Baldi, P., Chauvin, Y., Hunkapillar, T., & McClure, M. #1994#. Hidden Markov models of biological primary sequence information. PNAS, 91, 1059#1063.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a set of generative models, each of which is trained over one class of data. An unknown sequence is evaluated by each generative model to determine which class (or protein family) is most likely to have generated the protein sequence. These models include approaches such as hidden Markov models [25, 10, 2, 24], probabilistic suf x trees [3, 1] and pro les [13] In contrast, discriminative models are trained over data containing multiple classes and directly classify an unknown sequence into a class. Discriminative models have been successfully applied to protein homology using support vector machines ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91(3):10591063, 1994.

....model) should be such that PM (s) is significant if s is a member of the sequence family. These probabilities can be derived from a multiple alignment of the sequence family, but more importantly, several methods exist to estimate them (or train the model) if a multiple alignment is not available [14, 35, 37]. 6.3 Co emission probability of two models When using a profile hidden Markov model, it is sometimes su#cient just to focus on the most probable path through the model, e.g. when using a profile hidden Markov model to generate alignments. It is, however, well known that profile hidden Markov ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91:1059-- 1063, 1994.

....model) should be such that PM (s) is significant if s is a member of the sequence family. These probabilities can be derived from a multiple alignment of the sequence family, but more importantly, several methods exist to estimate them (or train the model) if a multiple alignment is not available [21, 46, 49]. 6.3 Co Emission Probability of Two Models When using a profile hidden Markov model, it is sometimes su#cient just to focus on the most probable path through the model, e.g. when using a profile hidden Markov model to generate alignments. It is, however, well known that profile hidden Markov ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden markov models of biological primary sequence information. In Proceedings of the National Academy of Science of the USA, volume 91, pages 1059--1063,

....model) should be such that PM (s) is signi cant if s is a member of the sequence family. These probabilities can be derived from a multiple alignment of the sequence family, but more importantly, several methods exist to estimate them (or train the model) if a multiple alignment is not available [2, 6, 8]. 3 Co emission probability of two models When using a pro le hidden Markov model, it is sometimes sucient just to focus on the most probable path through the model, e.g. when using a pro le hidden Markov model to generate alignments. It is, however, well known that pro le hidden Markov ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden markov models of biological primary sequence information. In Proceedings of the National Academy of Science, USA, volume 91, pages 1059-1063, 1994.

....models where a model is trained over one class of data. An unknown protein sequence is evaluated by each protein family model to determine which protein family is most likely to have generated the protein sequence. These models include approaches such as hidden Markov modelbased approaches [24, 9, 2, 23], probabilistic suffix tree based approaches [3, 1] and profiles based approaches [12] Recently discriminative models have been applied to protein homology and approaches have included using support vector machines [21] and sparse Markov transducer approach [10] In discriminative models, the ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91(3):1059--1063, 1994.

....the sequence of states that is most likely to have generated a given observation sequence. The Baum Welch algorithm, an instantiation of EM, can be used to estimate the most likely HMM parameters given a collection of observation sequences. Speech recognition [11] and computational biochemistry [1] are well known applications of HMMs. Non hidden) Markov model algorithms that are used for part of speech tagging [3] and for information extraction [14] require each observation (i.e. token) of the observation sequences (documents) used for training to be labeled with the state (corresponding ....

P. Baldi, Y. Chauvin, Y. Hunkapliier, and M. McClure. Hidden markov models of biological primary sequence information. Proceedings of the National Academy of Sciences, 91(3):1059{ 1063, 1994.

....system. Rather than looking at the nal scoring system, this paper will concentrate on methods that can be used for estimating the probabilities themselves. In more sophisticated models than single sequence alignments, such as multiple alignments, pro les [7] and hidden Markov models [14, 3], we may have more than one reference sequence in our training set. Each position in such a model de nes a context for which we need to estimate the probabilities of the twenty amino acids. In this paper, s refers to a sample of amino acids from a column and s(i) to the number of times that amino ....

P. Baldi, Y. Chauvin, T. Hunkapillar, and M. McClure. Hidden Markov models of biological primary sequence information. PNAS, 91:1059-1063, 1994.

....Automated generation of a multiple alignment of large numbers of low identity, low similarity protein sequences sufficient for maximal recovery of the OSM and MIRs remains a challenge in the field of bioinformatics. The HMM approachtomultiple sequence alignment (Baldi, Chauvin et al. 1994 [2]; Krogh, Brown et al. 1994 [8] Eddy 1995 [5] Hughey and Krogh 1996 [6] provides a flexible method that can incorporate a priori knowledge into the model. Wehave demonstrated that anchoring an OSM in the same position within a set of subclass HMMs creates a series of models that generate better ....

Baldi, P., Chauvin, Y., et al., Hidden Markov models of biological primary sequence information, Proc. Natl. Acad. Sci., USA, 91:1059--1063, 1994.

....promoter detection and the method may not be applicable to prokaryotes due to the di erence in transcription regulation models between the two organisms. The second type of Markov chain that has been employed to model and predict site sequences in dna, rna and proteins is hidden Markov chains [7] [56] also called hidden Markov models (abbreviated into HMMs) It corresponds to a stochastic automaton. An example of such an automatopn is given in Figure 1. Others may be found in [29] When gaps are considered in the matrix models, as is the case of Hertz s algorithm [39] the di erence ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059-1063, 1994.

....Automated generation of a multiple alignment of large numbers of low identity, low similarity protein sequences su#cient for maximal recovery of the OSM and MIRs remains a challenge in the field of bioinformatics. The HMM approach to multiple sequence alignment (Baldi, Chauvin et al. 1994 [2]; Krogh, Brown et al. 1994 [8] Eddy 1995 [5] Hughey and Krogh 1996 [6] provides a flexible method that can incorporate a priori knowledge into the model. We have demonstrated that anchoring an OSM in the same position within a set of subclass HMMs creates a series of models that generate better ....

Baldi, P., Chauvin, Y., et al., Hidden Markov models of biological primary sequence information, Proc. Natl. Acad. Sci., USA, 91:1059--1063, 1994.

....series data. Second, they have been demonstrated empirically to be capable of modeling the structure of the generative processes underlying a wide variety of real world time series. HMMs have met with success in domains such as speech recognition (Jelinek 1997) computational molecular biology (Baldi et al. 1994), and gesture recognition (Bregler 1997) Given a set of time series, it is possible to induce an HMM that models these data. However, algorithms for inducing HMMs do not directly address the problem of identifying qualitatively di erent regimes in the data; they simply attempt to t a single ....

Baldi, P.; Chauvin, Y.; Hunkapiller, T.; and McClure, M. 1994. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences 91(3):1059-1063.

....handwriting. 1. Introduction Hidden Markov models (HMMs) have become the method of choice for modeling stochastic processes and sequences in applications such as speech and handwriting recognition (Rabiner, 1986) Nag et al. 1985) and computational molecular biology (Krogh et al. 1993) (Baldi et al. 1994). Hidden Markov models are also used for natural language modeling (see e.g. Jelinek, 1985) In most of these applications the model s topology is determined in advance and the model parameters are estimated by an EM procedure (Dempster et al. 1977) known as the Baum Welch (or ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. McClure. Hidden Markov models of biological primary sequence information. Proc. Nat. Acd. Sci. (USA), 91(3):1059--1063, 1994.

....model) should be such that PM (s) is signi cant if s is a member of the sequence family. These probabilities can be derived from a multiple alignment of the sequence family, but more importantly, several methods exist to estimate them (or train the model) if a multiple alignment is not available (Baldi et al. 1994; Durbin et al. 1998; Eddy 1998) Co emission probability of two models When using a pro le hidden Markov model, it is sometimes sucient just to focus on the most probable path through the model, e.g. when using a pro le hidden Markov model to generate alignments. It is, however, well known that ....

Baldi, P.; Chauvin, Y.; Hunkapiller, T.; and McClure, M. A. 1994. Hidden markov models of biological primary sequence information. In Proceedings of the National Academy of Science, USA, volume 91, 1059{ 1063.

....model) should be such that PM (s) is signi cant if s is a member of the sequence family. These probabilities can be derived from a multiple alignment of the sequence family, but more importantly, several methods exist to estimate them (or train the model) if a multiple alignment is not available [2, 6, 8]. 3 Co emission probability of two models When using a pro le hidden Markov model, it is sometimes sucient just to focus on the most probable path through the model, e.g. when using a pro le hidden Markov model to generate alignments. It is, however, well known that pro le hidden Markov models ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden markov models of biological primary sequence information. In Proceedings of the National Academy of Science, USA, volume 91, pages 1059-1063, 1994.

....the question is, whether this sequence ts into one of the known families. In this setting, several methods have been developed, including templates (Taylor, 1986) pro les (Gribskov, McLachlan, Eisenberg, 1987; Luthy, Xenarios, Bucher, 1994) hidden Markov models (Krogh et al. 1994; Baldi et al. 1994; Eddy, Mitchison, Durbin, 1995) Bayesian models calculating posterior distributions on possible motifs in a family (Liu, Neuwald, Lawrence, 1995) and discriminative approaches like the combination of support vector machines and the Fisher kernel method (Jaakkola, Diekhans, Haussler, ....

Baldi, P.; Chauvin, Y.; Hunkapiller, T.; and McClure, M. 1994. Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA 1;91(3):1059-1063.

.... conserved regions in protein or DNA sequences as ungapped blocks (Lawrence and Reilly 1990; Lawrence et al. 1993; Liu 1994; Liu et al. 1995; Neuwald et al. 1995) and the hidden Markov model (HMM) that treats the observed sequences as generated by a hypothetical ancestral model via mutations (Baldi et al. 1994; Eddy 1995; Haussler et al. 1994) An important common advantage of both methods is that they employ explicit statistical models and treat the multiple alignment problem as a statistical missing data problem. The resulting statistical models form the basis of substantially more sensitive database ....

Baldi, P., Chauvin, Y., McClure, M. & Hunkapiller, T. (1994), "Hidden Markov Models of Biological Primary Sequence Information, " Proc. Nat. Acad. Sci. USA 91, 1059-63.

.... related and have a common ancestor the sequences are usually aligned, and the problem is to find the alignment that maximizes the probability that the two sequences are related: To actually calculate these probabilities, one applies a Markovian model for sequence evolution (Krogh et al. 1994; Baldi et al. 1994). This begins with an alignment of the two sequences, e.g. VNRLQQNIVSL EVDHKVANYKPQVEPFGHGPIFMATALVPGLYLLPL VNRLQQSIVSLRDAFNDGTKLLEELDHRVLNYKPQANPFGNGPIFMVTAIVPGLHLLPI The gaps arise from insertions (or their counterpart deletions) during divergent evolution. The alignment is ....

Baldi, P., Chauvin, Y., Hunkapiller, T., and McClure, M. A. (1994). Hidden markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059--1063.

....outside the family. The probability score can thus be interpreted as a measure of the extent to which a new protein sequence is homologous to the protein family of interest. Considerable recent work has been done in refining HMMs for the purpose of identifying weak protein homologies in this way [34, 5, 14, 24, 33]. Let X = x 1 , x n ] denote a protein sequence, where each x i is an amino acid residue. Suppose that we are interested in a particular protein family such as immunoglobulins and have estimated an HMM, H 1 , for this family (for details of the estimation process see, e.g. 12] We use P ....

P. Baldi, Y. Chauvin, T. Hunkapillar, and M. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the USA, 91:1059--1063, 1994.

.... s 1 , s 2 # # are related and have a common ancestor the sequences are usually aligned, and the problem is to find the alignment that maximizes the probability that the two sequences are related: To actually calculate these probabilities, one applies a Markovian model for sequence evolution [25, 3]. This begins with an alignment of the two sequences, e.g. 1 A: RPCVCP VLRQAAQ QVLQRQIIQGPQQLRRLF AA B: RPCACP VLRQVVQ QALQRQIIQGPQQLRRLF AA C: KPCLCPKQAAVKQAAH QQLYQGQLQGPKQVRRAFRLL D: KPCVCPRQLVLRQAAHLAQQLYQGQ RQVRRAF VA E: KPCVCPRQLVLRQAAH QQLYQGQ RQVRRLF AA Figure 1. The ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059--1063, 1994.

.... HMMs or related to HMMs, also for speech recognition, can be found in the collection of papers [25] Recently, HMMs have been applied to a variety of applications outside of speech recognition, such as handwriting recognition [26, 27, 28, 29, 30, 31, 32] pattern recognition in molecular biology [33, 34, 35, 36, 3], and fault detection [37] The variants and extensions of HMMs discussed here also include language models [38, 39, 13] econometrics [14, 15, 40] time series [41] and signal processing. An analysis of the sample and computational complexity of approximating a distribution using an HMM or a ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. McClure, "Hidden markov models of biological primary sequence information," Proc. Nat. Acad. Sci. (USA), vol. 91, no. 3, pp. 1059--1063, 1995.

.... models (e.g. Longford, 1993) longitudinal models (e.g. Cowles, Carlin, and Connett, 1993) mixture models (e.g. West, 1992) and specific models for problems such as AIDS incidence (e.g. Lange, Carlin, and Gelfand, 1992, and Bacchetti, Segal, and Jewell, 1993) genetic sequencing (e.g. Baldi et al. 1994), epidemiology (e.g. Clayton and Bernardinelli, 1992, and Gilks and Richardson, 1993) and survival analysis (e.g. Kuo and Smith, 1992) Until recently, these problems were handled either in a partially Bayesian manner (which typically meant that some aspects of uncertainty in the models were ....

Baldi, P., Chauvin, Y., McClure, M., and Hunkapiller, T. (1994). Hidden Markov models of biological primary sequence information, Proceedings of the National Academy of Science USA.

....The explicit use of feature table information is probably a unique aspect. It helps avoid the common pitfall of using sequence title as annotations, which might be intended for a different region of the sequence[10] Many bells and whistles can be added: the incorporation of ClustalW [17] hmmPfam[16, 6], SEG[21] etc. Due to page Figure 1: The Feature BLAST on line demonstration web page. Figure 2: This view offers information similar to BLASTP. Figure 3: This view provides an overall sense of relevant features in homologs from BLASTP. Figure 4: This view provides more precise information of ....

P. Baldi, Y. Chauvin, T. Hunkapiller, M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of National Academy of Science, 91(3):1059--1063, 1994.

....this can be corrected and how to create an optimal scoring matrix to estimate distances. This scoring matrix is optimal within a large class of estimators. Finally we present a complete example. 1 Introduction 1. 1 Model of Evolution The model we consider here is a Markovian model of evolution [1], which assumes that amino acids mutate independently of each other, with probabilities which depend only on the amino acids and on the amount of evolution. In mathematical terms we can describe the model with mutation matrices: a mutation matrix, denoted by M , describes the probabilities of ....

....hold. M = 2 6 6 6 6 6 4 0:9920 0:007612 0:001144 0:004677 0:003761 0:9819 0:002670 0:003118 0:001410 0:006660 0:9931 0:006235 0:002821 0:003806 0:003051 0:9860 3 7 7 7 7 7 5 The frequency vector f can be computed from the eigenvector of M whose eigenvalue is 1 or from the first row column of M [1]. f i = M i1 M 1i P j M j1 =M 1j f 1 = 3003 f 2 = 1484 f 3 = 3702 f 4 = 1811 The eigenvalues of M are 1 = 1:0000 2 = 9914 3 = 9830 4 = 9786 In this case we want to find the optimal scoring matrix for d in the range 100 d 200. After setting E 11 = Gamma1 and E 12 = 1 and ....

Pierre Baldi, Yves Chauvin, Tim Hunkapiller, and Marcella A. McClure. Hidden markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059--1063, 1994.

....paper we propose a method to identify relationships between molecular sequence families by aligning hidden Markov models. Hidden Markov models (HMMs) are probabilistic models that, in computational biology, have been applied to model the primary structure of a sequence family (Krogh et al. 1994; Baldi et al. 1994; Eddy, 1995, 1996; Eddy et al. 1995; Hughey and Krogh, 1996) Given the sequences or a multiple alignment of a sequence family, an HMM can be trained or built to describe the sequence consensus of this family. Therefore, we can study the evolutionary relationship between two sequence families by ....

Baldi, P., Chauvin, Y., Hunkapiller, T. and McClure, M.A. (1994) Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91, 1059-1063.

....is computed [40, 30] More sophisticated homology detection methods involve two steps: first building a statistical model of the family and then comparing that model to each sequence in the database. For example, hidden Markov models (HMMs) have been used extensively to model protein families [26, 10, 16]. These sta2 tistical models have a strong theoretical basis in probability and are supported by efficient algorithms for training, database searching, and multiple sequence alignment. The model parameters are learned via expectation maximization, and the homology detection algorithm is a form of ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91(3):1059--1063, 1994.

....and as a result, researchers in computational biology have recently begun to use them for analysis of DNA and protein sequences. HMMs have been used for finding periodicities in DNA [2] for exploring structural similarities of families of genes [6] for producing multiple sequence alignments [13, 3], for finding palindromic repeats [12] and a To be precise, our system does not simply find genes. Rather, it finds coding regions beginning with a start codon and ending with a stop codon. It does not find the beginning or end of transcription. All of the major gene finding systems perform ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. McClure. Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059--1063, February 1994.

....handwriting. 1. Introduction Hidden Markov models (HMMs) have become the method of choice for modeling stochastic processes and sequences in applications such as speech and handwriting recognition (Rabiner, 1986) Nag et al. 1985) and computational molecular biology (Krogh et al. 1993) (Baldi et al. 1994). Hidden Markov models are also used for natural language modeling (see e.g. Jelinek, 1985) In most of these applications the model s topology is determined in advance and the model parameters are estimated by an EM procedure (Dempster et al. 1977) known as the forwardbackward (or Baum Welch) ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. McClure. Hidden Markov models of biological primary sequence information. Proc. Nat. Acd. Sci. (USA), 91(3):1059--1063, 1994.

....is computed [27] More sophisticated homology detection methods involve two steps: first building a statistical model of the family and then comparing that model to each sequence in the database. For example, hidden Markov models (HMMs) have been used extensively to model protein families [24, 11, 16]. These statistical models have a strong theoretical basis in probability and are supported by efficient algorithms for training, database searching, and multiple sequence alignment. The model parameters are learned via expectation maximization, and the homology detection algorithm is a form of ....

P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91(3):1059--1063, 1994.

.... protein or DNA sequences as ungapped blocks (Lawrence and Reilly 1990; Lawrence et al. 1993; Liu 1994; Liu et al. 1995; Neuwald, Liu and Lawrence 1995) and the hidden Markov model (HMM) that treats the observed sequences as though they were generated by a hypothetical ancestral model via mutation (Baldi, Chauvin, McClure, and Hunkapiller 1994; Eddy 1995; Krogh, Brown, Mian, Sjolander, and Haussler 1994) By using a model similar to the HMM to describe how two sequences relate to each other, Allison and Wallace (1994) presented useful algorithms for conducting multiple alignment considering information on evolution (i.e. assuming that ....

....a powerful statistical modeling tool and has been widely applied in signal processing, speech recognition, time series analysis, etc. Rabiner 1989) The method was first applied to model biological sequences by Churchill (1989) and has become very popular recently in multiple sequence alignment (Baldi et al. 1994; Krogh et al. 1994; Lazareva and Churchill 1997) The basic form of an HMM can be written as y t f t (y j h t ) 2) h t g t (h j h t Gamma1 ) 3) where f t and g t are probability distributions (known up to some estimable parameters) and the y t are observations. The h t form a (possibly ....

[Article contains additional citation context not shown here]

Baldi, P., Chauvin, Y., McClure, M., and Hunkapiller, T. (1994), "Hidden Markov Models of Biological Primary Sequence Information," Proceedings of the National Academy of Science, 91, 1059-1063.

....structure in 16S and 23S rRNA. Introduction Multiple alignment of structural RNA is a more difficult problem than multiple alignment of protein. It requires a different type of search that is computationally more expensive than the standard Hidden Markov Model method (Krogh et al. 1994; Baldi et al. 1994; Krogh Hughey 1995) used for aligning proteins or DNA because the base pairing that forms the secondary structure of RNA can t be modeled by an HMM. Humans align RNA using an iterative technique known as Comparative Sequence Analysis, described in detail in (James, Olsen, Pace 1989) This ....

Baldi, P.; Chauvin, Y.; Hunkapillar, T.; and McClure, M. 1994. Hidden Markov models of biological primary sequence information. PNAS 91:1059--1063.

.... 1990) Sequence target (Mulligan et al. 1984) Bucher Bairoch 1994) Generalized profile Weight matrix (e.g. Staden 1984, Stormo 1988) Profile (Gribskov et al. 1987, 1990) Consensus sequence with mismatches Consensus sequence with degenerate positions Exact word (e.g. Krogh et al. 1994, Baldi et al..1994) Linear hidden Markov model General hidden Markov model Stochastic context free grammar (Sakakibara, et al. 1994) Figure 1: Relationships between various motif descriptors. Motif descriptors are arranged by increasing complexity along the vertical axis. An arrow indicates that the upper ....

....Although simpler in structure, profiles constitute a higher level of generality than flexible patterns or sequence targets. Recently, hidden Markov models (hmms) of a specific architecture (here called linear hidden Markov models) were introduced to molecular biology [Haussler et al. 1993, Baldi et al. 1994] These models resemble previously described motif descriptors in that they also assign a number, in this case a probability, to a specific alignment of a sequence to the model. The architectures proposed contain a higher number of parameters per length than profiles, allowing for a more flexible ....

Baldi, P., Chauvin, Y., Hunkapillar, T., and McClure, M. (1994). Hidden Markov models of biological primary sequence information. PNAS, 91:1059--1063.

....than looking at the final scoring system, this paper will concentrate on the methods that can be used for estimating the probabilities themselves. In more sophisticated models than single sequence alignments, such as multiple alignments, profiles [GME87] and hidden Markov models [KBM 94, BCHM94] we may have more than one reference sequence in our training set. Each position of such a model will define a context for which we to want to estimate the probabilities of the twenty amino acids. The only information we will use about the context is the sampling of the amino acids we have seen ....

P. Baldi, Y. Chauvin, T. Hunkapillar, and M. McClure. Hidden Markov models of biological primary sequence information. PNAS, 91:1059--1063, 1994.

.... and efficiency of its parameter estimation algorithm, the hidden Markov model (HMM) has emerged as one of the basic statistical tools for modeling discrete time series, finding widespread application in the areas of speech recognition (Juang and Rabiner, 1991) and computational molecular biology (Baldi et al. 1994). An HMM is essentially a mixture model, encoding information about the history of a time series in the value of a single multinomial variable (the hidden state) This multinomial assumption allows an efficient parameter estimation algorithm to be derived (the Baum Welch algorithm) However, it ....

Baldi, P., Chauvin, Y., Hunkapiller, T., and McClure, M. (1994). Hidden Markov models of biological primary sequence information. Proc. Nat. Acad. Sci. (USA), 91(3):1059--1063.

.... and efficiency of its parameter estimation algorithm, the hidden Markov model (HMM) has emerged as one of the basic statistical tools for modeling discrete time series, finding widespread application in the areas of speech recognition (Rabiner and Juang, 1986) and computational molecular biology (Baldi et al. 1994). An HMM is essentially a mixture model, encoding information about the history of a time series in the value of a single multinomial variable (the hidden state) This multinomial assumption allows an efficient parameter estimation algorithm to be derived (the Baum Welch algorithm) However, it ....

Baldi, P., Chauvin, Y., Hunkapiller, T., and McClure, M. (1994). Hidden Markov models of biological primary sequence information. Proc. Nat. Acad. Sci. (USA), 91(3):1059--1063.

.... a variety of data sources from simple flat file formats to full blown OODBMS (Object Oriented Database Management Systems) As an example, ObjectData has been used as the foundation for linking biological data stored in the ObjectStore OODBMS (from ObjectDesign) to a hidden Markov model simulator [6] for biological sequence analysis built on top of ObjectNet and ObjectComp. ObjectStat statistical objects can be layered on top of ObjectData, allowing ObjectNet components to get access to data either directly through ObjectData or through ObjectStat. ObjectData hides the underlying data base ....

P. Baldi, Y. Chauvin, T. Hunkapillar, and M. McClure. Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA, 91:1059--1063, 1994.

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P. Baldi, Y. Chauvin, T. Hunkapiller and M.A. McClure, "Hidden Markov models of biological primary sequence information" Proc. Natl. Acad. Sci., USA 91, 1059 (1994).

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Baldi, P., Chauvin, Y., Hunkapillar, T., & McClure, M. #1994#. Hidden Markov models of biological primary sequence information. PNAS, 91, 1059#1063.

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Baldi, P., Y. Chauvin, T. Hunkapillar, and M. McClure (1994). Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Science 91, 1059--1063.

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P. Baldi, Y. Chauvin, T. Hunkapiller, and M.A. McClure. Hidden Markov models of biological primary sequence information. Proc. Nat. Acad. Sci. (USA), 91(3):1059--1063, 1994.

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P. Baldi, Y. Chauvin, Y. Hunkapliier, and M. McClure. Hidden markov models of biological primary sequence information. Proceedings of the National Academy of Sciences, 91(3):1059--1063, 1994.

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P. Baldi, Y. Chauvin, Y. Hunkapliier, and M. McClure. Hidden markov models of biological primary sequence information. Proceedings of the National Academy of Sciences, 91(3):1059{ 1063, 1994.

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P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden markov models of biological primary sequence information. PNAS, 91(3):1059--1063, 1994.

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P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America, 91(3):1059--1063, 1994.

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Baldi,P., Chauvin,Y., Hunkapiller,T., and McClure,M. A. (1994) Hidden Markov models of biological primary sequence information. PNAS, 91(3):1059--1063.

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P. Baldi, Y. Chauvin, Y. Hunkapliier, and M. McClure. Hidden markov models of biological primary sequence information. Proceedings of the National Academy of Sciences, 91(3):1059--1063, 1994.

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Baldi, P., Y. Chauvin, T. Hunkapiler, and M. A. McClure. 1994. Hidden Markov models of biological primary sequence information. Proc. Natl. Acad. Sci. USA 91:1059.

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Baldi,P., Chauvin,Y., Hunkapiller,T. and McClure,M.A. (1994) Hidden Markov models of biological primary sequence information. Proc. Natl Acad. Sci. USA, 91, 1059--1063.

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Baldi,P., Chauvin,Y., Hunkapillar,T. and McClure,M. (1994) Hidden Markov models of biological primary sequence information. Proc. Natl Acad. Sci. USA, 91, 1059--1063.

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Baldi, P, Chauvin, Y & Hunkapiller, T (1994) Hidden Markov Models of Biological Primary Sequence Information. Proc. Natl. Acad. Sci. 91,

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#17#:3578#3580, September 1994. #11# P. Baldi, Y. Chauvin, T. Hunkapiller, and M. A. McClure. Hidden Markov models of biological primary sequence information. Proceedings of the National Academy of Sciences of the United States of America,

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