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We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…
In this paper, we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence, weak law of large numbers, strong law of large numbers, some exponential inequalities, central limit…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…
We investigate the asymptotic behavior of the least squares estimator of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on inherited and environmental effects, we establish the…
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…
In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables…
This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage…
Mixture proportion estimation (MPE) aims to estimate class priors from unlabeled data. This task is a critical component in weakly supervised learning, such as PU learning, learning with label noise, and domain adaptation. Existing MPE…
Autoregressive models use chain rule to define a joint probability distribution as a product of conditionals. These conditionals need to be normalized, imposing constraints on the functional families that can be used. To increase…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…
We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…
A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with copula-joint innovations is studied. Different parameter estimation methods are analyzed and compared via Monte Carlo simulations with emphasis on estimation of…
Threshold selection is a critical issue for extreme value analysis with threshold-based approaches. Under suitable conditions, exceedances over a high threshold have been shown to follow the generalized Pareto distribution (GPD)…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…