Graphs have been commonly used to represent complex data structures. In models dealing with graph-structured data, multivariate parameters may not only exhibit sparse patterns but have structured sparsity and smoothness in the sense that both zero and non-zero parameters tend to cluster together. We propose a new prior for high-dimensional parameters with graphical relations, referred to as the Treebased Low-rank Horseshoe (T-LoHo) model, that generalizes the popular univariate Bayesian horseshoe shrinkage prior to the multivariate setting to detect structured sparsity and smoothness simultaneously. The T-LoHo prior can be embedded in many high-dimensional hierarchical models. To illustrate its utility, we apply it to regularize a Bayesian high-dimensional regression problem where the regression coefficients are linked by a graph, so that the resulting clusters have flexible shapes and satisfy the cluster contiguity constraint with respect to the graph. We design an efficient Markov chain Monte Carlo algorithm that delivers full Bayesian inference with uncertainty measures for model parameters such as the number of clusters. We offer theoretical investigations of the clustering effects and posterior concentration results. Finally, we illustrate the performance of the model with simulation studies and a real data application for anomaly detection on a road network. The results indicate substantial improvements over other competing methods such as the sparse fused lasso.

We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective. The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PACBayes objectives - both with uninformed (data-independent) and informed (datadependent) priors.

We investigate the parameterized complexity of Bayesian Network Structure Learn-1 ing (BNSL), a classical problem that has received significant attention in empirical2 but also purely theoretical studies. We follow up on previous works that have3 analyzed the complexity of BNSL w.r.t. the so-called superstructure of the input.4 While known results imply that BNSL is unlikely to be fixed-parameter tractable5 even when parameterized by the size of a vertex cover in the superstructure, here we6 show that a different kind of parameterization--notably by the size of a feedback7 edge set--yields fixed-parameter tractability. We proceed by showing that this8 result can be strengthened to a localized version of the feedback edge set, and9 provide corresponding lower bounds that complement previous results to provide a10 complexity classification of BNSL w.r.t.

We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events. Our key tool is probability generating functions: they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments. Our inference method is provably correct and fully automated in a tool called Genfer, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra. Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy. On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.

ABayesian pseudocoreset is a small synthetic dataset for which the posterior over parameters approximates that of the original dataset. While promising, the scalability of Bayesian pseudocoresets is not yet validated in realistic problems such as image classification with deep neural networks. On the other hand, dataset distillation methods similarly construct a small dataset such that the optimization using the synthetic dataset converges to a solution with performance competitive with optimization using full data. Although dataset distillation has been empirically verified in large-scale settings, the framework is restricted to point estimates, and their adaptation to Bayesian inference has not been explored. This paper casts two representative dataset distillation algorithms as approximations to methods for constructing pseudocoresets by minimizing specific divergence measures: reverse KL divergence and Wasserstein distance. Furthermore, we provide a unifying view of such divergence measures in Bayesian pseudocoreset construction. Finally, we propose a novel Bayesian pseudocoreset algorithm based on minimizing forward KL divergence. Our empirical results demonstrate that the pseudocoresets constructed from these methods reflect the true posterior even in high-dimensional Bayesian inference problems.

This paper presents PolyDiffuse, a novel structured reconstruction algorithm that transforms visual sensor data into polygonal shapes with Diffusion Models (DM), an emerging machinery amid exploding generative AI, while formulating reconstruction as a generation process conditioned on sensor data. The task of structured reconstruction poses two fundamental challenges to DM: 1) A structured geometry is a "set" (e.g., a set of polygons for a floorplan geometry), where a sample of N elements has N! different but equivalent representations, making the denoising highly ambiguous; and 2) A "reconstruction" task has a single solution, where an initial noise needs to be chosen carefully, while any initial noise works for a generation task. Our technical contribution is the introduction of a Guided Set Diffusion Model where 1) the forward diffusion process learns guidance networks to control noise injection so that one representation of a sample remains distinct from its other permutation variants, thus resolving denoising ambiguity; and 2) the reverse denoising process reconstructs polygonal shapes, initialized and directed by the guidance networks, as a conditional generation process subject to the sensor data. We have evaluated our approach for reconstructing two types of polygonal shapes: floorplan as a set of polygons and HD map for autonomous cars as a set of polylines. Through extensive experiments on standard benchmarks, we demonstrate that PolyDiffuse significantly advances the current state of the art and enables broader practical applications. The code and data are available on our project page: https://poly-diffuse.github.io.