38,811 research outputs found
Heavy-tailed Independent Component Analysis
Independent component analysis (ICA) is the problem of efficiently recovering
a matrix from i.i.d. observations of
where is a random vector with mutually independent
coordinates. This problem has been intensively studied, but all existing
efficient algorithms with provable guarantees require that the coordinates
have finite fourth moments. We consider the heavy-tailed ICA problem
where we do not make this assumption, about the second moment. This problem
also has received considerable attention in the applied literature. In the
present work, we first give a provably efficient algorithm that works under the
assumption that for constant , each has finite
-moment, thus substantially weakening the moment requirement
condition for the ICA problem to be solvable. We then give an algorithm that
works under the assumption that matrix has orthogonal columns but requires
no moment assumptions. Our techniques draw ideas from convex geometry and
exploit standard properties of the multivariate spherical Gaussian distribution
in a novel way.Comment: 30 page
High-Performance FPGA Implementation of Equivariant Adaptive Separation via Independence Algorithm for Independent Component Analysis
Independent Component Analysis (ICA) is a dimensionality reduction technique
that can boost efficiency of machine learning models that deal with probability
density functions, e.g. Bayesian neural networks. Algorithms that implement
adaptive ICA converge slower than their nonadaptive counterparts, however, they
are capable of tracking changes in underlying distributions of input features.
This intrinsically slow convergence of adaptive methods combined with existing
hardware implementations that operate at very low clock frequencies necessitate
fundamental improvements in both algorithm and hardware design. This paper
presents an algorithm that allows efficient hardware implementation of ICA.
Compared to previous work, our FPGA implementation of adaptive ICA improves
clock frequency by at least one order of magnitude and throughput by at least
two orders of magnitude. Our proposed algorithm is not limited to ICA and can
be used in various machine learning problems that use stochastic gradient
descent optimization
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