2,152 research outputs found
Information Theoretic Limits for Standard and One-Bit Compressed Sensing with Graph-Structured Sparsity
In this paper, we analyze the information theoretic lower bound on the
necessary number of samples needed for recovering a sparse signal under
different compressed sensing settings. We focus on the weighted graph model, a
model-based framework proposed by Hegde et al. (2015), for standard compressed
sensing as well as for one-bit compressed sensing. We study both the noisy and
noiseless regimes. Our analysis is general in the sense that it applies to any
algorithm used to recover the signal. We carefully construct restricted
ensembles for different settings and then apply Fano's inequality to establish
the lower bound on the necessary number of samples. Furthermore, we show that
our bound is tight for one-bit compressed sensing, while for standard
compressed sensing, our bound is tight up to a logarithmic factor of the number
of non-zero entries in the signal
Structured, sparse regression with application to HIV drug resistance
We introduce a new version of forward stepwise regression. Our modification
finds solutions to regression problems where the selected predictors appear in
a structured pattern, with respect to a predefined distance measure over the
candidate predictors. Our method is motivated by the problem of predicting
HIV-1 drug resistance from protein sequences. We find that our method improves
the interpretability of drug resistance while producing comparable predictive
accuracy to standard methods. We also demonstrate our method in a simulation
study and present some theoretical results and connections.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS428 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Learning the String Partial Order
We show that most structured prediction problems can be solved in linear time
and space by considering them as partial orderings of the tokens in the input
string. Our method computes real numbers for each token in an input string and
sorts the tokens accordingly, resulting in as few as 2 total orders of the
tokens in the string. Each total order possesses a set of edges oriented from
smaller to greater tokens. The intersection of total orders results in a
partial order over the set of input tokens, which is then decoded into a
directed graph representing the desired structure. Experiments show that our
method achieves 95.4 LAS and 96.9 UAS by using an intersection of 2 total
orders, 95.7 LAS and 97.1 UAS with 4 on the English Penn Treebank dependency
parsing benchmark. Our method is also the first linear-complexity coreference
resolution model and achieves 79.2 F1 on the English OntoNotes benchmark, which
is comparable with state of the art.Comment: 12 page
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