55,906 research outputs found
Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method
Understanding the dynamics of neural networks is a major challenge in
experimental neuroscience. For that purpose, a modelling of the recorded
activity that reproduces the main statistics of the data is required. In a
first part, we present a review on recent results dealing with spike train
statistics analysis using maximum entropy models (MaxEnt). Most of these
studies have been focusing on modelling synchronous spike patterns, leaving
aside the temporal dynamics of the neural activity. However, the maximum
entropy principle can be generalized to the temporal case, leading to Markovian
models where memory effects and time correlations in the dynamics are properly
taken into account. In a second part, we present a new method based on
Monte-Carlo sampling which is suited for the fitting of large-scale
spatio-temporal MaxEnt models. The formalism and the tools presented here will
be essential to fit MaxEnt spatio-temporal models to large neural ensembles.Comment: 41 pages, 10 figure
An Empirical Examination of Maximum Entropy Estimation.
Maximum entropy estimation is a relatively new estimation technique in econometrics. We carry out several Monte Carlo experiments using real data as a basis in order to understand the properties of the maximum entropy estimator. We compare the maximum entropy and generalized maximum entropy estimators to traditional estimation techniques in linear regression, binary choice, and multinomial choice models. In addition, we discuss maximum entropy estimation in censored and truncated regression models. We find that the generalized maximum entropy estimator dominates the logit estimator and the multinomial logit estimator in Monte Carlo experiments. The generalized maximum entropy estimator in discrete choice models allows us to jointly estimate the unknown probabilities and the unknown errors resulting in more uniform predicted probabilities and reducing the variance of the parameter estimates. In the linear regression problem, the generalized maximum entropy estimator allows us to impose nonsample information about the unknown parameters and errors. However, we must impose a set of support points for unknown parameters and errors, which is not always an easy thing to do. We find that when we do specify nonsample information that is correct, the generalized maximum entropy estimator has lower risk than either the ordinary least squares or the inequality restricted least squares estimators. From our sampling experiments using real data, we find that maximum entropy estimation is a viable estimation technique in several econometric models
Selection of proposal distributions for generalized importance sampling estimators
The standard importance sampling (IS) estimator, generally does not work well
in examples involving simultaneous inference on several targets as the
importance weights can take arbitrarily large values making the estimator
highly unstable. In such situations, alternative generalized IS estimators
involving samples from multiple proposal distributions are preferred. Just like
the standard IS, the success of these multiple IS estimators crucially depends
on the choice of the proposal distributions. The selection of these proposal
distributions is the focus of this article. We propose three methods based on
(i) a geometric space filling coverage criterion, (ii) a minimax variance
approach, and (iii) a maximum entropy approach. The first two methods are
applicable to any multi-proposal IS estimator, whereas the third approach is
described in the context of Doss's (2010) two-stage IS estimator. For the first
method we propose a suitable measure of coverage based on the symmetric
Kullback-Leibler divergence, while the second and third approaches use
estimates of asymptotic variances of Doss's (2010) IS estimator and Geyer's
(1994) reverse logistic estimator, respectively. Thus, we provide consistent
spectral variance estimators for these asymptotic variances. The proposed
methods for selecting proposal densities are illustrated using various detailed
examples
Numerical Study of the Oscillatory Convergence to the Attractor at the Edge of Chaos
This paper compares three different types of ``onset of chaos'' in the
logistic and generalized logistic map: the Feigenbaum attractor at the end of
the period doubling bifurcations; the tangent bifurcation at the border of the
period three window; the transition to chaos in the generalized logistic with
inflection 1/2 (), in which the main bifurcation
cascade, as well as the bifurcations generated by the periodic windows in the
chaotic region, collapse in a single point. The occupation number and the
Tsallis entropy are studied. The different regimes of convergence to the
attractor, starting from two kinds of far-from-equilibrium initial conditions,
are distinguished by the presence or absence of log-log oscillations, by
different power-law scalings and by a gap in the saturation levels. We show
that the escort distribution implicit in the Tsallis entropy may tune the
log-log oscillations or the crossover times.Comment: 10 pages, 5 figure
Origins of the Combinatorial Basis of Entropy
The combinatorial basis of entropy, given by Boltzmann, can be written , where is the dimensionless entropy, is the
number of entities and is number of ways in which a given
realization of a system can occur (its statistical weight). This can be
broadened to give generalized combinatorial (or probabilistic) definitions of
entropy and cross-entropy: and , where is the probability of a given
realization, is a convenient transformation function, is a
scaling parameter and an arbitrary constant. If or
satisfy the multinomial weight or distribution, then using
and , and asymptotically
converge to the Shannon and Kullback-Leibler functions. In general, however,
or need not be multinomial, nor may they approach an
asymptotic limit. In such cases, the entropy or cross-entropy function can be
{\it defined} so that its extremization ("MaxEnt'' or "MinXEnt"), subject to
the constraints, gives the ``most probable'' (``MaxProb'') realization of the
system. This gives a probabilistic basis for MaxEnt and MinXEnt, independent of
any information-theoretic justification.
This work examines the origins of the governing distribution ....
(truncated)Comment: MaxEnt07 manuscript, version 4 revise
Quantitative Comparison of Abundance Structures of Generalized Communities: From B-Cell Receptor Repertoires to Microbiomes
The \emph{community}, the assemblage of organisms co-existing in a given
space and time, has the potential to become one of the unifying concepts of
biology, especially with the advent of high-throughput sequencing experiments
that reveal genetic diversity exhaustively. In this spirit we show that a tool
from community ecology, the Rank Abundance Distribution (RAD), can be turned by
the new MaxRank normalization method into a generic, expressive descriptor for
quantitative comparison of communities in many areas of biology. To illustrate
the versatility of the method, we analyze RADs from various \emph{generalized
communities}, i.e.\ assemblages of genetically diverse cells or organisms,
including human B cells, gut microbiomes under antibiotic treatment and of
different ages and countries of origin, and other human and environmental
microbial communities. We show that normalized RADs enable novel quantitative
approaches that help to understand structures and dynamics of complex
generalize communities
- âŠ