Related papers: Probabilistic learning inference of boundary value…

This paper introduces an algorithm to select demonstration examples for in-context learning of a query set. Given a set of $n$ examples, how can we quickly select $k$ out of $n$ to best serve as the conditioning for downstream inference?…

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

We characterize Martin-L\"of randomness and Schnorr randomness in terms of the merging of opinions, along the lines of the Blackwell-Dubins Theorem. After setting up a general framework for defining notions of merging randomness, we focus…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of…

This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…

Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational…

We consider optimal sequential allocation in the context of the so-called stochastic multi-armed bandit model. We describe a generic index policy, in the sense of Gittins [J. R. Stat. Soc. Ser. B Stat. Methodol. 41 (1979) 148-177], based on…

This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…

We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation…

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

Empirical researchers increasingly use upstream machine-learning (ML) methods to construct proxies for latent target variables from complex, unstructured data. A naive plug-in use of such proxies in downstream econometric models, however,…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

In the loss function of Variational Autoencoders there is a well known tension between two components: the reconstruction loss, improving the quality of the resulting images, and the Kullback-Leibler divergence, acting as a regularizer of…

We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…

We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…