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Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and…
We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that…
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…
Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
In this study, multivalued generalizations of certain classes of single-valued transformations defined on metric spaces are obtained. Building upon recently introduced concepts such as mappings contracting perimeters of triangles, new…
This paper was was first drafted in 2001 as a formalization of the system described in U.S. patent U.S. 7,392,174. It describes a system for implementing a parser based on a kind of cross-product over vectors of contextually similar words.…
We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…
In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured…
Generalized Word Length Pattern (GWLP) is an important and widely-used tool for comparing fractional factorial designs. We consider qualitative factors, and we code their levels using the roots of the unity. We write the GWLP of a fraction…
Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous…
We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are $n\in\mathbb{N}$ cars of lengths $\mathbf{y}=(y_1,y_2,\ldots,y_n)\in\mathbb{N}^n$ entering a one-way street…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
In 1989 Manin and Schechtman defined the discriminantal arrangement $\mathcal{B}(n, k,\mathcal{A})$ associated to a generic arrangement $\mathcal{A}$ of $n$ hyperplanes in a $k$-dimensional space. An equivalent notion was already introduced…
A rate-distortion-perception (RDP) tradeoff has recently been proposed by Blau and Michaeli and also Matsumoto. Focusing on the case of perfect realism, which coincides with the problem of distribution-preserving lossy compression studied…
A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
We introduce a new approach for smoothing and improving the quality of word embeddings. We consider a method of fusing word embeddings that were trained on the same corpus but with different initializations. We project all the models to a…
We present a machine-learning method for the nonparametric extraction of generalized parton distributions (GPDs) from Compton form factors (CFFs) constrained by experimental data. The method addresses the longstanding inverse problem posed…
In many physical, statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in…