We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.

We employ an efficient method using Bayesian and linear classifiers for analyzing the dynamics of information in high-dimensional states of generic cortical microcircuit models. It is shown that such recurrent circuits of spiking neurons have an inherent capability to carry out rapid computations on complex spike patterns, merging information contained in the order of spike arrival with previously acquired context information.

Clustering aims at extracting hidden structure in dataset. While the problem of finding compact clusters has been widely studied in the literature, extracting arbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm which tackles the problem by a two step procedure: first the data are transformed in such a way that elongated structures become compact ones. In a second step, these new objects are clustered by optimizing a compactness-based criterion. The advantages of the method over related approaches are threefold: (i) robustness properties of compactness-based criteria naturally transfer to the problem of extracting elongated structures, leading to a model which is highly robust against outlier objects; (ii) the transformed distances induce a Mercer kernel which allows us to formulate a polynomial approximation scheme to the generally N P-hard clustering problem; (iii) the new method does not contain free kernel parameters in contrast to methods like spectral clustering or mean-shift clustering.

In pattern classification tasks, errors are introduced because of differences between the true model and the one obtained via model estimation. Using likelihood-ratio based classification, it is possible to correct for this discrepancy by finding class-pair specific terms to adjust the likelihood ratio directly, and that can make class-pair preference relationships intransitive. In this work, we introduce new methodology that makes necessary corrections to the likelihood ratio, specifically those that are necessary to achieve perfect classification (but not perfect likelihood-ratio correction which can be overkill). The new corrections, while weaker than previously reported such adjustments, are analytically challenging since they involve discontinuous functions, therefore requiring several approximations. We test a number of these new schemes on an isolatedword speech recognition task as well as on the UCI machine learning data sets. Results show that by using the bias terms calculated in this new way, classification accuracy can substantially improve over both the baseline and over our previous results.

We compute approximate analytical bootstrap averages for support vector classification using a combination of the replica method of statistical physics and the TAP approach for approximate inference. We test our method on a few datasets and compare it with exact averages obtained by extensive Monte-Carlo sampling.

At a cocktail party, a listener can selectively attend to a single voice and filter out other acoustical interferences. How to simulate this perceptual ability remains a great challenge. This paper describes a novel supervised learning approach to speech segregation, in which a target speech signal is separated from interfering sounds using spatial location cues: interaural time differences (ITD) and interaural intensity differences (IID). Motivated by the auditory masking effect, we employ the notion of an ideal time-frequency binary mask, which selects the target if it is stronger than the interference in a local time-frequency unit. Within a narrow frequency band, modifications to the relative strength of the target source with respect to the interference trigger systematic changes for estimated ITD and IID.

Clustering aims at extracting hidden structure in dataset. While the problem of finding compact clusters has been widely studied in the literature, extracting arbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm which tackles the problem by a two step procedure: first the data are transformed in such a way that elongated structures become compact ones. In a second step, these new objects are clustered by optimizing a compactness-based criterion. The advantages of the method over related approaches are threefold: (i) robustness properties of compactness-based criteria naturally transfer to the problem of extracting elongated structures, leading to a model which is highly robust against outlier objects; (ii) the transformed distances induce a Mercer kernel which allows us to formulate a polynomial approximation scheme to the generally N P-hard clustering problem; (iii) the new method does not contain free kernel parameters in contrast to methods like spectral clustering or mean-shift clustering.

Is there a way for an algorithm linked to an unknown body to infer by itself information about this body and the world it is in? Taking the case of space for example, is there a way for this algorithm to realize that its body is in a three dimensional world? Is it possible for this algorithm to discover how to move in a straight line? And more basically: do these questions make any sense at all given that the algorithm only has access to the very high-dimensional data consisting of its sensory inputs and motor outputs? We demonstrate in this article how these questions can be given a positive answer. We show that it is possible to make an algorithm that, by analyzing the law that links its motor outputs to its sensory inputs, discovers information about the structure of the world regardless of the devices constituting the body it is linked to. We present results from simulations demonstrating a way to issue motor orders resulting in "fundamental" movements of the body as regards the structure of the physical world.

In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions which allow nonlinear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our nonlinear algorithm can be further kernelised leading to'twin kernel PCA' in which a mapping between feature spaces occurs.

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.