Related papers: Reduction of Maximum Entropy Models to Hidden Mark…
In pursuit of explainability, we develop generative models for sequential data. The proposed models provide state-of-the-art classification results and robust performance for speech phone classification. We combine modern neural networks…
Since the early days of digital communication, hidden Markov models (HMMs) have now been also routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. In an HMM $(X_i,Y_i)_{i\ge 1}$, observations…
We show that the mutual information between the representation of a learning machine and the hidden features that it extracts from data is bounded from below by the relevance, which is the entropy of the model's energy distribution. Models…
We formulate the entropy of a quantized artificial neural network as a differentiable function that can be plugged as a regularization term into the cost function minimized by gradient descent. Our formulation scales efficiently beyond the…
We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…
The hidden Markov model (HMM) is a classic modeling tool with a wide swath of applications. Its inception considered observations restricted to a finite alphabet, but it was quickly extended to multivariate continuous distributions. In this…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
Motivated by the analysis of accelerometer data, we introduce a specific finite mixture of hidden Markov models with particular characteristics that adapt well to the specific nature of this type of data. Our model allows for the…
In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…
Labeling of sequential data is a prevalent meta-problem for a wide range of real world applications. While the first-order Hidden Markov Models (HMM) provides a fundamental approach for unsupervised sequential labeling, the basic model does…
Many applications require that we learn the parameters of a model from data. EM is a method used to learn the parameters of probabilistic models for which the data for some of the variables in the models is either missing or hidden. There…
We propose masked particle modeling (MPM) as a self-supervised method for learning generic, transferable, and reusable representations on unordered sets of inputs for use in high energy physics (HEP) scientific data. This work provides a…
A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…
Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this paper, we consider a Hidden Markov Model involving several correlated hidden processes at the same time.…
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…
Stock market forecasting is a classic problem that has been thoroughly investigated using machine learning and artificial neural network based tools and techniques. Interesting aspects of this problem include its time reliance as well as…
Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…
The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a…
We investigate whether the hidden states of large language models (LLMs) can be used to estimate and impute economic and financial statistics. Focusing on county-level (e.g. unemployment) and firm-level (e.g. total assets) variables, we…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…