4,185 research outputs found
Nonparametric likelihood based estimation of linear filters for point processes
We consider models for multivariate point processes where the intensity is
given nonparametrically in terms of functions in a reproducing kernel Hilbert
space. The likelihood function involves a time integral and is consequently not
given in terms of a finite number of kernel evaluations. The main result is a
representation of the gradient of the log-likelihood, which we use to derive
computable approximations of the log-likelihood and the gradient by time
discretization. These approximations are then used to minimize the approximate
penalized log-likelihood. For time and memory efficiency the implementation
relies crucially on the use of sparse matrices. As an illustration we consider
neuron network modeling, and we use this example to investigate how the
computational costs of the approximations depend on the resolution of the time
discretization. The implementation is available in the R package ppstat.Comment: 10 pages, 3 figure
Learning Multiple Visual Tasks while Discovering their Structure
Multi-task learning is a natural approach for computer vision applications
that require the simultaneous solution of several distinct but related
problems, e.g. object detection, classification, tracking of multiple agents,
or denoising, to name a few. The key idea is that exploring task relatedness
(structure) can lead to improved performances.
In this paper, we propose and study a novel sparse, non-parametric approach
exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued
functions. We develop a suitable regularization framework which can be
formulated as a convex optimization problem, and is provably solvable using an
alternating minimization approach. Empirical tests show that the proposed
method compares favorably to state of the art techniques and further allows to
recover interpretable structures, a problem of interest in its own right.Comment: 19 pages, 3 figures, 3 table
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