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This talk is about representation learning with a nontrivial geometry
of variables. 

A convolutional neural network can be viewed as a statistical machine to
detect and count features in an image progressively through a multi-scale
system. The constructed features are insensitive to nuance variations in
the input, while sufficiently discriminative to predict labels. We
introduce the Haar scattering transform as a model of such a system for
unsupervised learning. Employing Haar wavelets makes it applicable to data
lying on graphs that are not necessarily pixel grids. When the underlying
graph is unknown, an adaptive version of the algorithm infers the geometry
of variables by optimizing the construction of the Haar basis so as to
minimize data variation. Given time, I will also mention an undergoing
project of flow cytometry data analysis, where histogram-like features are
used for comparing empirical distributions. After "binning" samples on a
mesh in space, the problem can be closely related to feature learning when
a variable geometry is present.