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Star sampling (SS) is a random sampling procedure on a graph wherein each sample consists of a randomly selected vertex (the star center) and its (one-hop) neighbors (the star points). We consider the use of SS to find any member of a…
Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps…
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…
Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…
We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $\lambda \in [0,1] $, interpolating between the completely asymmetric processes [1] (for $\lambda =1$) and the n=1…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
In this work, we present a novel inner product design for stochastic computing. Stochastic computing is an emerging computing technique, that encodes a number in the probability of observing a one in a random bit stream. This leads to…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
We study a class of dynamically constructed point processes in which at every step a new point (particle) is added to the current configuration with a distribution depending on the local structure around a uniformly chosen particle. This…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
In most practical adaptive signal processing systems, e.g., active noise control, active vibration control, and acoustic echo cancellation, substantial nonlinearities that cannot be neglected exist. In this paper, we analyze the behaviors…
A Gaussian process has been one of the important approaches for emulating computer simulations. However, the stationarity assumption for a Gaussian process and the intractability for large-scale dataset limit its availability in practice.…
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…
In this chapter we review some examples, methods, and recent results involving comparison of clustering properties of point processes. Our approach is founded on some basic observations allowing us to consider void probabilities and moment…
This study investigates a multiplicative integer system using a method that was developed for studying pattern generation problems. The entropy and the Minkowski dimensions of general multiplicative systems can thus be computed. A…
An encoder observes a point pattern---a finite number of points in the interval $[0,T]$---which is to be described to a reconstructor using bits. Based on these bits, the reconstructor wishes to select a subset of $[0,T]$ that contains all…
In comparison to numerous enhanced sampling methods for equilbrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here we derive a time-reversal path sampling…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…