20,326 research outputs found
Lexical representation explains cortical entrainment during speech comprehension
Results from a recent neuroimaging study on spoken sentence comprehension
have been interpreted as evidence for cortical entrainment to hierarchical
syntactic structure. We present a simple computational model that predicts the
power spectra from this study, even though the model's linguistic knowledge is
restricted to the lexical level, and word-level representations are not
combined into higher-level units (phrases or sentences). Hence, the cortical
entrainment results can also be explained from the lexical properties of the
stimuli, without recourse to hierarchical syntax.Comment: Submitted for publicatio
New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit
In this paper we define a new coherence index, named the global 2-coherence,
of a given dictionary and study its relationship with the traditional mutual
coherence and the restricted isometry constant. By exploring this relationship,
we obtain more general results on sparse signal reconstruction using greedy
algorithms in the compressive sensing (CS) framework. In particular, we obtain
an improved bound over the best known results on the restricted isometry
constant for successful recovery of sparse signals using orthogonal matching
pursuit (OMP).Comment: arXiv admin note: substantial text overlap with arXiv:1307.194
On Nesting Monte Carlo Estimators
Many problems in machine learning and statistics involve nested expectations
and thus do not permit conventional Monte Carlo (MC) estimation. For such
problems, one must nest estimators, such that terms in an outer estimator
themselves involve calculation of a separate, nested, estimation. We
investigate the statistical implications of nesting MC estimators, including
cases of multiple levels of nesting, and establish the conditions under which
they converge. We derive corresponding rates of convergence and provide
empirical evidence that these rates are observed in practice. We further
establish a number of pitfalls that can arise from naive nesting of MC
estimators, provide guidelines about how these can be avoided, and lay out
novel methods for reformulating certain classes of nested expectation problems
into single expectations, leading to improved convergence rates. We demonstrate
the applicability of our work by using our results to develop a new estimator
for discrete Bayesian experimental design problems and derive error bounds for
a class of variational objectives.Comment: To appear at International Conference on Machine Learning 201
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