相关论文: Relative Jump Distance: a diagnostic for Nested Sa…

Piecewise-deterministic Markov processes (PDMPs) offer a powerful stochastic modeling framework that combines deterministic trajectories with random perturbations at random times. Estimating their local characteristics (particularly the…

The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…

We consider estimation of a step function $f$ from noisy observations of a deconvolution $\phi*f$, where $\phi$ is some bounded $L_1$-function. We use a penalized least squares estimator to reconstruct the signal $f$ from the observations,…

When we want to simulate the realization of a symmetric simple random walk on $\mathbb Z^d$, we use $(2d)$-side fair dice to decide to which neighbor it jumps at each step if $d\geq 2$ or we simply use a fair coin when $d=1$. Assume that…

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…

We study the relaxation time in the random walk with jumps. The random walk with jumps combines random walk based sampling with uniform node sampling and improves the performance of network analysis and learning tasks. We derive various…

In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is…

We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This distance, inspired by optimal transport, facilitates stability results; one can quantify how seriously issues like sampling bias,…

We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any…

Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable…

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…

Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…

Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…

The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…

In this article, we first give a comprehensive description of random walk (RW) problem focusing on self-similarity, dynamic scaling and its connection to diffusion phenomena. One of the main goals of our work is to check how robust the RW…

In this paper, we study the fundamental problem of random walk for network embedding. We propose to use non-Markovian random walk, variants of vertex-reinforced random walk (VRRW), to fully use the history of a random walk path. To solve…