CONDITIONAL MARKOV PROCESSES

By R. L. Stratonovich. 1960

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “…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 Chauvin…”
A comprehensive survey on machine learning for networking: evolution, applications and research opportunities (2018, background): “In 1977, in the area of statistical learning, Dempster et al. proposed EM, a generalization of the previous iterative, unsupervised methods, such as the Baum-Welch algorithm, for learning the unknown parameters of statistical HMM models [115].”
A Critical Review of Recurrent Neural Networks for Sequence Learning (2015, unknown): “n Markov models (HMMs), which model an observed sequence as probabilistically dependent upon a sequence of unobserved states, were described in the 1950s and have been widely studied since the 1960s [Stratonovich, 1960]. However, traditional Markov model approaches are limited because their states m”
A Tutorial on Bernoulli Filters: Theory, Implementation and Applications (2013, methodology): “Kalman and Bucy [30], [31] formulated the linear filtering theory, while Stratonovich [32] and Kushner [33] pioneered the development of the probabilistic approach to nonlinear filtering.”
Textually Customized Video Summaries (2017, methodology): “A probable rational behind the better performance of this marginal posterior method is that the marginalization in the Markov process has a smoothing effect over neighboring information [24, 25, 34], while the Viterbi algorithm maxes out a speciﬁc value from neighbors during decoding.”
Inference in Hidden Markov Models (2006, methodology): “The forward measure, named w in the work of Stratonovich (1960), is defined as wk(x) = Pν(Xk = x |Y0:k) , which coincides with the definition of the filtering probability φν,k for a discrete X. Also recall that φν,k corresponds to the normalized forward variable ᾱν,k = [αν,k(1)]−1αν,k. Instead of th”
Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering (2000, methodology): “For a detailed discussion of the filtering problem the reader is referred to the pioneering paper of Stratonovich [104] and to the more rigorous studies of Shiryaev [99] and Kallianpur-Striebel [72].”
Reinforcement Learning Upside Down: Don't Predict Rewards - Just Map Them to Actions (2019, background): “This reward is assumed to be independent of the history of previous actions and observations (Markov assumption [63]). z ij can be updated incrementally and cheaply whenever a j is executed in s i in Step 3 of Algorithm A1, and the resulting immediate reward is observed.”
State Space LSTM Models with Particle MCMC Inference (2017, background): “…(HMM) and linear dynamical systems (LDS), have been the workhorse of sequence modeling in the past decades From a graphical model perspective, efﬁcient message passing algorithms (Stratonovich, 1960; Kalman, 1960) are available in compact closed form thanks to their simple linear Markov structure.”
Inference in hidden Markov models (2010, methodology): “The forward measure, named w in the work of Stratonovich (1960), is defined as wk(x) = Pν(Xk = x |Y0:k) , which coincides with the definition of the filtering probability φν,k for a discrete X. Also recall that φν,k corresponds to the normalized forward variable ᾱν,k = [αν,k(1)]αν,k. Instead of the ”
The stability of conditional Markov processes and Markov chains in random environments (2008, methodology): “This observation dates back to the work of Stratonovich [33], and has recently been applied to obtain quantitative stability results for various special filtering models [7, 20, 35].”