22,172 research outputs found
The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction
Stimulus dimensionality-reduction methods in neuroscience seek to identify a
low-dimensional space of stimulus features that affect a neuron's probability
of spiking. One popular method, known as maximally informative dimensions
(MID), uses an information-theoretic quantity known as "single-spike
information" to identify this space. Here we examine MID from a model-based
perspective. We show that MID is a maximum-likelihood estimator for the
parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical
single-spike information corresponds to the normalized log-likelihood under a
Poisson model. This equivalence implies that MID does not necessarily find
maximally informative stimulus dimensions when spiking is not well described as
Poisson. We provide several examples to illustrate this shortcoming, and derive
a lower bound on the information lost when spiking is Bernoulli in discrete
time bins. To overcome this limitation, we introduce model-based dimensionality
reduction methods for neurons with non-Poisson firing statistics, and show that
they can be framed equivalently in likelihood-based or information-theoretic
terms. Finally, we show how to overcome practical limitations on the number of
stimulus dimensions that MID can estimate by constraining the form of the
non-parametric nonlinearity in an LNP model. We illustrate these methods with
simulations and data from primate visual cortex
On the Hardness of Entropy Minimization and Related Problems
We investigate certain optimization problems for Shannon information
measures, namely, minimization of joint and conditional entropies ,
, , and maximization of mutual information , over
convex regions. When restricted to the so-called transportation polytopes (sets
of distributions with fixed marginals), very simple proofs of NP-hardness are
obtained for these problems because in that case they are all equivalent, and
their connection to the well-known \textsc{Subset sum} and \textsc{Partition}
problems is revealed. The computational intractability of the more general
problems over arbitrary polytopes is then a simple consequence. Further, a
simple class of polytopes is shown over which the above problems are not
equivalent and their complexity differs sharply, namely, minimization of
and is trivial, while minimization of and
maximization of are strongly NP-hard problems. Finally, two new
(pseudo)metrics on the space of discrete probability distributions are
introduced, based on the so-called variation of information quantity, and
NP-hardness of their computation is shown.Comment: IEEE Information Theory Workshop (ITW) 201
Resampling methods for parameter-free and robust feature selection with mutual information
Combining the mutual information criterion with a forward feature selection
strategy offers a good trade-off between optimality of the selected feature
subset and computation time. However, it requires to set the parameter(s) of
the mutual information estimator and to determine when to halt the forward
procedure. These two choices are difficult to make because, as the
dimensionality of the subset increases, the estimation of the mutual
information becomes less and less reliable. This paper proposes to use
resampling methods, a K-fold cross-validation and the permutation test, to
address both issues. The resampling methods bring information about the
variance of the estimator, information which can then be used to automatically
set the parameter and to calculate a threshold to stop the forward procedure.
The procedure is illustrated on a synthetic dataset as well as on real-world
examples
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