13 accepted papers
Despite their remarkable success, a rigorous theoretical understanding of how latent variables (LVs) govern the generalization performance of Variational Autoencoders (VAEs) remains largely elusive. Existing theoretical analyses are confined to supervised learning or models with discrete latent spac…
Calibration is a critical requirement for reliable probabilistic prediction, especially in high-risk applications. However, the theoretical understanding of which learning algorithms can simultaneously achieve high accuracy and good calibration remains limited, and many existing studies provide empi…
Bayesian inference is widely used in practice due to its ability to assess epistemic uncertainty (EU) in predictions. However, its computational complexity necessitates the use of approximation methods, such as variational inference (VI). When estimating EU within the VI framework, metrics such as t…
Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in supervised learning, similar analyses for unsupervised models such…
Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary classification, creating a significant gap with practical app…
Bayesian inference is often used to quantify uncertainty. Several recent analyses have rigorously decomposed uncertainty in prediction by Bayesian inference into two types: the inherent randomness in the data generation process and the variability due to lack of data respectively. Existing studies h…
While the expected calibration error (ECE), which employs binning, is widely adopted to evaluate the calibration performance of machine learning models, theoretical understanding of its estimation bias is limited. In this paper, we present the first comprehensive analysis of the estimation bias in t…
We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our bounds are time-independent and decay to zero as the sample…
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 predicti…
Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to efficiently capture the information in the posterior distribution…
Posterior distribution approximation is a central task in Bayesian inference. Stochastic gradient Langevin dynamics (SGLD) and its extensions have been practically used and theoretically studied. While SGLD updates a single particle at a time, ensemble methods that update multiple particles simultan…
Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner’s optimization…
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which contains Student-t distributions as family members and thus all…