Luis Gonzalo Sánchez Giraldo::Research

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RKHSs provide an elegant representation framework that generalizes well-known linear algorithms. The mainstream of research devoted to the construction of positive definite kernels and algorithm variants the employ the kernel based representation. More recent efforts have moved towards exploring the use of RKHSs in computing high order statistics of the data. Potential uses of high order statistics are not limited to problems such as hypothesis testing, but also provide means to the creation of new learning algorithms that employ these quantities as objective functions. In the context of adaptive systems, information theoretic learning investigates the uses of well-know quantities in information theory as surrogate measures of performance for task-specific measures such as mean squared error, probability of misclassification error, and detection error. For instance, a measure of mutual information between the input and the output of an adaptive system can be used in learning the parameters of such system. Nevertheless, to be able to adapt from experience, it is necessary to estimate the information theoretic quantities directly from data. My work has focused on investigating the relations between RKHSs and information theoretic quantities to provide estimators of information theoretic quantities that exploit the representational capabilities of RKHSs. The proposed estimators can be regarded as statistics based on reproducing kernels that can be applied to a variety of learning algorithms based on information theoretic objective functions.

Information Theoretic Learning

Mutual information animation
metric learning animation
forepaw locations monkey directions
    PRI denoising

Online Kernel-Based Learning

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Last update: Feb 5, 2019