Probabilistic prediction and context tree identification in the Goalkeeper game.

In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions-left, center or right-to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: (1) the shape of the context tree summarizing the dependencies between present and past directions; (2) the entropy of the stochastic chain used to generate the sequences of events; (3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.

Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data.

Using a new probabilistic approach we model the relationship between sequences of auditory stimuli generated by stochastic chains and the electroencephalographic (EEG) data acquired while 19 participants were exposed to those stimuli. The structure of the chains generating the stimuli are characterized by rooted and labeled trees whose leaves, henceforth called contexts, represent the sequences of past stimuli governing the choice of the next stimulus. A classical conjecture claims that the brain assigns probabilistic models to samples of stimuli. If this is true, then the context tree generating the sequence of stimuli should be encoded in the brain activity. Using an innovative statistical procedure we show that this context tree can effectively be extracted from the EEG data, thus giving support to the classical conjecture.

Support vector regression for functional data in multivariate calibration problems.

Quantitative analyses involving instrumental signals, such as chromatograms, NIR, and MIR spectra have been successfully applied nowadays for the solution of important chemical tasks. Multivariate calibration is very useful for such purposes and the commonly used methods in chemometrics consider each sample spectrum as a sequence of discrete data points. An alternative way to analyze spectral data is to consider each sample as a function, in which a functional data is obtained. Concerning regression, some linear and nonparametric regression methods have been generalized to functional data. This paper proposes the use of the recently introduced method, support vector regression for functional data (FDA-SVR) for the solution of linear and nonlinear multivariate calibration problems. Three different spectral datasets were analyzed and a comparative study was carried out to test its performance with respect to some traditional calibration methods used in chemometrics such as PLS, SVR and LS-SVR. The satisfactory results obtained with FDA-SVR suggest that it can be an effective and promising tool for multivariate calibration tasks.