Learning blind source separation
The problem of recovering signals from linear mixtures, with only partial knowledge of the mixing process and the signals---a problem often referred to as blind source separation---is a central problem in signal processing. It has applications in many fields, including speech processing, network tomography and biomedical imaging. 
Current algorithms can only be applied successfully with specific assumptions regarding the mixing process and the underlying sources. In this thesis, we proposed three sets of algorithms that allow to relax some of those assumptions, using tools from machine learning. 
In the situation where sources are assumed statistically independent and there are as many sources as sensors, a problem usually referred to as independent component analysis (ICA), we propose an algorithm that is robust to source densities, that make use of a measure of independence based on reproducing kernel Hilbert spaces. 
We also propose an algorithm to relax the assumption of independence made by most ICA algorithms, by using statistical dependencies based on probabilistic graphical models. By using tree-structured graphical models, we are able to estimate jointly the mixing process parameters and the pattern of dependencies among the underlying sources. 
Finally, we present an algorithm dedicated to blind separation of speech signals from only one sensor. We formulate the problem of speech separation as a problem in segmenting the spectrogram of the signal into two or more disjoint sets. We then build feature sets for our segmenter using classical cues from speech psychophysics. By taking advantage of the fact that we can generate training examples for segmentation by artificially superposing separately-recorded signals, we can learn parameters of similarity matrices that can be used for spectral clustering.