Related papers: Pac-Bayesian Supervised Classification: The Thermo…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…

We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous…

We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…

Hebbian learning theory is rooted in Pavlov's Classical Conditioning. While mathematical models of the former have been proposed and studied in the past decades, especially in spin glass theory, only recently it has been numerically shown…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed…

Meta learning automatically infers an inductive bias, that includes the hyperparameter of the base-learning algorithm, by observing data from a finite number of related tasks. This paper studies PAC-Bayes bounds on meta generalization gap.…

In this paper, we establish novel data-dependent upper bounds on the generalization error through the lens of a "variable-size compressibility" framework that we introduce newly here. In this framework, the generalization error of an…

This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced…

Bayesian deep learning plays an important role especially for its ability evaluating epistemic uncertainty (EU). Due to computational complexity issues, approximation methods such as variational inference (VI) have been used in practice to…