To check the accuracy of Bayesian computations, it is common to use rank-based simulation-based calibration (SBC). However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric. We propose to replace the marginal rank test with a flexible classification approach that learns test statistics from data. This measure typically has a higher statistical power than the SBC test and returns an interpretable divergence measure of miscalibration, computed from classification accuracy. This approach can be used with different data generating processes to address simulation-based inference or traditional inference methods like Markov chain Monte Carlo or variational inference. We illustrate an automated implementation using neural networks and statistically-inspired features, and validate the method with numerical and real data experiments.

Reinforcement learning (RL) has gained increasing popularity for resource management in cloud services such as serverless computing. As self-interested users compete for shared resources in a cluster, the multi-tenancy nature of serverless platforms necessitates multi-agent reinforcement learning (MARL) solutions, which often suffer from severe scalability issues. In this paper, we propose a mean-field game (MFG) approach to cloud resource management that is scalable to a large number of users and applications and incorporates function approximation to deal with the large state-action spaces in real-world serverless platforms. Specifically, we present an online natural actor-critic algorithm for learning in MFGs compatible with various forms of function approximation. We theoretically establish its finite-time convergence to the regularized Nash equilibrium under linear function approximation and softmax parameterization.

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty---a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our formulation directly applicable to posterior inference of nonstandard Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. Using DiBS, we devise an efficient, general purpose variational inference method for approximating distributions over structural models.

In this paper, we tackle the important yet under-investigated problem of making long-horizon prediction of event sequences. Existing state-of-the-art models do not perform well at this task due to their autoregressive structure. We propose HYPRO, a hybridly normalized probabilistic model that naturally fits this task: its first part is an autoregressive base model that learns to propose predictions; its second part is an energy function that learns to reweight the proposals such that more realistic predictions end up with higher probabilities. We also propose efficient training and inference algorithms for this model. Experiments on multiple real-world datasets demonstrate that our proposed HYPRO model can significantly outperform previous models at making long-horizon predictions of future events.

Sampling-based inference and learning techniques, especially Bayesian inference, provide an essential approach to handling uncertainty in machine learning (ML). As these techniques are increasingly used in daily life, it becomes essential to safeguard the ML systems with various trustworthy-related constraints, such as fairness, safety, interpretability. Mathematically, enforcing these constraints in probabilistic inference can be cast into sampling from intractable distributions subject to general nonlinear constraints, for which practical efficient algorithms are still largely missing. In this work, we propose a family of constrained sampling algorithms which generalize Langevin Dynamics (LD) and Stein Variational Gradient Descent (SVGD) to incorporate a moment constraint specified by a general nonlinear function. By exploiting the gradient flow structure of LD and SVGD, we derive two types of algorithms for handling constraints, including a primal-dual gradient approach and the constraint controlled gradient descent approach.

In many real-world scenarios it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. However, learning PCs on heterogeneous data is challenging and densities of some parametric distributions are not available in closed form, limiting their potential use. We introduce characteristic circuits (CCs), a family of tractable probabilistic models providing a unified formalization of distributions over heterogeneous data in the spectral domain. The one-to-one relationship between characteristic functions and probability measures enables us to learn high-dimensional distributions on heterogeneous data domains and facilitates efficient probabilistic inference even when no closed-form density function is available. We show that the structure and parameters of CCs can be learned efficiently from the data and find that CCs outperform state-of-the-art density estimators for heterogeneous data domains on common benchmark data sets.

Recent advances in coreset methods have shown that a selection of representative datapoints can replace massive volumes of data for Bayesian inference, preserving the relevant statistical information and significantly accelerating subsequent downstream tasks. Existing variational coreset constructions rely on either selecting subsets of the observed datapoints, or jointly performing approximate inference and optimizing pseudodata in the observed space akin to inducing points methods in Gaussian Processes. So far, both approaches are limited by complexities in evaluating their objectives for general purpose models, and require generating samples from a typically intractable posterior over the coreset throughout inference and testing. In this work, we present a black-box variational inference framework for coresets that overcomes these constraints and enables principled application of variational coresets to intractable models, such as Bayesian neural networks. We apply our techniques to supervised learning problems, and compare them with existing approaches in the literature for data summarization and inference.

Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only marginal improvement of GNNs has been observed in practice over their linear counterparts. Previous works provide very few understandings of this phenomenon. In this work, we resort to Bayesian learning to give an in-depth investigation of the functions of non-linearity in GNNs for node classification tasks. Given a graph generated from the statistical model CSBM, we observe that the max-a-posterior estimation of a node label given its own and neighbors' attributes consists of two types of non-linearity, the transformation of node attributes and a ReLU-activated feature aggregation from neighbors.

A popular perspective in Reinforcement learning (RL) casts the problem as probabilistic inference on a graphical model of the Markov decision process (MDP). The core object of study is the probability of each state-action pair being visited under the optimal policy. Previous approaches to approximate this quantity can be arbitrarily poor, leading to algorithms that do not implement genuine statistical inference and consequently do not perform well in challenging problems. In this work, we undertake a rigorous Bayesian treatment of the posterior probability of state-action optimality and clarify how it flows through the MDP. We first reveal that this quantity can indeed be used to generate a policy that explores efficiently, as measured by regret.

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an O(\sqrt{T}) regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games.