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This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss…
Group fairness in machine learning is often enforced by adding a regularizer that reduces the dependence between model predictions and sensitive attributes. However, existing regularizers are built on heterogeneous distance measures and…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
The Cauchy-Schwarz (CS) divergence was developed by Pr\'{i}ncipe et al. in 2000. In this paper, we extend the classic CS divergence to quantify the closeness between two conditional distributions and show that the developed conditional CS…
We answer a question from Raghavan and Stepr{\=a}ns' paper on weakly tight families by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under…
Consider the family of power divergence statistics based on $n$ trials, each leading to one of $r$ possible outcomes. This includes the log-likelihood ratio and Pearson's statistic as important special cases. It is known that in certain…
In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature…
Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of…
We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its…
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive $p$-adic groups, analogous to Deligne-Lusztig theory for finite reductive groups. In this paper we establish a new instance of Lusztig's…
Distribution alignment has many applications in deep learning, including domain adaptation and unsupervised image-to-image translation. Most prior work on unsupervised distribution alignment relies either on minimizing simple non-parametric…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…
Another new family of continuous probability distribution is proposed by using Generalized Marshal-Olkin distribution as the base line distribution in the Kumaraswamy-G distribution. This family includes (Cordeiro and de Castro, 2011) and…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular…
A new family of Gaussian-type SIGMA basis sets, termed reduced SIGMA basis sets, is introduced and preliminarily tested. Sharing the same composition as Dunning basis sets, they enhance performance by reducing linear dependencies in large…
We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…