AISTATS 2023 Papers

We present Parallel Feasible Pareto Frontier Entropy Search ($\{\mathrm{PF}\}^2$ES) — a novel information-theoretic acquisition function for multi-objective Bayesian optimization supporting unknown constraints and batch queries. Due to the complexity of characterizing the mutual information between candidate evaluations and (feasible) Pareto frontiers, existing approaches must either employ crude approximations that significantly hamper their performance or rely on expensive inference schemes that substantially increase the optimization’s computational overhead. By instead using a variational lower bound, $\{\mathrm{PF}\}^2$ES provides a low-cost and accurate estimate of the mutual information. We benchmark $\{\mathrm{PF}\}^2$ES against other information-theoretic acquisition functions, demonstrating its competitive performance for optimization across synthetic and real-world design problems.

Preferential Bayesian optimization (PBO) is a framework for optimizing a decision maker’s latent utility function using preference feedback. This work introduces the expected utility of the best option (qEUBO) as a novel acquisition function for PBO. When the decision maker’s responses are noise-free, we show that qEUBO is one-step Bayes optimal and thus equivalent to the popular knowledge gradient acquisition function. We also show that qEUBO enjoys an additive constant approximation guarantee to the one-step Bayes-optimal policy when the decision maker’s responses are corrupted by noise. We provide an extensive evaluation of qEUBO and demonstrate that it outperforms the state-of-the-art acquisition functions for PBO across many settings. Finally, we show that, under sufficient regularity conditions, qEUBO’s Bayesian simple regret converges to zero at a rate $o(1/n)$ as the number of queries, $n$, goes to infinity. In contrast, we show that simple regret under qEI, a popular acquisition function for standard BO often used for PBO, can fail to converge to zero. Enjoying superior performance, simple computation, and a grounded decision-theoretic justification, qEUBO is a promising acquisition function for PBO.

Automated AI classifiers should be able to defer the prediction to a human decision maker to ensure more accurate predictions. In this work, we jointly train a classifier with a rejector, which decides on each data point whether the classifier or the human should predict. We show that prior approaches can fail to find a human-AI system with low mis-classification error even when there exists a linear classifier and rejector that have zero error (the realizable setting). We prove that obtaining a linear pair with low error is NP-hard even when the problem is realizable. To complement this negative result, we give a mixed-integer-linear-programming (MILP) formulation that can optimally solve the problem in the linear setting. However, the MILP only scales to moderately-sized problems. Therefore, we provide a novel surrogate loss function that is realizable-consistent and performs well empirically. We test our approaches on a comprehensive set of datasets and compare to a wide range of baselines.

In recent years, graph neural networks (GNNs) have emerged as a promising tool for solving machine learning problems on graphs. Most GNNs are members of the family of message passing neural networks (MPNNs). There is a close connection between these models and the Weisfeiler-Leman (WL) test of isomorphism, an algorithm that can successfully test isomorphism for a broad class of graphs. Recently, much research has focused on measuring the expressive power of GNNs. For instance, it has been shown that standard MPNNs are at most as powerful as WL in terms of distinguishing non-isomorphic graphs. However, these studies have largely ignored the distances between the representations of the nodes/graphs which are of paramount importance for learning tasks. In this paper, we define a distance function between nodes which is based on the hierarchy produced by the WL algorithm, and propose a model that learns representations which preserve those distances between nodes. Since the emerging hierarchy corresponds to a tree, to learn these representations, we capitalize on recent advances in the field of hyperbolic neural networks. We empirically evaluate the proposed model on standard graph and node classification datasets where it achieves competitive performance with state-of-the-art models.

Weather forecasting is one of the cornerstones of meteorological work. In this paper, we present a new benchmark dataset named Weather2K, which aims to make up for the deficiencies of existing weather forecasting datasets in terms of real-time, reliability, and diversity, as well as the key bottleneck of data quality. To be specific, our Weather2K is featured from the following aspects: 1) Reliable and real-time data. The data is hourly collected from 2,130 ground weather stations covering an area of 6 million square kilometers. 2) Multivariate meteorological variables. 20 meteorological factors and 3 constants for position information are provided with a length of 40,896 time steps. 3) Applicable to diverse tasks. We conduct a set of baseline tests on time series forecasting and spatio-temporal forecasting. To the best of our knowledge, our Weather2K is the first attempt to tackle weather forecasting task by taking full advantage of the strengths of observation data from ground weather stations. Based on Weather2K, we further propose Meteorological Factors based Multi-Graph Convolution Network (MFMGCN), which can effectively construct the intrinsic correlation among geographic locations based on meteorological factors. Sufficient experiments show that MFMGCN improves both the forecasting performance and temporal robustness. We hope our Weather2K can significantly motivate researchers to develop efficient and accurate algorithms to advance the task of weather forecasting. The dataset can be available at https://github.com/bycnfz/weather2k/.

We focus on robust estimation of the unobserved state of a discrete-time stochastic system with linear dynamics. A standard analysis of this estimation problem assumes a baseline innovation model; with Gaussian innovations we recover the Kalman filter. However, in many settings, there is insufficient or corrupted data to validate the baseline model. To cope with this problem, we minimize the worst-case mean-squared estimation error of adversarial models chosen within a Wasserstein neighborhood around the baseline. We also constrain the adversarial innovations to form a martingale difference sequence. The martingale constraint relaxes the i.i.d. assumptions which are often imposed on the baseline model. Moreover, we show that the martingale constraints guarantee that the adversarial dynamics remain adapted to the natural time-generated information. Therefore, adding the martingale constraint allows to improve upon over-conservative policies that also protect against unrealistic omniscient adversaries. We establish a strong duality result which we use to develop an efficient subgradient method to compute the distributionally robust estimation policy. If the baseline innovations are Gaussian, we show that the worst-case adversary remains Gaussian. Our numerical experiments indicate that the martingale constraint may also aid in adding a layer of robustness in the choice of the adversarial power.

Learning function-on-scalar predictive models for conditional densities and identifying factors that influence the entire probability distribution are vital tasks in many data-driven applications. We present an efficient Majorization-Minimization optimization algorithm, Wasserstein Distributional Learning (WDL), that trains Semi-parametric Conditional Gaussian Mixture Models (SCGMM) for conditional density functions and uses the Wasserstein distance $W_2$ as a proper metric for the space of density outcomes. We further provide theoretical convergence guarantees and illustrate the algorithm using boosted machines. Experiments on the synthetic data and real-world applications demonstrate the effectiveness of the proposed WDL algorithm.

Time series generation (TSG) studies have mainly focused on the use of Generative Adversarial Networks (GANs) combined with recurrent neural network (RNN) variants. However, the fundamental limitations and challenges of training GANs still remain. In addition, the RNN-family typically has difficulties with temporal consistency between distant timesteps. Motivated by the successes in the image generation (IMG) domain, we propose TimeVQVAE, the first work, to our knowledge, that uses vector quantization (VQ) techniques to address the TSG problem. Moreover, the priors of the discrete latent spaces are learned with bidirectional transformer models that can better capture global temporal consistency. We also propose VQ modeling in a time-frequency domain, separated into low-frequency (LF) and high-frequency (HF). This allows us to retain important characteristics of the time series and, in turn, generate new synthetic signals that are of better quality, with sharper changes in modularity, than its competing TSG methods. Our experimental evaluation is conducted on all datasets from the UCR archive, using well-established metrics in the IMG literature, such as Frechet inception distance and inception scores. Our implementation on GitHub: https://github.com/ML4ITS/TimeVQVAE.

We introduce vector optimization problems with stochastic bandit feedback, in which preferences among designs are encoded by a polyhedral ordering cone $C$. Our setup generalizes the best arm identification problem to vector-valued rewards by extending the concept of Pareto set beyond multi-objective optimization. We characterize the sample complexity of ($\epsilon,\delta$)-PAC Pareto set identification by defining a new cone-dependent notion of complexity, called the ordering complexity. In particular, we provide gap-dependent and worst-case lower bounds on the sample complexity and show that, in the worst-case, the sample complexity scales with the square of ordering complexity. Furthermore, we investigate the sample complexity of the na{ı̈}ve elimination algorithm and prove that it nearly matches the worst-case sample complexity. Finally, we run experiments to verify our theoretical results and illustrate how $C$ and sampling budget affect the Pareto set, the returned ($\epsilon,\delta$)-PAC Pareto set, and the success of identification.

Neyman-Scott processes (NSPs) have been applied across a range of fields to model points or temporal events with a hierarchy of clusters. Markov chain Monte Carlo (MCMC) is typically used for posterior sampling in the model. However, MCMC’s mixing time can cause the resulting inference to be slow, and thereby slow down model learning and prediction. We develop the first variational inference (VI) algorithm for NSPs, and give two examples of suitable variational posterior point process distributions. Our method minimizes the inclusive Kullback-Leibler (KL) divergence for VI to obtain the variational parameters. We generate samples from the approximate posterior point processes much faster than MCMC, as we can directly estimate the approximate posterior point processes without any MCMC steps or gradient descent. We include synthetic and real-world data experiments that demonstrate our VI algorithm achieves better prediction performance than MCMC when computational time is limited.

Gradient boosting machines (GBMs) based on decision trees consistently demonstrate state-of-the-art results on regression and classification tasks with tabular data, often outperforming deep neural networks. However, these models do not provide well-calibrated predictive uncertainties, which prevents their use for decision making in high-risk applications. The Bayesian treatment is known to improve predictive uncertainty calibration, but previously proposed Bayesian GBM methods are either computationally expensive, or resort to crude approximations. Variational inference is often used to implement Bayesian neural networks, but is difficult to apply to GBMs, because the decision trees used as weak learners are non-differentiable. In this paper, we propose to implement Bayesian GBMs using variational inference with soft decision trees, a fully differentiable alternative to standard decision trees introduced by Irsoy et al. Our experiments demonstrate that variational soft trees and variational soft GBMs provide useful uncertainty estimates, while retaining good predictive performance. The proposed models show higher test likelihoods when compared to the state-of-the-art Bayesian GBMs in 7/10 tabular regression datasets and improved out-of-distribution detection in 5/10 datasets.

In this paper, we study the memorization and generalization behaviour of deep neural networks (DNNs) using sliced mutual information (SMI), which is the average of the mutual information (MI) between one-dimensional random projections. We argue that the SMI between features in a DNN ($T$) and ground truth labels ($Y$), $SI(T;Y)$, can be seen as a form of usable information that the features contain about the labels. We show theoretically that $SI(T;Y)$ can encode geometric properties of the feature distribution, such as its spherical soft-margin and intrinsic dimensionality, in a way that MI cannot. Additionally, we present empirical evidence showing how $SI(T;Y)$ can capture memorization and generalization in DNNs. In particular, we find that, in the presence of label noise, all layers start to memorize but the earlier layers stabilize more quickly than the deeper layers. Finally, we point out that, in the context of Bayesian Neural Networks, the SMI between the penultimate layer and the output represents the worst case uncertainty of the network’s output.

We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key assumption that observations are conditionally independent given latents, the RPM combines parametric prior and observation-conditioned latent distributions with non-parametric observation marginals. This approach leads to a flexible learnt recognition model capturing latent dependence between observations, without the need for an explicit, parametric generative model. The RPM admits exact maximum-likelihood learning for discrete latents, even for powerful neural network-based recognition. We develop effective approximations applicable in the continuous latent case. Experiments demonstrate the effectiveness of the RPM on high-dimensional data, learning image classification from weak indirect supervision; direct image-level latent Dirichlet allocation; and Recognition-Parametrised Gaussian Process Factor Analysis (RP-GPFA) applied to multi-factorial spatiotemporal datasets. The RPM provides a powerful framework to discover meaningful latent structure underlying observational data, a function critical to both animal and artificial intelligence.

Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents’ expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture’s intelligence is the weighted average of the original agents’ intelligence. This operation enables various interesting new theorems that shed light on the geometry of RL agent intelligence, namely: results about symmetries, convex agent-sets, and local extrema. We also show that any RL agent intelligence measure based on average performance across environments, subject to certain weak technical conditions, is identical (up to a constant factor) to performance within a single environment dependent on said intelligence measure.

We consider a global representation of a regression or classification function by decomposing it into the sum of main and interaction components of arbitrary order. We propose a new identification constraint that allows for the extraction of interventional SHAP values and partial dependence plots, thereby unifying local and global explanations. With our proposed identification, a feature’s partial dependence plot corresponds to the main effect term plus the intercept. The interventional SHAP value of feature $k$ is a weighted sum of the main component and all interaction components that include $k$, with the weights given by the reciprocal of the component’s dimension. This brings a new perspective to local explanations such as SHAP values which were previously motivated by game theory only. We show that the decomposition can be used to reduce direct and indirect bias by removing all components that include a protected feature. Lastly, we motivate a new measure of feature importance. In principle, our proposed functional decomposition can be applied to any machine learning model, but exact calculation is only feasible for low-dimensional structures or ensembles of those. We provide an algorithm and efficient implementation for gradient-boosted trees (xgboost) and random planted forest. Conducted experiments suggest that our method provides meaningful explanations and reveals interactions of higher orders. The proposed methods are implemented in an R package, available at https://github.com/PlantedML/glex.

A key challenge to deploying reinforcement learning in practice is avoiding excessive (harmful) exploration in individual episodes. We propose a natural constraint on exploration—uniformly outperforming a conservative policy (adaptively estimated from all data observed thus far), up to a per-episode exploration budget. We design a novel algorithm that uses a UCB reinforcement learning policy for exploration, but overrides it as needed to satisfy our exploration constraint with high probability. Importantly, to ensure unbiased exploration across the state space, our algorithm adaptively determines when to explore. We prove that our approach remains conservative while minimizing regret in the tabular setting. We experimentally validate our results on a sepsis treatment task and an HIV treatment task, demonstrating that our algorithm can learn while ensuring good performance compared to the baseline policy for every patient; the latter task also demonstrates that our approach extends to continuous state spaces via deep reinforcement learning.

This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relaxed estimation method. To develop the estimation problem, we construct an unconstrained maximum likelihood estimator to perform DRE with a stratified sampling scheme. We further propose a novel class of probability divergences, called the Density Ratio Metrics (DRMs), that interpolates the KL-divergence and the IPMs. In addition to these findings, we also introduce some applications of the DRMs, such as DRE and generative adversarial networks. In experiments, we validate the effectiveness of our proposed methods.

Uni6D is the first 6D pose estimation approach to employ a unified backbone network to extract features from both RGB and depth images. We discover that the principal reasons of Uni6D performance limitations are Instance-Outside and Instance-Inside noise. Uni6D’s simple pipeline design inherently introduces Instance-Outside noise from background pixels in the receptive field, while ignoring Instance-Inside noise in the input depth data. In this paper, we propose a two-step denoising approach for dealing with the aforementioned noise in Uni6D. To reduce noise from non-instance regions, an instance segmentation network is utilized in the first step to crop and mask the instance. A lightweight depth denoising module is proposed in the second step to calibrate the depth feature before feeding it into the pose regression network. Extensive experiments show that our Uni6Dv2 reliably and robustly eliminates noise, outperforming Uni6D without sacrificing too much inference efficiency. It also reduces the need for annotated real data that requires costly labeling.

We study the problem of inferring heterogeneous treatment effects (HTEs) from time-to-event data in the presence of competing events. Albeit its great practical relevance, this problem has received little attention compared to its counterparts studying HTE estimation without time-to-event data or competing events. We take an outcome modeling approach to estimating HTEs, and consider how and when existing prediction models for time-to-event data can be used as plug-in estimators for potential outcomes. We then investigate whether competing events present new challenges for HTE estimation – in addition to the standard confounding problem –, and find that, because there are multiple definitions of causal effects in this setting – namely total, direct and separable effects –, competing events can act as an additional source of covariate shift depending on the desired treatment effect interpretation and associated estimand. We theoretically analyze and empirically illustrate when and how these challenges play a role when using generic machine learning prediction models for the estimation of HTEs.