17,849 research outputs found
Measuring complexity with zippers
Physics concepts have often been borrowed and independently developed by
other fields of science. In this perspective a significant example is that of
entropy in Information Theory. The aim of this paper is to provide a short and
pedagogical introduction to the use of data compression techniques for the
estimate of entropy and other relevant quantities in Information Theory and
Algorithmic Information Theory. We consider in particular the LZ77 algorithm as
case study and discuss how a zipper can be used for information extraction.Comment: 10 pages, 3 figure
Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality
The mutual information between stimulus and spike-train response is commonly
used to monitor neural coding efficiency, but neuronal computation broadly
conceived requires more refined and targeted information measures of
input-output joint processes. A first step towards that larger goal is to
develop information measures for individual output processes, including
information generation (entropy rate), stored information (statistical
complexity), predictable information (excess entropy), and active information
accumulation (bound information rate). We calculate these for spike trains
generated by a variety of noise-driven integrate-and-fire neurons as a function
of time resolution and for alternating renewal processes. We show that their
time-resolution dependence reveals coarse-grained structural properties of
interspike interval statistics; e.g., -entropy rates that diverge less
quickly than the firing rate indicate interspike interval correlations. We also
find evidence that the excess entropy and regularized statistical complexity of
different types of integrate-and-fire neurons are universal in the
continuous-time limit in the sense that they do not depend on mechanism
details. This suggests a surprising simplicity in the spike trains generated by
these model neurons. Interestingly, neurons with gamma-distributed ISIs and
neurons whose spike trains are alternating renewal processes do not fall into
the same universality class. These results lead to two conclusions. First, the
dependence of information measures on time resolution reveals mechanistic
details about spike train generation. Second, information measures can be used
as model selection tools for analyzing spike train processes.Comment: 20 pages, 6 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/trdctim.ht
Predictability, complexity and learning
We define {\em predictive information} as the mutual
information between the past and the future of a time series. Three
qualitatively different behaviors are found in the limit of large observation
times : can remain finite, grow logarithmically, or grow
as a fractional power law. If the time series allows us to learn a model with a
finite number of parameters, then grows logarithmically with
a coefficient that counts the dimensionality of the model space. In contrast,
power--law growth is associated, for example, with the learning of infinite
parameter (or nonparametric) models such as continuous functions with
smoothness constraints. There are connections between the predictive
information and measures of complexity that have been defined both in learning
theory and in the analysis of physical systems through statistical mechanics
and dynamical systems theory. Further, in the same way that entropy provides
the unique measure of available information consistent with some simple and
plausible conditions, we argue that the divergent part of
provides the unique measure for the complexity of dynamics underlying a time
series. Finally, we discuss how these ideas may be useful in different problems
in physics, statistics, and biology.Comment: 53 pages, 3 figures, 98 references, LaTeX2
Learning Discriminative Stein Kernel for SPD Matrices and Its Applications
Stein kernel has recently shown promising performance on classifying images
represented by symmetric positive definite (SPD) matrices. It evaluates the
similarity between two SPD matrices through their eigenvalues. In this paper,
we argue that directly using the original eigenvalues may be problematic
because: i) Eigenvalue estimation becomes biased when the number of samples is
inadequate, which may lead to unreliable kernel evaluation; ii) More
importantly, eigenvalues only reflect the property of an individual SPD matrix.
They are not necessarily optimal for computing Stein kernel when the goal is to
discriminate different sets of SPD matrices. To address the two issues in one
shot, we propose a discriminative Stein kernel, in which an extra parameter
vector is defined to adjust the eigenvalues of the input SPD matrices. The
optimal parameter values are sought by optimizing a proxy of classification
performance. To show the generality of the proposed method, three different
kernel learning criteria that are commonly used in the literature are employed
respectively as a proxy. A comprehensive experimental study is conducted on a
variety of image classification tasks to compare our proposed discriminative
Stein kernel with the original Stein kernel and other commonly used methods for
evaluating the similarity between SPD matrices. The experimental results
demonstrate that, the discriminative Stein kernel can attain greater
discrimination and better align with classification tasks by altering the
eigenvalues. This makes it produce higher classification performance than the
original Stein kernel and other commonly used methods.Comment: 13 page
Artificial Sequences and Complexity Measures
In this paper we exploit concepts of information theory to address the
fundamental problem of identifying and defining the most suitable tools to
extract, in a automatic and agnostic way, information from a generic string of
characters. We introduce in particular a class of methods which use in a
crucial way data compression techniques in order to define a measure of
remoteness and distance between pairs of sequences of characters (e.g. texts)
based on their relative information content. We also discuss in detail how
specific features of data compression techniques could be used to introduce the
notion of dictionary of a given sequence and of Artificial Text and we show how
these new tools can be used for information extraction purposes. We point out
the versatility and generality of our method that applies to any kind of
corpora of character strings independently of the type of coding behind them.
We consider as a case study linguistic motivated problems and we present
results for automatic language recognition, authorship attribution and self
consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression
approach to Information Extraction and Classification" by A. Baronchelli and
V. Loreto. 15 pages; 5 figure
Estimating selection pressures on HIV-1 using phylogenetic likelihood models
Human immunodeficiency virus (HIV-1) can rapidly evolve due to selection pressures exerted by HIV-specific immune responses, antiviral agents, and to allow the virus to establish infection in different compartments in the body. Statistical models applied to HIV-1 sequence data can help to elucidate the nature of these selection pressures through comparisons of non-synonymous (or amino acid changing) and synonymous (or amino acid preserving) substitution rates. These models also need to take into account the non-independence of sequences due to their shared evolutionary history. We review how we have developed these methods and have applied them to characterize the evolution of HIV-1 in vivo.To illustrate our methods, we present an analysis of compartment-specific evolution of HIV-1 env in blood and cerebrospinal fluid and of site-to-site variation in the gag gene of subtype C HIV-1
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