Related papers: Determinantal point processes for machine learning
We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified…
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 $\beta=2$)…
In many scientific domains, clustering aims to reveal interpretable latent structure that reflects relevant subpopulations or processes. Widely used Bayesian mixture models for model-based clustering often produce overlapping or redundant…
We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational)…
We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees).…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
Markov decision processes (MDPs) are a standard model for sequential decision-making problems and are widely used across many scientific areas, including formal methods and artificial intelligence (AI). MDPs do, however, come with the…
Temporal point processes (TPP) are probabilistic generative models for continuous-time event sequences. Neural TPPs combine the fundamental ideas from point process literature with deep learning approaches, thus enabling construction of…
Discrete Determinantal Point Processes (DPPs) have a wide array of potential applications for subsampling datasets. They are however held back in some cases by the high cost of sampling. In the worst-case scenario, the sampling cost scales…
Negative dependence is becoming a key driver in advancing learning capabilities beyond the limits of traditional independence. Recent developments have evidenced support towards negatively dependent systems as a learning paradigm in a broad…
We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small models, thereby disproving a conjecture of Brunel, Moitra,…
Herein, we address the expectations of frame potentials of three types of determinantal point processes(DPPs) on the d-dimensional unit sphere: (i) spherical ensembles on the 2-dimensional unit sphere; (ii) harmonic ensembles on the…
Stochastic gradient descent (SGD) is a cornerstone of machine learning. When the number N of data items is large, SGD relies on constructing an unbiased estimator of the gradient of the empirical risk using a small subset of the original…
The most important obstacles facing multi-document summarization include excessive redundancy in source descriptions and the looming shortage of training data. These obstacles prevent encoder-decoder models from being used directly, but…
Probabilistic programming (PP) is a programming paradigm that allows for writing statistical models like ordinary programs, performing simulations by running those programs, and analyzing and refining their statistical behavior using…
We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…
Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In…
A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures $\Xi$ on a space $S$ with measure $\lambda$, whose correlation functions are all given by determinants specified by an integral kernel…
We introduce new families of determinantal point processes (DPPs) on a complex plane ${\mathbb{C}}$, which are classified into seven types following the irreducible reduced affine root systems, $R_N=A_{N-1}$, $B_N$, $B^{\vee}_N$, $C_N$,…