Related papers: Recovering the state sequence of hidden Markov mod…
This paper proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a…
A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward,…
This paper addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e. the observation model) is given explicitly or at least parametrically. We…
We discuss the notorious problem of order selection in hidden Markov models, i.e. of selecting an adequate number of states, highlighting typical pitfalls and practical challenges arising when analyzing real data. Extensive simulations are…
Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image…
Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states.We consider the problem of…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
Consider a stationary discrete random process with alphabet size d, which is assumed to be the output process of an unknown stationary Hidden Markov Model (HMM). Given the joint probabilities of finite length strings of the process, we are…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
In the phase retrieval problem one seeks to recover an unknown $n$ dimensional signal vector $\mathbf{x}$ from $m$ measurements of the form $y_i = |(\mathbf{A} \mathbf{x})_i|$, where $\mathbf{A}$ denotes the sensing matrix. Many algorithms…
Consider a sequence $P_n$ of positive recurrent transition matrices or kernels that approximate a limiting infinite state matrix or kernel $P_{\infty}$. Such approximations arise naturally when one truncates an infinite state Markov chain…
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…
We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
Mean-field variational inference is one of the most popular approaches to inference in discrete random fields. Standard mean-field optimization is based on coordinate descent and in many situations can be impractical. Thus, in practice,…
Inferring a state sequence from a sequence of measurements is a fundamental problem in bioinformatics and natural language processing. The Viterbi and the Beam Search (BS) algorithms are popular inference methods, but they have limitations…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
Nature, as far as we know, evolves continuously through space and time. Yet the ubiquitous hidden Markov model (HMM)--originally developed for discrete time and space analysis in natural language processing--remains a central tool in…