AISTATS 2022 论文列表

Since the Bayesian inference works poorly under model misspecification, various solutions have been explored to counteract the shortcomings. Recently proposed predictive Bayes (PB) that directly optimizes the Kullback Leibler divergence between the empirical distribution and the approximate predictive distribution shows excellent performances not only under model misspecification but also for over-parametrized models. However, its behavior and superiority are still unclear, which limits the applications of PB. Specifically, the superiority of PB has been shown only in terms of the predictive test log-likelihood and the performance in the sense of parameter estimation has not been investigated yet. Also, it is not clear why PB is superior with misspecified and over-parameterized models. In this paper, we clarify these ambiguities by studying PB in the framework of risk-seeking optimization. To achieve this, first, we provide a consistency theory for PB and then present intuition of robustness of PB to model misspecification using a response function theory. Thereafter, we theoretically and numerically show that PB has an implicit regularization effect that leads to flat local minima in over-parametrized models.

Black box optimization requires specifying a search space to explore for solutions, e.g. a d-dimensional compact space, and this choice is critical for getting the best results at a reasonable budget. Unfortunately, determining a high quality search space can be challenging in many applications. For example, when tuning hyperparameters for machine learning pipelines on a new problem given a limited budget, one must strike a balance between excluding potentially promising regions and keeping the search space small enough to be tractable. The goal of this work is to motivate—through example applications in tuning deep neural networks—the problem of predicting the quality of search spaces conditioned on budgets, as well as to provide a simple scoring method based on a utility function applied to a probabilistic response surface model, similar to Bayesian optimization. We show that the method we present can compute meaningful budget-conditional scores in a variety of situations. We also provide experimental evidence that accurate scores can be useful in constructing and pruning search spaces. Ultimately, we believe scoring search spaces should become standard practice in the experimental workflow for deep learning.

Predicting the impact of treatments from ob- servational data only still represents a major challenge despite recent significant advances in time series modeling. Treatment assignments are usually correlated with the predictors of the response, resulting in a lack of data support for counterfactual predictions and therefore in poor quality estimates. Developments in causal inference have lead to methods addressing this confounding by requiring a minimum level of overlap. However, overlap is difficult to assess and usually not satisfied in practice. In this work, we propose Counterfactual ODE (CF-ODE), a novel method to predict the impact of treatments continuously over time using Neural Ordinary Differential Equations equipped with uncertainty estimates. This allows to specifically assess which treatment outcomes can be reliably predicted. We demonstrate over several longitudinal datasets that CF-ODE provides more accurate predictions and more reliable uncertainty estimates than previously available methods.

In convex optimization, the problem of finding near-stationary points has not been adequately studied yet, unlike other optimality measures such as the function value. Even in the deterministic case, the optimal method (OGM-G, due to Kim and Fessler (2021)) has just been discovered recently. In this work, we conduct a systematic study of algorithmic techniques for finding near-stationary points of convex finite-sums. Our main contributions are several algorithmic discoveries: (1) we discover a memory-saving variant of OGM-G based on the performance estimation problem approach (Drori and Teboulle, 2014); (2) we design a new accelerated SVRG variant that can simultaneously achieve fast rates for minimizing both the gradient norm and function value; (3) we propose an adaptively regularized accelerated SVRG variant, which does not require the knowledge of some unknown initial constants and achieves near-optimal complexities. We put an emphasis on the simplicity and practicality of the new schemes, which could facilitate future work.

Many reinforcement learning (RL) environments in practice feature enormous state spaces that may be described compactly by a "factored" structure, that may be modeled by Factored Markov Decision Processes (FMDPs). We present the first polynomial time algorithm for RL in Factored State MDPs (generalizing FMDPs) that neither relies on an oracle planner nor requires a linear transition model; it only requires a linear value function with a suitable local basis with respect to the factorization, permitting efficient variable elimination. With this assumption, we can solve this family of Factored State MDPs in polynomial time by constructing an efficient separation oracle for convex optimization. Importantly, and in contrast to prior work on FMDPs, we do not assume that the transitions on various factors are conditionally independent.

We study the problem of learning individualized dose intervals using observational data. There are very few previous works for policy learning with continuous treatment, and all of them focused on recommending an optimal dose rather than an optimal dose interval. In this paper, we propose a new method to estimate such an optimal dose interval, named probability dose interval (PDI). The potential outcomes for doses in the PDI are guaranteed better than a pre-specified threshold with a given probability (e.g., $50%$). The associated nonconvex optimization problem can be efficiently solved by the Difference-of-Convex functions (DC) algorithm. We prove that our estimated policy is consistent, and its risk converges to that of the best-in-class policy at a root-n rate. Numerical simulations show the advantage of the proposed method over outcome modeling based benchmarks. We further demonstrate the performance of our method in determining individualized Hemoglobin A1c (HbA1c) control intervals for elderly patients with diabetes.

Hard integrals arise frequently in reinforcement learning, for example when computing expectations in policy evaluation and policy iteration. They are often analytically intractable and typically estimated with Monte Carlo methods, whose sampling contributes to high variance in policy values and gradients. In this work, we propose to replace Monte Carlo samples with low-discrepancy point sets. We combine policy gradient methods with Randomized Quasi-Monte Carlo, yielding variance-reduced formulations of policy gradient and actor-critic algorithms. These formulations are effective for policy evaluation and policy improvement, as they outperform state-of-the-art algorithms on standardized continuous control benchmarks. Our empirical analyses validate the intuition that replacing Monte Carlo with Quasi-Monte Carlo yields significantly more accurate gradient estimates.

Generative models can be used to synthesize 3D objects of high quality and diversity. However, there is typically no control over the properties of the generated object.This paper proposes a novel generative adversarial network (GAN) setup that generates 3D point cloud shapes conditioned on a continuous parameter. In an exemplary application, we use this to guide the generative process to create a 3D object with a custom-fit shape. We formulate this generation process in a multi-task setting by using the concept of auxiliary classifier GANs. Further, we propose to sample the generator label input for training from a kernel density estimation (KDE) of the dataset. Our ablations show that this leads to significant performance increase in regions with few samples. Extensive quantitative and qualitative experiments show that we gain explicit control over the object dimensions while maintaining good generation quality and diversity.

Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include additional information as general likelihood terms. We show that second-order differential equations should be directly provided to the solver, instead of transforming the problem to first order. Additionally, by including higher-order information or physical conservation laws in the model, solutions become more accurate and more physically meaningful. Lastly, we demonstrate the utility of flexible information operators by solving differential-algebraic equations. In conclusion, the probabilistic formulation of numerical solvers offers a flexible way to incorporate various types of information, thus improving the resulting solutions.

Deep kernel learning is a promising combination of deep neural networks and nonparametric function estimation. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data, especially in extrapolation tasks. To address these limitations, we propose Physics Informed Deep Kernel Learning (PI-DKL) that exploits physics knowledge represented by differential equations with latent sources. Specifically, we use the posterior function sample of the Gaussian process as the surrogate for the solution of the differential equation, and construct a generative component to integrate the equation in a principled Bayesian hybrid framework. For efficient and effective inference, we marginalize out the latent variables in the joint probability and derive a collapsed model evidence lower bound (ELBO), based on which we develop a stochastic model estimation algorithm. Our ELBO can be viewed as a nice, interpretable posterior regularization objective. On synthetic datasets and real-world applications, we show the advantage of our approach in both prediction accuracy and uncertainty quantification. The code is available at https://github.com/GregDobby/PIDKL.

Recent work on permutation equivariant neural networks has mostly focused on the first order case (sets) and second order case (graphs). We describe the machinery for generalizing permutation equivariance to arbitrary $k$-ary interactions between entities for any value of $k$. We demonstrate the effectiveness of higher order permutation equivariant models on several real world applications and find that our results compare favorably to existing permutation invariant/equivariant baselines.

Deployed supervised machine learning models make predictions that interact with and influence the world. This phenomenon is called

Adversarial training defense (ATD) and virtual adversarial training (VAT) are the two most effective methods to improve model robustness against attacks and model generalization. While ATD is usually applied in robust machine learning, VAT is used in semi-supervised learning and domain adaption. In this paper, we introduce a novel adversarial local distribution regularization. The adversarial local distribution is defined by a set of all adversarial examples within a ball constraint given a natural input. We illustrate this regularization is a general form of previous methods (e.g., PGD, TRADES, VAT and VADA). We conduct comprehensive experiments on MNIST, SVHN and CIFAR10 to illustrate that our method outperforms well-known methods such as PGD, TRADES and ADT in robust machine learning, VAT in semi-supervised learning and VADA in domain adaption. Our implementation is on Github: https://github.com/PotatoThanh/ALD-Regularization.

We study model selection in linear bandits, where the learner must adapt to the dimension (denoted by $d_\star$) of the smallest hypothesis class containing the true linear model while balancing exploration and exploitation. Previous papers provide various guarantees for this model selection problem, but have limitations; i.e., the analysis requires favorable conditions that allow for inexpensive statistical testing to locate the right hypothesis class or are based on the idea of “corralling” multiple base algorithms, which often performs relatively poorly in practice. These works also mainly focus on upper bounds. In this paper, we establish the first lower bound for the model selection problem. Our lower bound implies that, even with a fixed action set, adaptation to the unknown dimension $d_\star$ comes at a cost: There is no algorithm that can achieve the regret bound $\widetilde{O}(\sqrt{d_\star T})$ simultaneously for all values of $d_\star$. We propose Pareto optimal algorithms that match the lower bound. Empirical evaluations show that our algorithm enjoys superior performance compared to existing ones.

The goal of this paper is to develop a practical and general-purpose approach to construct confidence intervals for differentially private parametric estimation. We find that the parametric bootstrap is a simple and effective solution. It cleanly reasons about variability of both the data sample and the randomized privacy mechanism and applies "out of the box" to a wide class of private estimation routines. It can also help correct bias caused by clipping data to limit sensitivity. We prove that the parametric bootstrap gives consistent confidence intervals in two broadly relevant settings, including a novel adaptation to linear regression that avoids accessing the covariate data multiple times. We demonstrate its effectiveness for a variety of estimators, and find empirically that it provides confidence intervals with good coverage even at modest sample sizes and performs better than alternative approaches.

A class of parameter-free online linear optimization algorithms is proposed that harnesses the structure of an adversarial sequence by adapting to some side information. These algorithms combine the reduction technique of Orabona and Pal (2016) for adapting coin betting algorithms for online linear optimization with universal compression techniques in information theory for incorporating sequential side information to coin betting. Concrete examples are studied in which the side information has a tree structure and consists of quantized values of the previous symbols of the adversarial sequence, including fixed-order and variable-order Markov cases. By modifying the context-tree weighting technique of Willems, Shtarkov, and Tjalkens (1995), the proposed algorithm is further refined to achieve the best performance over all adaptive algorithms with tree-structured side information of a given maximum order in a computationally efficient manner.

Embarrassingly parallel Markov Chain Monte Carlo (MCMC) exploits parallel computing to scale Bayesian inference to large datasets by using a two-step approach. First, MCMC is run in parallel on (sub)posteriors defined on data partitions. Then, a server combines local results. While efficient, this framework is very sensitive to the quality of subposterior sampling. Common sampling problems such as missing modes or misrepresentation of low-density regions are amplified – instead of being corrected – in the combination phase, leading to catastrophic failures. In this work, we propose a novel combination strategy to mitigate this issue. Our strategy, Parallel Active Inference (PAI), leverages Gaussian Process (GP) surrogate modeling and active learning. After fitting GPs to subposteriors, PAI (i) shares information between GP surrogates to cover missing modes; and (ii) uses active sampling to individually refine subposterior approximations. We validate PAI in challenging benchmarks, including heavy-tailed and multi-modal posteriors and a real-world application to computational neuroscience. Empirical results show that PAI succeeds where previous methods catastrophically fail, with a small communication overhead.

Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning, and contrastive learning. A classifier built upon the representations is expected to perform well in downstream classification; however, little theory has been given in literature so far and thereby the relationship between similarity and classification has remained elusive. Therefore, we tackle a fundamental question: can similarity information provably leads a model to perform well in downstream classification? In this paper, we reveal that a product-type formulation of similarity learning is strongly related to an objective of binary classification. We further show that these two different problems are explicitly connected by an excess risk bound. Consequently, our results elucidate that similarity learning is capable of solving binary classification by directly eliciting a decision boundary.

We initiate the study of fairness for ordinal regression. We adapt two fairness notions previously considered in fair ranking and propose a strategy for training a predictor that is approximately fair according to either notion. Our predictor has the form of a threshold model, composed of a scoring function and a set of thresholds, and our strategy is based on a reduction to fair binary classification for learning the scoring function and local search for choosing the thresholds. We provide generalization guarantees on the error and fairness violation of our predictor, and we illustrate the effectiveness of our approach in extensive experiments.