Richard Durbin

Product units: a computationally powerful and biologically plausible extension to backpropagation networks

We introduce a new form of computational unit for feedforward learning networks of the backpropagation type. Instead of calculating a weighted sum this unit calculates a weighted product, where each input is raised to a power determined by a variable weight. Such a unit can learn an arbitrary polynomial term, which would then feed into higher level standard summing units. We show how learning operates with product units, provide examples to show their efficiency for various types of problems, and argue that they naturally extend the family of theoretical feedforward net structures. There is a plausible neurobiological interpretation for one interesting configuration of product and summing units.

Biological sequence analysis: Markov chains and hidden Markov models

Having introduced some methods for pairwise alignment in Chapter 2, the emphasis will switch in this chapter to questions about a single sequence. The main aim of the chapter is to develop the theory for a very general form of probabilistic model for sequences of symbols, called a hidden Markov model (abbreviated HMM). The types of question we can use HMMs and their simpler cousins, Markov models, to consider are: ‘Does this sequence belong to a particular family?’ or ‘Assuming the sequence does come from some family, what can we say about its internal structure?’ An example of the second type of problem would be to try to identify alpha helix or beta sheet regions in a protein sequence. As well as giving examples from the biological sequence world, we also give the mathematics and algorithms for many of the operations on HMMs in a more general form. These methods, or close analogues of them, are applied in many other sections of the book. This chapter therefore contains a fairly large amount of mathematically technical material. We have tried to organise it so that the first half, approximately, leads the reader through the essential algorithms using a single biological example. In the later sections we introduce a variety of other examples to illustrate more complex extensions of the basic approaches. In the next chapter, we will see how HMMs can also be applied to the types of alignment problem discussed in Chapter 2, in Chapter 5 they are applied to searching databases for protein families, and in Chapter 6 to alignment of several sequences simultaneously.

Product Units with Trainable Exponents and Multi-Layer Networks

This chapter reviews and examines a variant type of computational unit which we have recently proposed for use in multi-layer neural networks [3]. Instead of the output of this unit depending on a weighted sum of the inputs, it depends on a weighted product. In justifying the introduction of a new type of unit we explore at some length the rationale behind the use of multi-layer neural networks, and the properties of the computational units within them. At the end of the chapter we discuss a biological model for a single complex neve cell with active dendritic membrane that uses the product units.

Biological sequence analysis: Profile HMMs for sequence families

So far we have concentrated on the intrinsic properties of single sequences, such as CpG islands in DNA, or on pairwise alignment of sequences. However, functional biological sequences typically come in families, and many of the most powerful sequence analysis methods are based on identifying the relationship of an individual sequence to a sequence family. Sequences in a family will have diverged from each other in their primary sequence during evolution, having separated either by a duplication in the genome, or by speciation giving rise to corresponding sequences in related organisms. In either case they normally maintain the same or a related function. Therefore, identifying that a sequence belongs to a family, and aligning it to the other members, often allows inferences about its function. If you already have a set of sequences belonging to a family, you can perform a database search for more members using pairwise alignment with one of the known family members as the query sequence. To be more thorough, you could even search with all the known members one by one. However, pairwise searching with any one of the members may not find sequences distantly related to the ones you have already. An alternative approach is to use statistical features of the whole set of sequences in the search. Similarly, even when family membership is clear, accurate alignment can be often be improved significantly by concentrating on features that are conserved in the whole family.

Biological sequence analysis: Contents

Probablistic models are becoming increasingly important in analyzing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analyzing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it is accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time presents the state of the art in this new and important field.

Biological sequence analysis: Frontmatter

Probablistic models are becoming increasingly important in analyzing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analyzing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it is accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time presents the state of the art in this new and important field.

Biological sequence analysis: Subject index

Probablistic models are becoming increasingly important in analyzing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analyzing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it is accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time presents the state of the art in this new and important field.

Biological sequence analysis: Author index

Probablistic models are becoming increasingly important in analyzing the huge amount of data being produced by large-scale DNA-sequencing efforts such as the Human Genome Project. For example, hidden Markov models are used for analyzing biological sequences, linguistic-grammar-based probabilistic models for identifying RNA secondary structure, and probabilistic evolutionary models for inferring phylogenies of sequences from different organisms. This book gives a unified, up-to-date and self-contained account, with a Bayesian slant, of such methods, and more generally to probabilistic methods of sequence analysis. Written by an interdisciplinary team of authors, it is accessible to molecular biologists, computer scientists, and mathematicians with no formal knowledge of the other fields, and at the same time presents the state of the art in this new and important field.