I would like to use a simple model for some (prediction/estimation), Markov chain is very good candidate, however I wonder if there are some other models to do these stuffs.
Regards.
Handling Bayes' rule based on Reproducing Kernel Hilbert Spaces (RKHS), Kalman Filter (KF) and Recursive Least Squares (RLS) techniques leads to Kernel Kalman Rule (KKR) by Gebhardt et al. as an alternative to Hidden Markov Models (HMMs) for data prediction/estimation/filtering tasks.
Check out the following ordered references for more details:
- H.W. Sorenson, " Least-squares estimation: from Gauss to Kalman ", 1970 - https://www2.pv.infn.it/~fontana/download/lect/Sorenson.pdf
- Song et al., " Hilbert Space Embeddings of Hidden Markov Models ", 2010 - http://machinelearning.wustl.edu/mlpapers/paper_files/icml2010_SongSGS10.pdf
- Boots et al., " Hilbert Space Embeddings of Predictive State Representations ", 2013 - https://www.cs.cmu.edu/~ggordon/boots-gretton-gordon-HSE-PSRs.pdf
- Song et al., " Kernel Embeddings of Conditional Distributions: A Unified Kernel Framework for Nonparametric Inference in Graphical Models ", 2013 - http://booksc.org/book/33069566/2498d5
- Fukumizu et al., " Kernel Bayes’ Rule: Bayesian Inference with Positive Definite Kernels ", 2013 - https://pdfs.semanticscholar.org/9281/9d584f3fd50975242bc504e87f9925a58839.pdf
- Gebhardt et al., " The Kernel Kalman Rule— Efficient Nonparametric Inference with Recursive Least Squares ", 2017 - https://pdfs.semanticscholar.org/2b85/c85b3b72220b178cc62fa07a35afad28798c.pdf
Now there are plenty of alternatives to Markov model but they are considerably more difficult to study. Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses.
http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2966.2007.12353.x/abstract
In addition to my prior post and Ashwini Darekar's post (alternatively available from https://arxiv.org/pdf/0704.3704.pdf), here are three valuable references to bridge the gap between markov models, recurrent neural networks (RNNs) and statistical multiresolution (hierarchical) modeling:
- A.S. Willsky, " Multiresolution Markov Models for Signal and Image Processing ", 2002 - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.321.1110&rep=rep1&type=pdf
- Lee et al., " Likelihood Inference for Models with Unobservables: Another View ", 2010 - https://arxiv.org/pdf/1010.0303.pdf
- Choe et al., " Probabilistic Interpretations of Recurrent Neural Networks ", 2017 - https://www.cs.cmu.edu/~epxing/Class/10708-17/project-reports/project10.pdf
Regards
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