Statistical Inference for Probabilistic Functions of Finite State Markov Chains
1966/12/01 by Leonard E. Baum, Ted Petrie · 2,805 citations
Computer Science · Decision Sciences · Mathematics · #Applied mathematics #Artificial intelligence #Bayesian Modeling and Causal Inference #Computer science #Econometrics #Examples of Markov chains #Finite state #Inference #Markov chain #Markov model #Markov property #Mathematics #Probabilistic logic #Simulation Techniques and Applications #Statistical inference #Statistics
paper · pdf · doi:10.1214/aoms/1177699147
published in The Annals of Mathematical Statistics 37(6), 1554-1563 (Institute of Mathematical Statistics)
openalex publication_date 1966/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Cited by
- A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains
- Hidden semi-Markov models
- A tutorial on hidden Markov models and selected applications in speech recognition
- Interpretable EEG biomarkers with bag-of-waves: Spatial and temporal waveform dictionaries for low-data regimes
- Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach
- Infinite Factorial Finite State Machine for Blind Multiuser Channel Estimation
- Multiple Testing in Nonparametric Hidden Markov Models: An Empirical Bayes Approach
- Hidden Markov Model Identifiability via Tensors
- Infinite Mixture Models for Improved Modeling of Across-Site Evolutionary Variation
- Toward Universal Testing of Dynamic Network Models
- Statistical and Computational Guarantees for the Baum-Welch Algorithm
- Divide-and-Conquer Learning by Anchoring a Conical Hull
- Exact inference via quasi-conjugacy in two-parameter Poisson-Dirichlet hidden Markov models
- How Many Experts Are Enough? Towards Optimal Semantic Specialization for Mixture-of-Experts
- Rational Recurrences
- Conformal bandits: bringing statistical validity and reward efficiency under weak arm separability
- Balanced state of networks of winner-take-all units
- Deep Learning in Neural Networks: An Overview
- Inference of Markovian Properties of Molecular Sequences from NGS Data and Applications to Comparative Genomics
- Differentiable Dynamic Programming for Structured Prediction and Attention
- Tractable Probabilistic Models for Investment Planning
- The Cognitive Science of Extremist Ideologies Online
- Optimal control of the future via prospective learning with control
- Learning Hidden Markov Models for Linear Gaussian Systems with Applications to Event-based State Estimation
- Factorized Multimodal Transformer for Multimodal Sequential Learning
- Felzenszwalb-Baum-Welch: Event Detection by Changing Appearance
- Discrete Graph Structure Learning for Forecasting Multiple Time Series
- Signal automata and hidden Markov models
- Mining Personalized Climate Preferences for Assistant Driving
- Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows
- Temporal Registration in Application to In-utero MRI Time Series
- Analyticity, Convergence and Convergence Rate of Recursive Maximum Likelihood Estimation in Hidden Markov Models
- The Influence of Context on Dialogue Act Recognition
- FLASH Viterbi: Fast and Adaptive Viterbi Decoding for Modern Data Systems
- Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space
- Extending finite mixture models with skew-normal distributions and hidden Markov models for time series
- Online EM Algorithm for Hidden Markov Models
- Parameter Estimation of Hidden Diffusion Processes: Particle Filter vs. Modified Baum-Welch Algorithm
- An Explanation of In-context Learning as Implicit Bayesian Inference
- State Space Models over Directed Graphs
- A Statistical Test for Comparing the Linkage and Admixture Model Based on Central Limit Theorems
- Hidden Markov model segmentation of hydrological and enviromental time series
- Non singularity of the asymptotic Fisher information matrix in hidden Markov models
- On regularity of functions of Markov chains
- Listen, Attend and Spell
- A Bi-directional Transformer for Musical Chord Recognition
- Estimating causal effects from panel data with dynamic multivariate panel models
- Hidden Markov Models with Multiple Observation Processes
- Modelling Stochastic Inflow Patterns to a Reservoir with a Hidden Phase-Type Markov Model
- Density Operator Expectation Maximization
- Gaussian Process Volatility Model
- Posterior-based proposals for speeding up Markov chain Monte Carlo
- jahmm: A tool for discretizing multiple ChIP seq profiles
- Adaptive Online Estimation of Piecewise Polynomial Trends
- Combined parameter and state inference with automatically calibrated ABC
- Particle Filter on Episode
- Inference for Stochastically Contaminated Variable Length Markov Chains
- RNN Architecture Learning with Sparse Regularization
- A brief history of AI: how to prevent another winter (a critical review)
- Universal Minimax Discrete Denoising under Channel Uncertainty
- Modelling the Memory of Turbulence-Induced Beam Wander
- Analyticity of Entropy Rates of Continuous-State Hidden Markov Models
- Analyzing cross-talk between superimposed signals: Vector norm dependent hidden Markov models and applications to ion channels
- k-Contextuality as a Heuristic for Memory Separations in Learning
- A Faster Method for Tracking and Scoring Videos Corresponding to Sentences
- qDKT: Question-centric Deep Knowledge Tracing
- Critique of World Model
- The emergence of the two cell fates and their associated switching for a negative auto-regulating gene
- Dealing with separation problem in hidden Markov models with covariates based on a penalized maximum likelihood approach
- A New Perspective On AI Safety Through Control Theory Methodologies
- GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning
- Denoising the Future: Top-p Distributions for Moving Through Time
- A cautious user's guide in applying HMMs to physical systems
- Latent Variable Modelling by Supervised Diffusion
- Hidden Markov Chains, Entropic Forward-Backward, and Part-Of-Speech Tagging
- Comparative Analysis of Viterbi Training and Maximum Likelihood Estimation for HMMs
- Genomics of Parallel Ecological Speciation in Lake Victoria Cichlids
- Creativity: Generating Diverse Questions using Variational Autoencoders
- Heron Inference for Bayesian Graphical Models
- Convergence Rates of Variational Inference in Sparse Deep Learning
- Maximum Likelihood Learning of Latent Dynamics Without Reconstruction
- Interdependent Gibbs Samplers
- An overview of latent Markov models for longitudinal categorical data
- Blurred stochastic chains
- Predictive State Recurrent Neural Networks
- Probability Bracket Notation: Markov Sequence Projector of Visible and Hidden Markov Models in Dynamic Bayesian Networks
- Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
- Bioinformatics and Medicine in the Era of Deep Learning
- Change Point Detection by Cross-Entropy Maximization
- An Expectation-Maximization Algorithm for Continuous-time Hidden Markov Models
- Modeling and Forecasting the Evolution of Preferences over Time: A Hidden Markov Model of Travel Behavior
- A Survey on Recent Advances in Sequence Labeling from Deep Learning Models
- Clustering Time Series and the Surprising Robustness of HMMs
- A subcortical switchboard for exploratory, exploitatory, and disengaged states
- Time Adaptive Gaussian Model
- Gradient Computation In Linear-Chain Conditional Random Fields Using The\n Entropy Message Passing Algorithm
- Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)
- Continuous speech recognition by statistical methods
- Universal Filtering via Hidden Markov Modeling
- Maximum likelihood estimator for hidden Markov models in continuous time
- The Hierarchical Hidden Markov Model: Analysis and Applications
- A Functional Taxonomy of Music Generation Systems
- Ontology-Based Prediction and Prioritization of Gene Functional Annotations
- Subspace estimation and prediction methods for hidden Markov models
- Testing the Markov condition in ion channel recordings
- Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
- Fitting hidden semi-Markov models to breakpoint rainfall data
- Community detection and tracking on networks from a data fusion perspective
- SoPa: Bridging CNNs, RNNs, and Weighted Finite-State Machines
- Masked Conditional Random Fields for Sequence Labeling
- Stochastic Collapsed Variational Inference for Sequential Data
- Observed Fisher Information in hidden Markov models - Application to a noisy Gaussian random walk
- A Survey of Applications and Human Motion Recognition with Microsoft Kinect
- Machine Learning Paradigms for Speech Recognition: An Overview
- Optimisation of phonetic aware speech recognition through multi-objective evolutionary algorithms
- Efficient likelihood estimation in state space models
- A Road Map to Strong Intelligence
- Earthquake Forecasting Using Hidden Markov Models
- Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model
- Probabilistic Warnings in National Security Crises: Pearl Harbor Revisited
- Controlled Territory and Conflict Tracking (CONTACT): (Geo-)Mapping Occupied Territory from Open Source Intelligence
- State duration and interval modeling in hidden semi-Markov model for sequential data analysis
- Infinite Factorial Finite State Machine for Blind Multiuser Channel Estimation
- Machine learning for integrating data in biology and medicine: Principles, practice, and opportunities
- Adaptive estimation of the transition density of a particular hidden Markov chain
- Robot Language Learning, Generation, and Comprehension
- Transformation of industrial robotics with natural language models: Recent progress and future prospects
- Hidden semi-Markov model [wikipedia]
- Modelling malaria incidence with environmental dependency in a locality of Sudanese savannah area, Mali. [europepmc]
- Unsupervised genome-wide recognition of local relationship patterns. [europepmc]
- Copy number variation detection using next generation sequencing read counts. [europepmc]
- Automated systems for the de-identification of longitudinal clinical narratives: Overview of 2014 i2b2/UTHealth shared task Track 1. [europepmc]
- How to resolve microsecond current fluctuations in single ion channels: the power of beta distributions. [europepmc]
- Major depressive disorder as a nonlinear dynamic system: bimodality in the frequency distribution of depressive symptoms over time. [europepmc]
- A hidden Markov model for reconstructing animal paths from solar geolocation loggers using templates for light intensity. [europepmc]
- Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model. [europepmc]
- PhosphoPredict: A bioinformatics tool for prediction of human kinase-specific phosphorylation substrates and sites by integrating heterogeneous feature selection. [europepmc]
- Eyetracking Metrics in Young Onset Alzheimer's Disease: A Window into Cognitive Visual Functions. [europepmc]
- DRREP: deep ridge regressed epitope predictor. [europepmc]
- Hidden Markov models for monitoring circadian rhythmicity in telemetric activity data. [europepmc]
- Transcriptome and Comparative Genomics Analyses Reveal New Functional Insights on Key Determinants of Pathogenesis and Interbacterial Competition in Pectobacterium and Dickeya spp. [europepmc]
- Predicting Patient-ventilator Asynchronies with Hidden Markov Models. [europepmc]
- Statistical structure of locomotion and its modulation by odors. [europepmc]
- Conformational and dynamic plasticity in substrate-binding proteins underlies selective transport in ABC importers. [europepmc]
- Prognostic Modeling and Prevention of Diabetes Using Machine Learning Technique. [europepmc]
- Improving Imputation Quality in BEAGLE for Crop and Livestock Data. [europepmc]
- Emotion Recognition Using Eye-Tracking: Taxonomy, Review and Current Challenges. [europepmc]
- Quantifying information accumulation encoded in the dynamics of biochemical signaling. [europepmc]
- TAPAS: An Open-Source Software Package for Translational Neuromodeling and Computational Psychiatry. [europepmc]
- Principles and Practice of Explainable Machine Learning. [europepmc]
- Robust and accurate estimation of paralog-specific copy number for duplicated genes using whole-genome sequencing. [europepmc]
- Artificial intelligence and machine learning in precision and genomic medicine. [europepmc]
- Shotgun metagenomics reveals interkingdom association between intestinal bacteria and fungi involving competition for nutrients. [europepmc]