Related papers: Markov Properties of Discrete Determinantal Point …

Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection,…

While optimizing recommendation systems for user engagement is a well-established practice, effectively diversifying recommendations without negatively impacting core business metrics remains a significant industry challenge. In line with…

Cumulative prospect theory (CPT) is the first theory for decision-making under uncertainty that combines full theoretical soundness and empirically realistic features [P.P. Wakker - Prospect theory: For risk and ambiguity, Page 2]. While…

Planning under uncertainty is critical to robotics. The Partially Observable Markov Decision Process (POMDP) is a mathematical framework for such planning problems. It is powerful due to its careful quantification of the non-deterministic…

Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control…

We construct an abstract framework in which the dynamic programming principle (DPP) can be readily proven. It encompasses a broad range of common stochastic control problems in the weak formulation, and deals with problems in the…

This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics…

We consider risk-sensitive Markov decision processes (MDPs), where the MDP model is influenced by a parameter which takes values in a compact metric space. We identify sufficient conditions under which small perturbations in the model…

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…

We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling…

Piecewise-deterministic Markov processes (PDMPs) are often used to model abrupt changes in the global environment or capabilities of a controlled system. This is typically done by considering a set of "operating modes" (each with its own…

We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…

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,…

Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…

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…

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…

Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations…

We introduce Divnet, a flexible technique for learning networks with diverse neurons. Divnet models neuronal diversity by placing a Determinantal Point Process (DPP) over neurons in a given layer. It uses this DPP to select a subset of…