Related papers: Determinantal Point Processes in the Flat Limit
The bulk scaling limit of eigenvalue distribution on the complex plane ${\mathbb{C}}$ of the complex Ginibre random matrices provides a determinantal point process (DPP). This point process is a typical example of disordered hyperuniform…
We define a determinantal point process on the complex projective space that reduces to the so-called spherical ensemble for complex dimension 1 under identification of the 2-sphere with the Riemann sphere. Through this determinantal point…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
The Nystr\"om method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystr\"om using…
Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples…
Markov Decision Processes (MDPs) are stochastic optimization problems that model situations where a decision maker controls a system based on its state. Partially observed Markov decision processes (POMDPs) are generalizations of MDPs where…
We study the multiplicative statistics associated to the limiting determinantal point process describing unitary random matrices with a critical edge point, where limiting density vanishes like a power 5/2. We prove that these statistics…
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…
Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may…
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…
We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…
This paper investigates the performance limits of differential power processing (DPP) and presents quantitative and systematic design guidelines for the selection and comparison of DPP topologies. A stochastic model is developed to evaluate…
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we…
DPPs were introduced by Macchi as a model in quantum optics the 1970s. Since then, they have been widely used as models and subsampling tools in statistics and computer science. Most applications require sampling from a DPP, and given their…
We consider a family of determinantal random point processes on the two-dimensional lattice and prove that members of our family can be interpreted as a kind of Gibbs ensembles of nonintersecting paths. Examples include probability measures…
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
Markov Decision Processes (Mdps) form a versatile framework used to model a wide range of optimization problems. The Mdp model consists of sets of states, actions, time steps, rewards, and probability transitions. When in a given state and…
Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard decoding methods for autoregressive models, such as beam search, do not…
One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…
Product matrix processes are multi-level point processes formed by the singular values of random matrix products. In this paper we study such processes where the products of up to $m$ complex random matrices are no longer independent, by…