Related papers: Estimate exponential memory decay in Hidden Markov…
We consider the problem of predicting the next observation given a sequence of past observations, and consider the extent to which accurate prediction requires complex algorithms that explicitly leverage long-range dependencies. Perhaps…
We show that maximum entropy (maxent) models can be modeled with certain kinds of HMMs, allowing us to construct maxent models with hidden variables, hidden state sequences, or other characteristics. The models can be trained using the…
Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging…
We develop a recursion for hidden Markov model of any order h, which allows us to obtain the posterior distribution of the latent state at every occasion, given the previous h states and the observed data. With respect to the well-known…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of…
Loss development modelling is the actuarial practice of predicting the total 'ultimate' losses incurred on a set of policies once all claims are reported and settled. This poses a challenging prediction task as losses frequently take years…
In the paper, the approximate sequence for entropy of some binary hidden Markov models has been found to have two bound sequences, the low bound sequence and the upper bound sequence. The error bias of the approximate sequence is bound by a…
Reinforcement learning algorithms typically rely on the assumption that the environment dynamics and value function can be expressed in terms of a Markovian state representation. However, when state information is only partially observable,…
Training large deep neural networks is resource intensive. This study investigates whether Lyapunov exponents can accelerate this process by aiding in the selection of hyperparameters. To study this I formulate an optimization problem using…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows…
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation…
Given noisy, partial observations of a time-homogeneous, finite-statespace Markov chain, conceptually simple, direct statistical inference is available, in theory, via its rate matrix, or infinitesimal generator, $\mathsf{Q}$, since $\exp…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
People are living longer than ever before, and with this arises new complications and challenges for humanity. Among the most pressing of these challenges is of understanding the role of aging in the development of dementia. This paper is…