arXiv research

This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian non…

Study evaluates initialization strategies for infinite hidden Markov models.

Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In th…

Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.

Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the causality assumptions introduced by the choice of a specific tree visit direction. We w…

New method reduces forecasting error by up to 67% in various data types.

The Viterbi process can be extended indefinitely in a pairwise Markov model.

Since the early days of digital communication, Hidden Markov Models (HMMs) have now been routinely used in speech recognition, processing of natural languages, images, and in bioinformatics. An HMM $(X_i,Y_i)_{i\ge 1}$ assumes observations $X_1,X_2,...$ to be conditionally independent given an "explanotary" Markov proc…

Epsilon-machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense, as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization, though…

Expands Hidden Markov Model to include Markov chain observations.

We propose a restricted collapsed draw (RCD) sampler, a general Markov chain Monte Carlo sampler of simultaneous draws from a hierarchical Chinese restaurant process (HCRP) with restriction. Models that require simultaneous draws from a hierarchical Dirichlet process with restriction, such as infinite Hidden markov mod…

We describe a generalization of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) which is able to encode prior information that state transitions are more likely between "nearby" states. This is accomplished by defining a similarity function on the state space and scaling transition probabilities by pai…

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…

In this note we provide detailed derivations of two versions of small-variance asymptotics for hierarchical Dirichlet process (HDP) mixture models and the HDP hidden Markov model (HDP-HMM, a.k.a. the infinite HMM). We include derivations for the probabilities of certain CRP and CRF partitions, which are of more general…

Most existing approaches to clustering gene expression time course data treat the different time points as independent dimensions and are invariant to permutations, such as reversal, of the experimental time course. Approaches utilizing HMMs have been shown to be helpful in this regard, but are hampered by having to ch…

The paper estimates key metrics for linear models with Markov or hidden Markov sources.

Method infers causal structure from system behaviors using RKHS and kernel $ε$-machines.

Extends HMM to topological spaces for modeling complex data.

Hidden Markov Neural Networks balance adaptation and forgetting in time-series data.

The infinite Viterbi alignment is the limiting maximum a-posteriori estimate of the unobserved path in a hidden Markov model as the length of the time horizon grows. For models on state-space $\mathbb{R}^{d}$ satisfying a new ``decay-convexity'' condition, we develop an approach to existence of the infinite Viterbi ali…

This paper compares HMM and LSTM for time series forecasting.

Modified asymmetric hidden Markov models for time series with autoregressive components.

NoMoPy models noise as HMM/FHMM in Python.

Investor selects portfolios based on news attention in a hidden Markov model.

This work speeds up fHMM analysis by tensor algebra.

The paper introduces FMCI and hybrid decoding for hidden Markov models.

A new HMM model captures kernel dependencies using context-specific Bayesian networks.

Hierarchical hidden Markov models predict market trends in financial time series.

We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g. user behavior traces). We simplify the idea of capturing these patterns by hierarc…

New algorithm for collective Gaussian hidden Markov models inference.

The study uses Bayesian Hidden Markov Models to predict cryptocurrency returns.

We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone …

Detects anomalies in multiple processes using hidden Markov models.

New algorithm processes Riemannian data more efficiently.

The partially observable hidden Markov model is an extension of the hidden Markov Model in which the hidden state is conditioned on an independent Markov chain. This structure is motivated by the presence of discrete metadata, such as an event type, that may partially reveal the hidden state but itself emanates from a …

Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm for hidden Markov models, in a sequential data setting. Given a collapsed hidden Markov Model, we break its long M…

This research develops approximation theory for OOMs of infinite-dimensional processes.

Hybrid model improves traffic flow prediction accuracy.

Generalizes bits back coding for time-series models with latent Markov structures.

A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims.

This paper introduces a novel model-based clustering approach for clustering time series which present changes in regime. It consists of a mixture of polynomial regressions governed by hidden Markov chains. The underlying hidden process for each cluster activates successively several polynomial regimes during time. The…

As one of Bayesian analysis tools, Hidden Markov Model (HMM) has been used to in extensive applications. Most HMMs are solved by Baum-Welch algorithm (BWHMM) to predict the model parameters, which is difficult to find global optimal solutions. This paper proposes an optimized Hidden Markov Model with Particle Swarm Opt…

A new model separates persistence and transition priors in HDP-HMM.

The paper uses HMM and LSTM for stock market trend analysis.

Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.

Continuous Hidden Markov Models for Equity Returns

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing th…

New method infers hidden states in continuous-time phenomena better than traditional models.