Related papers: The conditional DPP approach to random matrix dist…
The purpose of this article is to develop a theory behind the occurrence of "path-integral" kernels in the study of extended determinantal point processes and non-intersecting line ensembles. Our first result shows how determinants…
Autonomous navigation in intelligent mobile systems represents a core research focus within artificial intelligence-driven robotics. Contemporary path planning approaches face constraints in dynamic environmental responsiveness and…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph $G=(V,E)$ and a positive semi-definite matrix $\mathbf{A}$ indexed by $E$, a spanning-tree DPP defines a distribution such that we draw…
Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a…
Discrete probabilistic programs (DPPs) provide a highly expressive formalism for compactly defining arbitrary finite probabilistic models. This expressivity comes at a price: DPP inference is PSPACE-hard. In this work, we show that DPP…
Large dimensional least-squares and regularised least-squares problems are expensive to solve. There exist many approximate techniques, some deterministic (like conjugate gradient), some stochastic (like stochastic gradient descent). Among…
We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product…
Learning rich skills under the option framework without supervision of external rewards is at the frontier of reinforcement learning research. Existing works mainly fall into two distinctive categories: variational option discovery that…
The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…
In this study, we propose a novel deep spatio-temporal point process model, Deep Kernel Mixture Point Processes (DKMPP), that incorporates multimodal covariate information. DKMPP is an enhanced version of Deep Mixture Point Processes…
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…
The fractional Poisson process (FPP) generalizes the standard Poisson process by replacing exponentially distributed return times with Mittag-Leffler distributed ones with an extra tail parameter, allowing for greater flexibility. The FPP…
Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated.…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
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…
Predicting when and where events will occur in cities, like taxi pick-ups, crimes, and vehicle collisions, is a challenging and important problem with many applications in fields such as urban planning, transportation optimization and…
We study the complexity of sampling from a distribution over all index subsets of the set $\{1,...,n\}$ with the probability of a subset $S$ proportional to the determinant of the submatrix $\mathbf{L}_S$ of some $n\times n$ p.s.d. matrix…