My goal in this chapter of lecture notes is to introduce the class of loglinear models and study them from the algebraic perspective. There are at least three different ways to introduce log-linear models: in statistics they are also called discrete exponential families and in algebraic geometry they are known as toric varieties. Our goal is to introduce these models from all three perspective ...

Recently, there have been remarkable advances in modeling the relationships between the sensory environment, neuronal responses, and behavior. However, most models cannot encompass variable stimulus-response relationships such as varying response latencies and state or context dependence of the neural code. Here, we consider response modeling as a dynamic alignment problem and model stimulus an...

The paper presents the application of Hidden Markov Models to text generation in Polish language. A program generating text, taking advantage of Hidden Markov Models was developed. The program uses a reference text to learn the possible sequences of letters. The results of text processing have been also discussed. The presented approach can be also helpful in speech recognition process. Key-Wor...

Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-v...

Hidden Markov Model Regression (HMMR) is an extension of the Hidden Markov Model (HMM) to regression analysis. We assume that the parameters of the regression model are determined by the outcome of a nite-state Markov chain and that the error terms are conditionally independent normally distributed with mean zero and state dependent variance. The theory of HMM regression is quite new, but some ...

Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents solutions to the three central inference problems for LOHMMs: evaluation, most likely hidden state sequence and parameter estimation. The resulting representation a...

Although much effort has been put into speech understanding systems there still exists a rather wide gap between acoustic recognition and linguistic interpretation. We propose a formalism for an extremely close interaction of acoustic recognition and higher level analysis. Instead of a strict horizontal interface at the level of hypothesized word sequences or lattices, a vertical interface to t...

MOTIVATION Statistical sequence comparison techniques, such as hidden Markov models and generalized profiles, calculate the probability that a sequence was generated by a given model. Log-odds scoring is a means of evaluating this probability by comparing it to a null hypothesis, usually a simpler statistical model intended to represent the universe of sequences as a whole, rather than the grou...

By thinking of each state in a hidden Markov model as corresponding to some spatial region of a fictitious topology space it is possible to naturally define neighbouring states as those which are connected in that space. The transition matrix can then be constrained to allow transitions only between neighbours; this means that all valid state sequences correspond to connected paths in the topol...