Related papers: Efficient simulation of the Ginibre point process
Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…
Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…
The interpretability of machine learning, particularly for deep neural networks, is crucial for decision making in real-world applications. One approach is replacing the un-interpretable machine learning model with a surrogate model, which…
Given a positive definite, bounded linear operator $A$ on the Hilbert space $\mathcal{H}_0:=l^2(E)$, we consider a reproducing kernel Hilbert space $\mathcal{H}_+$ with a reproducing kernel $A(x,y)$. Here $E$ is any countable set and…
The elliptic Ginibre ensemble of complex non-Hermitian random matrices allows to interpolate between the rotational invariant Ginibre ensemble and the Gaussian unitary ensemble of Hermitian random matrices. It corresponds to a…
Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space. However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and…
Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…
We present a list of algebraic, combinatorial, and analytic mechanisms that give rise to determinantal point processes.
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
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.…
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…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…
The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over…
Temporal point processes have been widely applied to model event sequence data generated by online users. In this paper, we consider the problem of how to design the optimal control policy for point processes, such that the stochastic…
We consider a dependent thinning of a regular point process with the aim of obtaining aggregation on the large scale and regularity on the small scale in the resulting target point process of retained points. Various parametric models for…
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…