 | This article includes a list of general references, but it lacks sufficient corresponding inline citations .(November 2020) |
The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM.
HHMMs and HMMs are useful in many fields, including pattern recognition. [1] [2]
It is sometimes useful to use HMMs in specific structures in order to facilitate learning and generalization. For example, even though a fully connected HMM could always be used if enough training data is available, it is often useful to constrain the model by not allowing arbitrary state transitions. In the same way it can be beneficial to embed the HMM into a greater structure; which, theoretically, may not be able to solve any other problems than the basic HMM but can solve some problems more efficiently when it comes to the amount of training data required.
In the hierarchical hidden Markov model (HHMM), each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM. This implies that the states of the HHMM emit sequences of observation symbols rather than single observation symbols as is the case for the standard HMM states.
When a state in an HHMM is activated, it will activate its own probabilistic model, i.e. it will activate one of the states of the underlying HHMM, which in turn may activate its underlying HHMM and so on. The process is repeated until a special state, called a production state, is activated. Only the production states emit observation symbols in the usual HMM sense. When the production state has emitted a symbol, control returns to the state that activated the production state. The states that do not directly emit observations symbols are called internal states. The activation of a state in an HHMM under an internal state is called a vertical transition. After a vertical transition is completed, a horizontal transition occurs to a state within the same level. When a horizontal transition leads to a terminating state, control is returned to the state in the HHMM, higher up in the hierarchy, that produced the last vertical transition.
Note that a vertical transition can result in more vertical transitions before reaching a sequence of production states and finally returning to the top level. Thus the production states visited give rise to a sequence of observation symbols that is "produced" by the state at the top level.
The methods for estimating the HHMM parameters and model structure are more complex than for HMM parameters, and the interested reader is referred to Fine et al. (1998).
The HMM and HHMM belong to the same class of classifiers. That is, they can be used to solve the same set of problems. In fact, the HHMM can be transformed into a standard HMM. However, the HHMM leverages its structure to solve a subset of the problems more efficiently.
Classical HHMMs require a pre-defined topology, meaning that the number and hierarchical structure of the submodels must be known in advance. [1] Samko et al. (2010) used information about states from feature space (i. e., from outside the Markov Model itself) in order to define the topology for a new HHMM in an unsupervised way. [2] However, such external data containing relevant information for HHMM construction may not be available in all contexts, e. g. in language processing.
Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers. It is also known as automatic speech recognition (ASR), computer speech recognition or speech to text (STT). It incorporates knowledge and research in the computer science, linguistics and computer engineering fields. The reverse process is speech synthesis.
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent Markov process. An HMM requires that there be an observable process whose outcomes depend on the outcomes of in a known way. Since cannot be observed directly, the goal is to learn about state of by observing By definition of being a Markov model, an HMM has an additional requirement that the outcome of at time must be "influenced" exclusively by the outcome of at and that the outcomes of and at must be conditionally independent of at given at time Estimation of the parameters in an HMM can be performed using maximum likelihood. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate the parameters.
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to mathematical logic. The word automata comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states and transitions. As the automaton sees a symbol of input, it makes a transition to another state, according to its transition function, which takes the previous state and current input symbol as its arguments.
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events, especially in the context of Markov information sources and hidden Markov models (HMM).
Grammar theory to model symbol strings originated from work in computational linguistics aiming to understand the structure of natural languages. Probabilistic context free grammars (PCFGs) have been applied in probabilistic modeling of RNA structures almost 40 years after they were introduced in computational linguistics.
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step.
The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions.
A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state up to that time.
The layered hidden Markov model (LHMM) is a statistical model derived from the hidden Markov model (HMM). A layered hidden Markov model (LHMM) consists of N levels of HMMs, where the HMMs on level i + 1 correspond to observation symbols or probability generators at level i. Every level i of the LHMM consists of Ki HMMs running in parallel.
GeneMark is a generic name for a family of ab initio gene prediction algorithms and software programs developed at the Georgia Institute of Technology in Atlanta. Developed in 1993, original GeneMark was used in 1995 as a primary gene prediction tool for annotation of the first completely sequenced bacterial genome of Haemophilus influenzae, and in 1996 for the first archaeal genome of Methanococcus jannaschii. The algorithm introduced inhomogeneous three-periodic Markov chain models of protein-coding DNA sequence that became standard in gene prediction as well as Bayesian approach to gene prediction in two DNA strands simultaneously. Species specific parameters of the models were estimated from training sets of sequences of known type. The major step of the algorithm computes for a given DNA fragment posterior probabilities of either being "protein-coding" in each of six possible reading frames or being "non-coding". The original GeneMark was an HMM-like algorithm; it could be viewed as approximation to known in the HMM theory posterior decoding algorithm for appropriately defined HMM model of DNA sequence.
Activity recognition aims to recognize the actions and goals of one or more agents from a series of observations on the agents' actions and the environmental conditions. Since the 1980s, this research field has captured the attention of several computer science communities due to its strength in providing personalized support for many different applications and its connection to many different fields of study such as medicine, human-computer interaction, or sociology.
Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli process. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. Thus, the computational complexity of TI-HBM for probability evaluation and state estimation is . The TI-HBM is able to model acoustic-unit duration by using a built-in parameter named survival probability. The TI-HBM is simpler and faster than HMM in a phoneme recognition task, but its performance is comparable to HMM.
HMMER is a free and commonly used software package for sequence analysis written by Sean Eddy. Its general usage is to identify homologous protein or nucleotide sequences, and to perform sequence alignments. It detects homology by comparing a profile-HMM to either a single sequence or a database of sequences. Sequences that score significantly better to the profile-HMM compared to a null model are considered to be homologous to the sequences that were used to construct the profile-HMM. Profile-HMMs are constructed from a multiple sequence alignment in the HMMER package using the hmmbuild program. The profile-HMM implementation used in the HMMER software was based on the work of Krogh and colleagues. HMMER is a console utility ported to every major operating system, including different versions of Linux, Windows, and macOS.
In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it. Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.
Structured prediction or structured (output) learning is an umbrella term for supervised machine learning techniques that involves predicting structured objects, rather than scalar discrete or real values.
In statistics, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming that the unknown values to be learnt are connected in a Markov chain rather than being conditionally independent of each other. MEMMs find applications in natural language processing, specifically in part-of-speech tagging and information extraction.
In machine learning, sequence labeling is a type of pattern recognition task that involves the algorithmic assignment of a categorical label to each member of a sequence of observed values. A common example of a sequence labeling task is part of speech tagging, which seeks to assign a part of speech to each word in an input sentence or document. Sequence labeling can be treated as a set of independent classification tasks, one per member of the sequence. However, accuracy is generally improved by making the optimal label for a given element dependent on the choices of nearby elements, using special algorithms to choose the globally best set of labels for the entire sequence at once.
Time-series segmentation is a method of time-series analysis in which an input time-series is divided into a sequence of discrete segments in order to reveal the underlying properties of its source. A typical application of time-series segmentation is in speaker diarization, in which an audio signal is partitioned into several pieces according to who is speaking at what times. Algorithms based on change-point detection include sliding windows, bottom-up, and top-down methods. Probabilistic methods based on hidden Markov models have also proved useful in solving this problem.
