Silent HMMs: Generalized Representation of Hidden Semi-Markov Models and Hierarchical HMMs
Modeling sequence data using probabilistic finite state machines (PFSMs) is a technique that analyzes the underlying dynamics in sequences of symbols. Hidden semi-Markov models (HSMMs) and hierarchical hidden Markov models (HHMMs) are PFSMs that have been successfully applied to a wide variety of applications by extending HMMs to make the extracted patterns easier to interpret. However, these models are independently developed with their own training algorithm, so that we cannot combine multiple kinds of structures to build a PFSM for a specific application. In this paper, we prove that silent hidden Markov models (silent HMMs) are flexible models that have more expressive power than HSMMs and HHMMs. Silent HMMs are HMMs that contain silent states, which do not emit any observations. We show that we can obtain silent HMM equivalent to given HSMMs and HHMMs. We believe that these results form a firm foundation to use silent HMMs as a unified representation for PFSM modeling.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach
In this paper, we propose circular Hidden Quantum Markov Models (c-HQMMs), which can be applied for modeling temporal data in quantum datasets (with classical datasets as a special case). We show that c-HQMMs are equival…
Second-Order Belief Hidden Markov Models
Hidden Markov Models (HMMs) are learning methods for pattern recognition. The probabilistic HMMs have been one of the most used techniques based on the Bayesian model. First-order probabilistic HMMs were adapted to the t…
Generalized Bayesian Filtering via Sequential Monte Carlo
We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GB…
Bayesian InferenceObject TrackingBridging HMMs and RNNs through Architectural Transformations
A distinct commonality between HMMs and RNNs is that they both learn hidden representations for sequential data. In addition, it has been noted that the backward computation of the Baum-Welch algorithm for HMMs is a spec…
Language ModelingLanguage ModellingLearning Hidden Markov Models When the Locations of Missing Observations are Unknown
The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard…