world instances from computer vision have nearby instances that are perturbation stable. These results suggest a new theoretical explanation for the excellent performance of this LP relaxation in practice.

While uncertainty estimation is a well-studied topic in deep learning, most such work focuses on marginal uncertainty estimates, i.e. the predictive mean and variance at individual input locations. But it is often more useful to estimate predictive correlations between the function values at different input locations. In this paper, we consider the problem of benchmarking how accurately Bayesian models can estimate predictive correlations. We first consider a downstream task which depends on posterior predictive correlations: transductive active learning (TAL). We find that TAL makes better use of models’ uncertainty estimates than ordinary active learning, and recommend this as a benchmark for evaluating Bayesian models. Since TAL is too expensive and indirect to guide development of algorithms, we introduce two metrics which more directly evaluate the predictive correlations and which can be computed efficiently: meta-correlations (i.e. the correlations between the models correlation estimates and the true values), and cross-normalized likelihoods (XLL). We validate these metrics by demonstrating their consistency with TAL performance and obtain insights about the relative performance of current Bayesian neural net and Gaussian process models.

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such ’likelihood-free’ algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to fill this gap: We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms including recent approaches employing neural networks and classical Approximate Bayesian Computation methods. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency. Neural network-based approaches generally exhibit better performance, but there is no uniformly best algorithm. We provide practical advice and highlight the potential of the benchmark to diagnose problems and improve algorithms. The results can be explored interactively on a companion website. All code is open source, making it possible to contribute further benchmark tasks and inference algorithms.

In estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating a single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.

We consider adversarial training of deep neural networks through the lens of Bayesian learning and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on techniques from constraint relaxation of non-convex optimisation problems and modify the standard cross-entropy error model to enforce posterior robustness to worst-case perturbations in $\epsilon-$balls around input points. We illustrate how the resulting framework can be combined with methods commonly employed for approximate inference of BNNs. In an empirical investigation, we demonstrate that the presented approach enables training of certifiably robust models on MNIST, FashionMNIST, and CIFAR-10 and can also be beneficial for uncertainty calibration. Our method is the first to directly train certifiable BNNs, thus facilitating their deployment in safety-critical applications.

Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the selected subset closely approximates the posterior inference using the full dataset. This manuscript revisits Bayesian coresets through the lens of sparsity constrained optimization. Leveraging recent advances in accelerated optimization methods, we propose and analyze a novel algorithm for coreset selection. We provide explicit convergence rate guarantees and present an empirical evaluation on a variety of benchmark datasets to highlight our proposed algorithm’s superior performance compared to state-of-the-art on speed and accuracy.

To achieve label efficiency for training supervised learning models, pool-based active learning sequentially selects samples from a set of candidates as queries to label by optimizing an acquisition function. One category of existing methods adopts one-step-look-ahead strategies based on acquisition functions tailored with the learning objectives, for example based on the expected loss reduction (ELR) or the mean objective cost of uncertainty (MOCU) proposed recently. These active learning methods are optimal with the maximum classification error reduction when one considers a single query. However, it is well-known that there is no performance guarantee in the long run for these myopic methods. In this paper, we show that these methods are not guaranteed to converge to the optimal classifier of the true model because MOCU is not strictly concave. Moreover, we suggest a strictly concave approximation of MOCU—Soft MOCU—that can be used to define an acquisition function to guide Bayesian active learning with theoretical convergence guarantee. For training Bayesian classifiers with both synthetic and real-world data, our experiments demonstrate the superior performance of active learning by Soft MOCU compared to other existing methods.

We study regret minimization in a stochastic multi-armed bandit setting, and establish a fundamental trade-off between the regret suffered under an algorithm, and its statistical robustness. Considering broad classes of underlying arms’ distributions, we show that bandit learning algorithms with logarithmic regret are always inconsistent and that consistent learning algorithms always suffer a super-logarithmic regret. This result highlights the inevitable statistical fragility of all ‘logarithmic regret’ bandit algorithms available in the literature - for instance, if a UCB algorithm designed for 1-subGaussian distributions is used in a subGaussian setting with a mismatched variance parameter, the learning performance could be inconsistent. Next, we show a positive result: statistically robust and consistent learning performance is attainable if we allow the regret to be slightly worse than logarithmic. Specifically, we propose three classes of distribution oblivious algorithms that achieve an asymptotic regret that is arbitrarily close to logarithmic.

Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family. Here, we introduce automatic structured variational inference (ASVI), a fully automated method for constructing structured variational families, inspired by the closed-form update in conjugate Bayesian models. These pseudo-conjugate families incorporate the forward pass of the input probabilistic program and can therefore capture complex statistical dependencies. Pseudo-conjugate families have the same space and time complexity of the input probabilistic program and are therefore tractable for a very large family of models including both continuous and discrete variables. We validate our automatic variational method on a wide range of both low- and high-dimensional inference problems. We find that ASVI provides a clear improvement in performance when compared with other popular approaches such as mean field family and inverse autoregressive flows. We provide a fully automatic open source implementation of ASVI in TensorFlow Probability.

Automatic Differentiation Variational Inference (ADVI) is a useful tool for efficiently learning probabilistic models in machine learning. Generally approximate posteriors learned by ADVI are forced to be unimodal in order to facilitate use of the reparameterization trick. In this paper, we show how stratified sampling may be used to enable mixture distributions as the approximate posterior, and derive a new lower bound on the evidence analogous to the importance weighted autoencoder (IWAE). We show that this "SIWAE" is a tighter bound than both IWAE and the traditional ELBO, both of which are special instances of this bound. We verify empirically that the traditional ELBO objective disfavors the presence of multimodal posterior distributions and may therefore not be able to fully capture structure in the latent space. Our experiments show that using the SIWAE objective allows the encoder to learn more complex distributions which regularly contain multimodality, resulting in higher accuracy and better calibration in the presence of incomplete, limited, or corrupted data.