Related papers: High Dimensional Inference with Random Maximum A-P…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
Consider the standard Gaussian linear regression model $Y=X\theta+\epsilon$, where $Y\in R^n$ is a response vector and $ X\in R^{n*p}$ is a design matrix. Numerous work have been devoted to building efficient estimators of $\theta$ when $p$…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…
We derive a new residual-type a posteriori estimator for a singularly perturbed reaction-diffusion problem with obstacle constraints. It generalizes robust residual estimators for unconstrained singularly perturbed equations. Upper and…
We present a theoretical analysis of Maximum a Posteriori (MAP) sequence estimation for binary symmetric hidden Markov processes. We reduce the MAP estimation to the energy minimization of an appropriately defined Ising spin model, and…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these…
The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…
In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…
High-dimensional probability density estimation for inference suffers from the "curse of dimensionality". For many physical inference problems, the full posterior distribution is unwieldy and seldom used in practice. Instead, we propose…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22],…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…