Related papers: LISA: Locally Interacting Sequential Adsorbtion
We consider $d$-dimensional linear stochastic approximation algorithms (LSAs) with a constant step-size and the so called Polyak-Ruppert (PR) averaging of iterates. LSAs are widely applied in machine learning and reinforcement learning…
This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of…
Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…
We study internal diffusion-limited aggregation with random starting points on Z^d. In this model, each new particle starts from a vertex chosen uniformly at random on the existing aggregate. We prove that the limiting shape of the…
We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching…
In the Diffusion Limited Aggregation (DLA) process on on $\mathbb{Z}^2$, or more generally $\mathbb{Z}^d$, particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a…
We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely…
A point process on a space is a random bag of elements of that space. In this paper we explore programming with point processes in a monadic style. To this end we identify point processes on a space X with probability measures of bags of…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use…
We study complex systems arising, in particular, in population dynamics, developmental biology, and bacterial metabolic processes, in which each individual element obeys a relatively simple hysteresis law (a non-ideal relay). Assuming that…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to…
In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the…