Concentration inequalities for mean field particle models

This article is concerned with the fluctuations and the concentration properties of a general class of discrete generation and mean field particle interpretations of nonlinear measure valued processes. We combine an original stochastic perturbation analysis with a concentration analysis for triangular arrays of conditionally independent random sequences, which may be of independent interest. Under some additional stability properties of the limiting measure valued processes, uniform concentration properties, with respect to the time parameter, are also derived. The concentration inequalities presented here generalize the classical Hoeffding, Bernstein and Bennett inequalities for independent random sequences to interacting particle systems, yielding very new results for this class of models. We illustrate these results in the context of McKean-Vlasov-type diffusion models, McKean collision-type models of gases and of a class of Feynman-Kac distribution flows arising in stochastic engineering sciences and in molecular chemistry.Comment: Published in at http://dx.doi.org/10.1214/10-AAP716 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-Armed Bandits for Intelligent Tutoring Systems

We present an approach to Intelligent Tutoring Systems which adaptively personalizes sequences of learning activities to maximize skills acquired by students, taking into account the limited time and motivational resources. At a given point in time, the system proposes to the students the activity which makes them progress faster. We introduce two algorithms that rely on the empirical estimation of the learning progress, RiARiT that uses information about the difficulty of each exercise and ZPDES that uses much less knowledge about the problem. The system is based on the combination of three approaches. First, it leverages recent models of intrinsically motivated learning by transposing them to active teaching, relying on empirical estimation of learning progress provided by specific activities to particular students. Second, it uses state-of-the-art Multi-Arm Bandit (MAB) techniques to efficiently manage the exploration/exploitation challenge of this optimization process. Third, it leverages expert knowledge to constrain and bootstrap initial exploration of the MAB, while requiring only coarse guidance information of the expert and allowing the system to deal with didactic gaps in its knowledge. The system is evaluated in a scenario where 7-8 year old schoolchildren learn how to decompose numbers while manipulating money. Systematic experiments are presented with simulated students, followed by results of a user study across a population of 400 school children

Robust brain-computer interfaces

A brain-computer interface (BCI) enables direct communication from the brain to devices, bypassing the traditional pathway of peripheral nerves and muscles. Current BCIs aimed at patients require that the user invests weeks, or even months, to learn the skill to intentionally modify their brain signals. This can be reduced to a calibration session of about half an hour per session if machine learning (ML) methods are used. The laborious recalibration is still needed due to inter-session differences in the statistical properties of the electroencephalography (EEG) signal. Further, the natural variability in spontaneous EEG violates basic assumptions made by the ML methods used to train the BCI classifier, and causes the classification accuracy to fluctuate unpredictably. These fluctuations make the current generation of BCIs unreliable. In this dissertation,we will investigate the nature of these variations in the EEG distributions, and introduce two new, complementary methods to overcome these two key issues. To confirm the problem of non-stationary brain signals, we first show that BCIs based on commonly used signal features are sensitive to changes in the mental state of the user. We proceed by describing a method aimed at removing these changes in signal feature distributions. We have devised a method that uses a second-order baseline (SOB) to specifically isolate these relative changes in neuronal firing synchrony. To the best of our knowledge this is the first BCI classifier that works on out-of-sample subjects without any loss of performance. Still, the assumption made by ML methods that the training data consists of samples that are independent and identically distributed (iid) is violated, because EEG samples nearby in time are highly correlated. Therefore we derived a generalization of the well-known support vector machine (SVM) classifier, that takes the resulting chronological structure of classification errors into account. Both on artificial data and real BCI data, overfitting is reduced with this dependent samples support vector machine (dSVM), leading to BCIs with an increased information throughput