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Inferring time-varying networks is important to understand the development and evolution of interactions over time. However, the vast majority of currently used models assume direct measurements of node states, which are often difficult to…

Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a…

A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…

While different neural models often exhibit latent spaces that are alike when exposed to semantically related data, this intrinsic similarity is not always immediately discernible. Towards a better understanding of this phenomenon, our work…

Continuous-time multistate models are widely used for analyzing interval-censored data on disease progression over time. Sometimes, diseases manifest differently and what appears to be a coherent collection of symptoms is the expression of…

This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…

Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation…

This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…

We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM)…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed,…

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…

Four-dimensional weak-constraint variational data assimilation estimates a state given partial noisy observations and dynamical model by minimizing a cost function that takes into account both discrepancy between the state and observations…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Interval-censored multi state data is collected when the state of a subject is observed periodically. The analysis of such data using non-parametric multi-state models was not possible until recently, but is very desirable as it allows for…

We propose a simple tractable pair hidden Markov model for pairwise sequence alignment that accounts for the presence of short tandem repeats. Using the framework of gain functions, we design several optimization criteria for decoding this…

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…