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…
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48 results for “Hidden Quantum Markov Models”
We extend quantum probabilistic models and develop a learning algorithm.
problem Characterize expressiveness and learn hidden quantum Markov models.
method Show HQMMs are a subclass of OOMs without negative probabilities. Develop a feasible gradient descent algorithm on the Stiefel manifold.
result Our learning algorithm is faster and scales better than previous methods.
RILA learns HQMMs robustly against adversarial corruption.
problem Robustness of HQMM learning algorithms under adversarial perturbations.
method Adversarially Corrupted HQMM (AC-HQMM) and Robust Iterative Learning Algorithm (RILA).
result RILA outperforms existing algorithms in convergence stability, corruption resilience, and physical validity.
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspond…
Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be formulated using quantum analogues of the sum rule and Bayes rule used in class…
New MBL hidden Born machine learns various tasks.
problem Learning from quantum many-body systems.
method MBL dynamics and hidden units for training.
result Enhanced trainability and stability in learning.
Markov Observation Modelsstat.ML
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
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…
Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian …
It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations and other kinds of correlations on any directed acyclic graph,…
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
Hidden Markov Neural Networks balance adaptation and forgetting in time-series data.
problem Balancing adaptation to new data and forgetting outdated information in time-series forecasting.
method Modeling weights as hidden states of a Hidden Markov model, using a filtering algorithm for learning a variational approximation of the posterior distribution over weights, and employing sequential Bayes by Backprop with variational DropConnect for regularization.
result Achieves strong predictive performance and effective uncertainty quantification on various tasks.
This paper compares HMM and LSTM for time series forecasting.
problem Comparing HMM and LSTM for time series forecasting.
method Discretization techniques and various training methods.
result HMM can outperform LSTM with limited labeled data.
Modified asymmetric hidden Markov models for time series with autoregressive components.
problem Dynamic relationships between variables in time series data.
method Introducing an asymmetric autoregressive component to recent asymmetric hidden Markov models.
result The model can choose the optimal autoregressive order for better likelihood.
NoMoPy models noise as HMM/FHMM in Python.
problem Modeling noise in data.
method Approximate and exact EM algorithms, cross-validation, confidence region estimation.
result Validated on example problems.
Investor selects portfolios based on news attention in a hidden Markov model.
problem Mean-variance portfolio selection in a dynamic attention context.
method Closed-loop equilibrium strategies via extended HJB equation and Markov chain approximation.
result Equilibrium strategies found through iterative algorithm and numerical examples.
This work speeds up fHMM analysis by tensor algebra.
problem Scalability issues in analyzing factorial hidden Markov models.
method Tensorized algorithms and scalable filtering methods.
result Significant improvement in computational performance.
The paper introduces FMCI and hybrid decoding for hidden Markov models.
problem Computing distributions and decoding hidden state sequences in HMMs.
method Finite Markov chain imbedding (FMCI) and hybrid decoding.
result Hybrid decoding improves performance over traditional methods.
A new HMM model captures kernel dependencies using context-specific Bayesian networks.
problem Traditional HMMs struggle with non-Gaussian data and independence assumptions.
method Kernel density estimation with context-specific Bayesian networks.
result The proposed model outperforms related HMMs in likelihood and classification accuracy.
A novel quantum model improves RBM performance and is efficiently trainable.
problem Improving the performance of RBM models.
method Quantum model with parametrically coupled fermions to classical signals.
result The model outperforms classical RBM with the same number of hidden units.
Hierarchical hidden Markov models predict market trends in financial time series.
problem Misinterpretation of short-term price fluctuations as long-term trend changes.
method Hierarchical hidden Markov models to capture both short- and long-term trends.
result Hierarchical models provide a comprehensive picture of financial markets.
New algorithm for collective Gaussian hidden Markov models inference.
problem Inference of collective Gaussian hidden Markov models from aggregate data.
method Collective Gaussian forward-backward algorithm, extending Sinkhorn belief propagation.
result Convergence guarantee and applicability to single individual Kalman filter.
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
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…
The study uses Bayesian Hidden Markov Models to predict cryptocurrency returns.
problem Predicting the volatility and trends of cryptocurrencies.
method Bayesian Hidden Markov Models with four states to capture different return characteristics.
result The NHHM model with four states outperforms other models in predicting cryptocurrency returns.
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent 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.
problem Detecting an anomalous process among many with hidden states.
method Sequential search strategy using ADHM algorithm.
result ADHM algorithm effectively leverages temporal correlations.
New algorithm processes Riemannian data more efficiently.
problem High memory usage and slow speed in previous Riemannian HMMs.
method Online algorithm based on Baum-Welch adapted for Riemannian manifolds.
result Significant improvements in speed and efficiency.
The Viterbi process can be extended indefinitely in a pairwise Markov model.
problem Estimating hidden chains in pairwise Markov models.
method Construction of barriers to ensure Viterbi path goes through states.
result The Viterbi process is regenerative in the PMM.
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…
Hybrid model improves traffic flow prediction accuracy.
problem Predicting traffic flow with high accuracy in short-term future.
method A hybrid model combining hidden Markov model and LSTM.
result Significant performance gains over conventional methods.
An adaptive simulated annealing EM algorithm for inference on non-homogeneous hidden Markov modelsstat.ML
New algorithm optimizes complex model selection for non-homogeneous hidden Markov models.
problem Complex combinatorial optimization problem for model selection in NHHMMs.
method Adaptive simulated annealing EM algorithm (ASA-EM).
result Joint optimization of models and parameters for a criterion of interest.
Generalizes bits back coding for time-series models with latent Markov structures.
problem Efficiently compressing time-series data with latent Markov structures.
method Extends bits back coding to time-series models with latent Markov structures, including HMMs and LGSSMs.
result Effective for small scale models, promising for larger scale settings like video compression.
Quantum algorithms for financial derivatives and credit risk.
problem Estimating credit risk and option pricing in realistic financial models.
method Developed a regime switching volatility model for financial markets, using a Markov chain to determine volatility parameters.
result Quantum algorithms can be applied to realistic financial models, bringing quantum computing closer to practical applications.
Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.
problem No finite expression exists for Shannon entropy rates of hidden Markov processes.
method Developed an efficient method to calculate entropy rates and identify minimal predictive features.
result Entropy rates can be accurately calculated for hidden Markov processes.
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.
Model-based clustering with Hidden Markov Model regression for time series with regime changesstat.ML
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.
problem Limitation of sticky HDP-HMM in expressing different persistence strengths.
method Developed a disentangled sticky HDP-HMM (DS-HDP-HMM) with novel Gibbs sampling algorithms.
result DS-HDP-HMM outperforms sticky HDP-HMM and HDP-HMM on synthetic and real data.
The paper uses HMM and LSTM for stock market trend analysis.
problem Predicting stock market trends using machine learning.
method Apply Hidden Markov Model and Long Short Term Memory to stock market data.
result The combination of GMM-HMM+LSTM and XGB-HMM+LSTM outperformed other models.
Continuous Hidden Markov Models for Equity Returns
problem Generating synthetic equity returns that match real return characteristics
method Continuous Hidden Markov Models
result Recovered volatility clustering and narrowed kurtosis gap
New method infers hidden states in continuous-time phenomena better than traditional models.
problem Traditional HSMM's are limited to discrete time grids and cannot handle irregularly spaced data.
method Formulated integro-differential forward and backward equations for CTSMC's, introduced scalable Viterbi-type algorithm.
result Efficiently solved equations for posterior marginals and path estimates.
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particul…
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…
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to perform inference in HSMMs. Unlike expectation maximization (EM), our approach cor…
This work restricts hidden cardinality in causal models to infer causal relations.
problem Causal relations between variables with a common unobserved cause cannot be directly inferred.
method Derive inequality constraints from d-separation in causal models with known cardinalities of unobserved variables.
result Inference of causal relations is possible with additional assumptions about cardinalities.
This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on Metropolis-Hastings algorithm. Next, by using MH algorithm, we simulate the data from Ising model…