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The detection of change-points in heterogeneous sequences is a statistical challenge with many applications in fields such as finance, signal analysis and biology. A wide variety of literature exists for finding an ideal set of…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw…
We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support…
An algorithm used to extract HMM parameters is revisited. Most parts of the extraction process are taken from implemented Hidden Markov Toolkit (HTK) program under name HInit. The algorithm itself shows a few variations compared to another…
In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time…
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
A generic method for inferring a dynamical hidden Markov model from a time series is proposed. Under reasonable hypothesis, the model is updated in constant time whenever a new measurement arrives.
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes. The algorithms can also be used as a suboptimal method for partially observed Markov…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…
The paper studies optimal coding of hidden Markov sources (HMS), which represent a broad class of practical sources obtained through noisy acquisition processes, beside their explicit modeling use in speech processing and recognition, image…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
In this paper, we introduce the notion of Bi-entangled hidden Markov processes. These are hidden quantum processes where the hidden processes themselves exhibit entangled Markov process, and the observable processes also exhibit…
A learning algorithm for multilayer perceptrons is presented which is based on finding the principal components of a correlation matrix computed from the example inputs and their target outputs. For large networks our procedure needs far…