Related papers: Solving high-dimensional parameter inference: marg…

With the advancement of data science, the collection of increasingly complex datasets has become commonplace. In such datasets, the data dimension can be extremely high, and the underlying data generation process can be unknown and highly…

Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…

Monte Carlo (MC) algorithms are commonly employed to explore high-dimensional parameter spaces constrained by data. All the statistical information obtained in the output of these analyses is contained in the Markov chains, which one needs…

It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. This motivates much of the recent theoretical study on linear MDPs. However, most approaches require a given…

We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is…

This paper presents a significant advancement in the estimation of the Composite Link Model within a penalized likelihood framework, specifically designed to address indirect observations of grouped count data. While the model is effective…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

We present an algorithm for producing discrete distributions with a prescribed nearest-neighbor distance function. Our approach is a combination of quasi-Monte Carlo (Q-MC) methods and weighted Riesz energy minimization: the initial…

Inferring directed acyclic graphs (DAGs) from data via Markov chain Monte Carlo (MCMC) is computationally challenging in moderate-to-high dimensional settings because their discrete sampling space grows super-exponentially with the number…

We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…

This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…

This paper tackles the issue of real-time parametric estimation of a wide class of probability density functions from limited datasets. This type of estimation addresses recent applications that require joint sensing and actuation. The…

In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…

The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article, we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables…

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…

A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…