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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 (an independent) 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 (instead of in the HMM case, where and are number of states and observation sequence length respectively). The TI-HBM is able to model acoustic-unit duration (e.g. phone/word 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.
In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability that is, the probability distribution of any single experiment that asks a yes–no question; the question results in a boolean-valued outcome, a single bit of information whose value is success/yes/true/one with probability p and failure/no/false/zero with probability q. It can be used to represent a coin toss where 1 and 0 would represent "heads" and "tails", respectively, and p would be the probability of the coin landing on heads or tails, respectively. In particular, unfair coins would have
Hidden Markov Model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved states.
In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes are important in the study of dynamical systems, as most such systems exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal.
For details, see or .
Speech processing is the study of speech signals and the processing methods of signals. The signals are usually processed in a digital representation, so speech processing can be regarded as a special case of digital signal processing, applied to speech signals. Aspects of speech processing includes the acquisition, manipulation, storage, transfer and output of speech signals. The input is called speech recognition and the output is called speech synthesis.
Speech recognition is the inter-disciplinary sub-field of computational linguistics that develops methodologies and technologies that enables 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 linguistics, computer science, and electrical engineering fields.
A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
Pattern recognition is the automated recognition of patterns and regularities in data. Pattern recognition is closely related to artificial intelligence and machine learning, together with applications such as data mining and knowledge discovery in databases (KDD), and is often used interchangeably with these terms. However, these are distinguished: machine learning is one approach to pattern recognition, while other approaches include hand-crafted rules or heuristics; and pattern recognition is one approach to artificial intelligence, while other approaches include symbolic artificial intelligence. A modern definition of pattern recognition is:
The field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories.
The Viterbi algorithm is a dynamic programming algorithm for finding 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.
Lawrence R. Rabiner is an electrical engineer working in the fields of digital signal processing and speech processing; in particular in digital signal processing for automatic speech recognition. He has worked on systems for AT&T Corporation for speech recognition.
In electrical engineering, computer science, statistical computing and bioinformatics, the Baum–Welch algorithm is used to find the unknown parameters of a hidden Markov model (HMM). It makes use of a forward-backward algorithm.
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.
Recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.
Conditional random fields (CRFs) are a class of statistical modeling method often applied in pattern recognition and machine learning and used for structured prediction. CRFs fall into the sequence modeling family. Whereas a discrete classifier predicts a label for a single sample without considering "neighboring" samples, a CRF can take context into account; e.g., the linear chain CRF predicts sequences of labels for sequences of input samples.
The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions , i.e. it computes, for all hidden state variables , the distribution . This inference task is usually called smoothing. The algorithm makes use of the principle of dynamic programming to efficiently compute the values that are required to obtain the posterior marginal distributions in two passes. The first pass goes forward in time while the second goes backward in time; hence the name forward–backward algorithm.
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.
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 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". Original GeneMark is an HMM-like algorithm; it can be viewed as approximation to known in the HMM theory posterior decoding algorithm for appropriately defined HMM.
In probability theory, lumpability is a method for reducing the size of the state space of some continuous-time Markov chains, first published by Kemeny and Snell.
In probability theory, a Markov model is a stochastic model used to model 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.
In machine learning, 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.
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.
 Jahanshah Kabudian, M. Mehdi Homayounpour, S. Mohammad Ahadi, "Bernoulli versus Markov: Investigation of state transition regime in switching-state acoustic models," Signal Processing, vol. 89, no. 4, pp. 662–668, April 2009.
 Jahanshah Kabudian, M. Mehdi Homayounpour, S. Mohammad Ahadi, "Time-inhomogeneous hidden Bernoulli model: An alternative to hidden Markov model for automatic speech recognition," Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4101–4104, Las Vegas, Nevada, USA, March 2008.