Related papers: Incremental inference of collective graphical mode…
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
When a statistical model $\{P_{\theta} : \theta \in \Theta\}$ lacks analytically tractable likelihoods, parametric statistical inference based on data generated from an unknown underlying distribution $P$ can still be performed as long as…
The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
A major benefit of graphical models is that most knowledge is captured in the model structure. Many models, however, produce inference problems with a lot of symmetries not reflected in the graphical structure and hence not exploitable by…
The belief propagation (BP) algorithm is an efficient way to solve "inference" problems in graphical models, such as Bayesian networks and Markov random fields. The system-state probability distribution of CSMA wireless networks is a Markov…
The Iterative Markovian Fitting (IMF) procedure, which iteratively projects onto the space of Markov processes and the reciprocal class, successfully solves the Schr\"odinger Bridge (SB) problem. However, an efficient practical…
We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the…
Many kinds of data can be represented as a network or graph. It is crucial to infer the latent structure underlying such a network and to predict unobserved links in the network. Mixed Membership Stochastic Blockmodel (MMSB) is a promising…
Community detection, which aims to cluster $N$ nodes in a given graph into $r$ distinct groups based on the observed undirected edges, is an important problem in network data analysis. In this paper, the popular stochastic block model (SBM)…
We apply belief propagation (BP) to multi--user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to estimate the correct conditional expectation of the input…
Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
We show how to utilize machine learning approaches to improve sliding window algorithms for approximate frequency estimation problems, under the ``algorithms with predictions'' framework. In this dynamic environment, previous…
Crowdsourcing systems enable us to collect large-scale dataset, but inherently suffer from noisy labels of low-paid workers. We address the inference and learning problems using such a crowdsourced dataset with noise. Due to the nature of…
The generalized belief propagation (GBP), introduced by Yedidia et al., is an extension of the belief propagation (BP) algorithm, which is widely used in different problems involved in calculating exact or approximate marginals of…
In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and…
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical…
We aim to incorporate variable selection routines into variable-by-variable (or sequential) imputation in clustered data to achieve computational improvement in applications with large-scale health data. Specifically, we utilize variable…