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