Related papers: An MCMC-free approach to post-selective inference
Completely random measures provide a principled approach to creating flexible unsupervised models, where the number of latent features is infinite and the number of features that influence the data grows with the size of the data set. Due…
Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…
Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
Multivariate normal (MVN) probabilities arise in myriad applications, but they are analytically intractable and need to be evaluated via Monte-Carlo-based numerical integration. For the state-of-the-art minimax exponential tilting (MET)…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
This work presents a novel posterior inference method for models with intractable evidence and likelihood functions. Error-guided likelihood-free MCMC, or EG-LF-MCMC in short, has been developed for scientific applications, where a…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…
Motivated by various computational applications, we investigate the problem of estimating nested expectations. Building upon recent work by the authors, we propose a novel Monte Carlo estimator for nested expectations, inspired by sparse…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…