Related papers: Hyperdeterminantal point processes
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
The maximum composite likelihood estimator for parametric models of determinantal point processes (DPPs) is discussed. Since the joint intensities of these point processes are given by determinant of positive definite kernels, we have the…
For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion…
Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…
Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…
Heralded by the initial success in speech recognition and image classification, learning-based approaches with neural networks, commonly referred to as deep learning, have spread across various fields. A primitive form of a neural network…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of…
A system of non-intersecting squared Bessel processes is considered which all start from one point and they all return to another point. Under the scaling of the starting and ending points when the macroscopic boundary of the paths touches…
In this paper we describe a general method to derive formulas relating the gap probability of some classical determinantal random point process (Airy, Pearcey and Hermite) with the gap probability of the processes related to the same…
We adopt an operatorial method based on the so-called creation, annihilation and number operators in the description of different systems in which two populations interact and move in a two-dimensional region. In particular, we discuss…
Consider a symmetrical conflict relationship between the points of a point process. The Mat\'ern type constructions provide a generic way of selecting a subset of this point process which is conflict-free. The simplest one consists in…
The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a…
A new matrix operation based on inserting columns and rows, similarly to the mediant operation between fractions, gives rise to the Farey determinants matrix or, equivalently, the matrix of the numerators of the differences of Farey…
The joint moments of the derivatives of the characteristic polynomial of a random unitary matrix, and also a variant of the characteristic polynomial that is real on the unit circle, in the large matrix size limit, have been studied…
The production mechanism of highly excited nuclei in the Fermi energy domain is investigated. A phenomenological approach, based on the exciton model, is used for the description of pre-equilibrium emission. A model of deep inelastic…
When the number of particles is finite, the noncolliding Brownian motion (the Dyson model) and the noncolliding squared Bessel process are determinantal diffusion processes for any deterministic initial configuration $\xi=\sum_{j \in…
For a determinantal point process $X$ with a kernel $K$ whose spectrum is strictly less than one, Andr{\'e} Goldman has established a coupling to its reduced Palm process $X^u$ at a point $u$ with $K(u,u)>0$ so that almost surely $X^u$ is…