758 research outputs found
Parametric inference in the large data limit using maximally informative models
Motivated by data-rich experiments in transcriptional regulation and sensory
neuroscience, we consider the following general problem in statistical
inference. When exposed to a high-dimensional signal S, a system of interest
computes a representation R of that signal which is then observed through a
noisy measurement M. From a large number of signals and measurements, we wish
to infer the "filter" that maps S to R. However, the standard method for
solving such problems, likelihood-based inference, requires perfect a priori
knowledge of the "noise function" mapping R to M. In practice such noise
functions are usually known only approximately, if at all, and using an
incorrect noise function will typically bias the inferred filter. Here we show
that, in the large data limit, this need for a pre-characterized noise function
can be circumvented by searching for filters that instead maximize the mutual
information I[M;R] between observed measurements and predicted representations.
Moreover, if the correct filter lies within the space of filters being
explored, maximizing mutual information becomes equivalent to simultaneously
maximizing every dependence measure that satisfies the Data Processing
Inequality. It is important to note that maximizing mutual information will
typically leave a small number of directions in parameter space unconstrained.
We term these directions "diffeomorphic modes" and present an equation that
allows these modes to be derived systematically. The presence of diffeomorphic
modes reflects a fundamental and nontrivial substructure within parameter
space, one that is obscured by standard likelihood-based inference.Comment: To appear in Neural Computatio
Equitability, mutual information, and the maximal information coefficient
Reshef et al. recently proposed a new statistical measure, the "maximal
information coefficient" (MIC), for quantifying arbitrary dependencies between
pairs of stochastic quantities. MIC is based on mutual information, a
fundamental quantity in information theory that is widely understood to serve
this need. MIC, however, is not an estimate of mutual information. Indeed, it
was claimed that MIC possesses a desirable mathematical property called
"equitability" that mutual information lacks. This was not proven; instead it
was argued solely through the analysis of simulated data. Here we show that
this claim, in fact, is incorrect. First we offer mathematical proof that no
(non-trivial) dependence measure satisfies the definition of equitability
proposed by Reshef et al.. We then propose a self-consistent and more general
definition of equitability that follows naturally from the Data Processing
Inequality. Mutual information satisfies this new definition of equitability
while MIC does not. Finally, we show that the simulation evidence offered by
Reshef et al. was artifactual. We conclude that estimating mutual information
is not only practical for many real-world applications, but also provides a
natural solution to the problem of quantifying associations in large data sets
Kerfuffle: a web tool for multi-species gene colocalization analysis
The evolutionary pressures that underlie the large-scale functional
organization of the genome are not well understood in eukaryotes. Recent
evidence suggests that functionally similar genes may colocalize (cluster) in
the eukaryotic genome, suggesting the role of chromatin-level gene regulation
in shaping the physical distribution of coordinated genes. However, few of the
bioinformatic tools currently available allow for a systematic study of gene
colocalization across several, evolutionarily distant species. Kerfuffle is a
web tool designed to help discover, visualize, and quantify the physical
organization of genomes by identifying significant gene colocalization and
conservation across the assembled genomes of available species (currently up to
47, from humans to worms). Kerfuffle only requires the user to specify a list
of human genes and the names of other species of interest. Without further
input from the user, the software queries the e!Ensembl BioMart server to
obtain positional information and discovers homology relations in all genes and
species specified. Using this information, Kerfuffle performs a multi-species
clustering analysis, presents downloadable lists of clustered genes, performs
Monte Carlo statistical significance calculations, estimates how conserved gene
clusters are across species, plots histograms and interactive graphs, allows
users to save their queries, and generates a downloadable visualization of the
clusters using the Circos software. These analyses may be used to further
explore the functional roles of gene clusters by interrogating the enriched
molecular pathways associated with each cluster.Comment: BMC Bioinformatics, In pres
Estimating mutual information and multi--information in large networks
We address the practical problems of estimating the information relations
that characterize large networks. Building on methods developed for analysis of
the neural code, we show that reliable estimates of mutual information can be
obtained with manageable computational effort. The same methods allow
estimation of higher order, multi--information terms. These ideas are
illustrated by analyses of gene expression, financial markets, and consumer
preferences. In each case, information theoretic measures correlate with
independent, intuitive measures of the underlying structures in the system
Dynamic plasticity in coupled avian midbrain maps
Internal mapping of the external environment is carried out using the receptive fields of topographic neurons in the brain, and in a normal barn owl the aural and visual subcortical maps are aligned from early experiences. However, instantaneous misalignment of the aural and visual stimuli has been observed to result in adaptive behavior, manifested by functional and anatomical changes of the auditory processing system. Using methods of information theory and statistical mechanics a model of the adaptive dynamics of the aural receptive field is presented and analyzed. The dynamics is determined by maximizing the mutual information between the neural output and the weighted sensory neural inputs, admixed with noise, subject to biophysical constraints. The reduced costs of neural rewiring, as in the case of young barn owls, reveal two qualitatively different types of receptive field adaptation depending on the magnitude of the audiovisual misalignment. By letting the misalignment increase with time, it is shown that the ability to adapt can be increased even when neural rewiring costs are high, in agreement with recent experimental reports of the increased plasticity of the auditory space map in adult barn owls due to incremental learning. Finally, a critical speed of misalignment is identified, demarcating the crossover from adaptive to nonadaptive behavior
Palpitations and asthenia associated with venlafaxine in a CYP2D6 poor metabolizer and CYP2C19 intermediate metabolizer
Cardiotoxicity has been extensively reported in venlafaxine (VEN) overdoses. Asthenia is also among the common side effects described for this antidepressant. VEN is metabolized mainly by CYP2D6 and to a minor extent by CYP2C19 to the major active metabolite O-desmethylvenlafaxine (ODV). Altered pharmacokinetic parameters in patients with polymorphisms in the CYP2D6 and CYP2C19 genes that result in decreased enzymatic activity have been documented. Here we describe a patient case of VEN associated palpitations and asthenia. The patient takes VEN extended release 150 mg twice daily. Genotyping confirmed the patient is a poor metabolizer for CYP2D6 and an intermediate metabolizer for CYP2C19. We propose that the palpitations and asthenia are related to sustained VEN exposure due to reduced metabolism
Relaxation of an electron system: Conserving approximation
The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to soften the plasmon dispersion of both two- and three-dimensional systems. Finally, we consider the consequences for a hydrodynamic theory of a d-dimensional interacting electron gas, and by incorporating the competition between relaxation and inertial effects we derive generalised hydrodynamic equations applicable to arbitrary frequencies
Reply to Murrell et al.: Noise matters
The concept of statistical “equitability” plays a central role in the 2011 paper by Reshef et al. (1). Formalizing equitability first requires formalizing the notion of a “noisy functional relationship,” that is, a relationship between two real variables, X and Y, having the form Y=f(X)+η, where f is a function and η is a noise term. Whether a dependence measure satisfies equitability strongly depends on what mathematical properties the noise term η is allowed to have: the narrower one’s definition of noise, the weaker the equitability criterion becomes
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