Related papers: Determinantal probability measures
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For…
We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
Determinantal point processes (DPPs) are well known models for diverse subset selection problems, including recommendation tasks, document summarization and image search. In this paper, we discuss a greedy deterministic adaptation of k-DPP.…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
We study some random interlaced configurations considering the eigenvalues of the main minors of Hermitian random matrices of the classical complex Lie algebras. We claim that these random configurations are determinantal and give their…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
Semi-parametric regression models are used in several applications which require comprehensibility without sacrificing accuracy. Typical examples are spline interpolation in geophysics, or non-linear time series problems, where the system…
Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the…
We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We present the conditional determinantal point process (DPP) approach to obtain new (mostly Fredholm determinantal) expressions for various eigenvalue statistics in random matrix theory. It is well-known that many (especially $\beta=2$)…