Statistical Inference for Probabilistic Functions of Finite State Markov Chains

By L. Baum, T. Petrie. 1966

Subfields: Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “For example, Song et al. (2010a) extends the spectral algorithm of Hsu for learning traditional hidden Markov models (HMMs), which are restricted to discrete latent state and discrete observations, to structured and non-Gaussian continuous distributions (see also Jaeger (2000) for a formulation of d”
Hacking smart machines with smarter ones: How to extract meaningful data from machine learning classifiers (2013, background): “An Hidden Markov Model, introduced in [16], is a particular type of Markov Model for modeling sequences that can be characterized by an underlying process generating an observable sequence.”
Deep learning in neural networks: An overview (2014, background): “DP algorithms are also essential for systems that combine concepts of NNs and graphical models, such as Hidden Markov Models (HMMs) (Baum & Petrie, 1966; Stratonovich, 1960) and ExpectationMaximization (EM) (Dempster, Laird, & Rubin, 1977; Friedman, Hastie, & Tibshirani, 2001), e.g., Baldi and…”
Hierarchical and Interpretable Skill Acquisition in Multi-task Reinforcement Learning (2017, methodology): “In an episode, the temporal sequence of e t and g (cid:48) t , i.e., {(cid:104) e t , g (cid:48) t ; t ≥ 0 } , can be seen as a ﬁnite state Markov chain (Baum & Petrie, 1966).”
Conditioning by adaptive sampling for robust design (2019, methodology): “…( x ) , can be modelled by training an appropriate generative model, such as a Variational Auto-Encoder (VAE) (Kingma & Welling, 2014), Real NVP (Dinh et al., 2017), an HMM (Baum & Petrie, 1966) or a Trans-former (Vaswani et al., 2017; Rives et al., 2019), on the chosen set of ‘realistic’ examples.”
Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm (1998, background): “It seems to have first appeared in the unclassified literature in two independent 1966 publications [6] , [11].”
Multi-attention Recurrent Network for Human Communication Comprehension (2018, background): “Multi-view Learning: Extensions of Hidden Markov Models (Baum and Petrie 1966) and Hidden Conditional Random Fields (Quattoni et al. 2007; Morency, Quattoni, and Darrell 2007) have been proposed for learning from multiple different views (modalities) (Song, Morency, and Davis 2012; Song, Morency, an”
Counterpoint by Convolution (2019, methodology): “Whereas previous work in statistical music modeling has relied mainly on sequence models such as Hidden Markov Models (HMMs [2]) and Recurrent Neural Networks (RNNs [31]), we instead employ convolutional neural networks due to their invariance properties and em-”
Learnability in Optimality Theory (2000, background): “Much of the work has addressed automatic speech recognition (mostly under the name ‘Hidden Markov Models,’ e.g., Baum and Petrie 1966, Bahl, Jelinek and Mercer 1983, Brown et al. 1990); these speech systems are simultaneously learning (i) when the acoustic data they are ‘hearing’ is an example of,”
Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States (2005, methodology): “be estimated using the Baum–Welch algorithm (Baum and Petrie, 1966), which is essentially an EM algorithm.”
Intentional motion on-line learning and prediction (2008, methodology): “Assuming that, for every observed trajectory the associated goal is known, learning may be performed using the Baum-Welch algorithm [ 10 ] which is a specialization of Expectation-Maximization [11] and has become the standard learning technique for HMM’s.”
Multistate Markov models for disease progression with classification error (2003, methodology): “Maximum likelihood estimation A type of EM algorithm known as the Baum- Welch or forward-backward algorithm (Baum and Petrie, 1966; Baum et al., 1970) is commonly used for hidden Markov model estimation in discrete time applications.”
Channel coding: The road to channel capacity (2006, methodology): “• the “belief propagation” and “belief revision” algorithms of Pearl [132], used for statistical inference on “Bayesian networks;” • the “forward-backward” (Baum-Welch) algorithm [133], use d for detection of hidden Markov models in signal processing, especially for speech recognition; • “Junction t”
Monte Carlo Hidden Markov Models: Learning Non-Parametric Models of Partially Observable Stochastic Processes (1999, methodology): “The well-known Baum-Welch algorithm [1, 20, 27] provides a computationally efficient and elegant approach for learning , , and .”
A Deep Learning Approach to Link Prediction in Dynamic Networks (2014, unknown): “Linear probability based models like Hidden Markov Models (HMM)[3] cannot efficiently model dynamic data with high variance due to the simple and discrete states defined in the model.”
A Survey on Programmatic Weak Supervision (2022, methodology): “To model such properties, Hidden Markov Models (HMM) [Baum and Petrie, 1966] have been proposed, which represent true labels as latent variables and inferring them from the independently observed noisy labels through expectation-maximization al-gorithm [Welch, 2003].”
Robustness and Pricing with Uncertain Growth (2002, methodology): “Baum and Petrie (1966) and Bonomo and Garcia (1996) allow for the state st to alter volatility and find it to be empirically plausible for postwar output data and century long consumption data.”