7,087 research outputs found
Algorithms for Learning Sparse Additive Models with Interactions in High Dimensions
A function is a Sparse Additive
Model (SPAM), if it is of the form where , . Assuming 's, to be unknown, there exists extensive work
for estimating from its samples. In this work, we consider a generalized
version of SPAMs, that also allows for the presence of a sparse number of
second order interaction terms. For some , with , the function is now assumed to be of the form:
. Assuming we have the
freedom to query anywhere in its domain, we derive efficient algorithms
that provably recover with finite sample bounds.
Our analysis covers the noiseless setting where exact samples of are
obtained, and also extends to the noisy setting where the queries are corrupted
with noise. For the noisy setting in particular, we consider two noise models
namely: i.i.d Gaussian noise and arbitrary but bounded noise. Our main methods
for identification of essentially rely on estimation of sparse
Hessian matrices, for which we provide two novel compressed sensing based
schemes. Once are known, we show how the
individual components , can be estimated via
additional queries of , with uniform error bounds. Lastly, we provide
simulation results on synthetic data that validate our theoretical findings.Comment: To appear in Information and Inference: A Journal of the IMA. Made
following changes after review process: (a) Corrected typos throughout the
text. (b) Corrected choice of sampling distribution in Section 5, see eqs.
(5.2), (5.3). (c) More detailed comparison with existing work in Section 8.
(d) Added Section B in appendix on roots of cubic equatio
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
- …