Related papers: Projection Theorems of Divergences and Likelihood …
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust…
Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…
In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the H\"older ordinary and reverse…
We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…
Dimensionality reduction-based dictionary learning methods in the literature have often used iterative random projections. The dimensionality of such a random projection matrix is a random number that might not lead to a separable subspace…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…