Ambiguous model learning made unambiguous with 1/f priors

What happens to the optimal interpretation of noisy data when there exists more than one equally plausible interpretation of the data? In a Bayesian model-learning framework the answer depends on the prior expectations of the dynamics of the model parameter that is to be inferred from the data. Local time constraints on the priors are insufficient to pick one interpretation over another. On the other hand, nonlocal time constraints, induced by a $1/f$ noise spectrum of the priors, is shown to permit learning of a specific model parameter even when there are infinitely many equally plausible interpretations of the data. This transition is inferred by a remarkable mapping of the model estimation problem to a dissipative physical system, allowing the use of powerful statistical mechanical methods to uncover the transition from indeterminate to determinate model learning.Comment: 8 pages, 2 figure

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

Developmental Coordination of Gene Expression between Synaptic Partners During GABAergic Circuit Assembly in Cerebellar Cortex

The assembly of neural circuits involves multiple sequential steps such as the specification of cell-types, their migration to proper brain locations, morphological and physiological differentiation, and the formation and maturation of synaptic connections. This intricate and often prolonged process is guided by elaborate genetic mechanisms that regulate each step. Evidence from numerous systems suggests that each cell-type, once specified, is endowed with a genetic program that unfolds in response to, and is regulated by, extrinsic signals, including cell–cell and synaptic interactions. To a large extent, the execution of this intrinsic program is achieved by the expression of specific sets of genes that support distinct developmental processes. Therefore, a comprehensive analysis of the developmental progression of gene expression in synaptic partners of neurons may provide a basis for exploring the genetic mechanisms regulating circuit assembly. Here we examined the developmental gene expression profiles of well-defined cell-types in a stereotyped microcircuit of the cerebellar cortex. We found that the transcriptomes of Purkinje cell and stellate/basket cells are highly dynamic throughout postnatal development. We revealed “phasic expression” of transcription factors, ion channels, receptors, cell adhesion molecules, gap junction proteins, and identified distinct molecular pathways that might contribute to sequential steps of cerebellar inhibitory circuit formation. We further revealed a correlation between genomic clustering and developmental co-expression of hundreds of transcripts, suggesting the involvement of chromatin level gene regulation during circuit formation

Cell non-autonomous interactions during non-immune stromal progression in the breast tumor microenvironment

Summary The breast tumor microenvironment of primary and metastatic sites is a complex milieu of differing cell populations, consisting of tumor cells and the surrounding stroma. Despite recent progress in delineating the immune component of the stroma, the genomic expression landscape of the non-immune stroma (NIS) population and their role in mediating cancer progression and informing effective therapies are not well understood. Here we obtained 52 cell-sorted NIS and epithelial tissue samples across 37 patients from i) normal breast, ii) normal breast adjacent to primary tumor, iii) primary tumor, and iv) metastatic tumor sites. Deep RNA-seq revealed diverging gene expression profiles as the NIS evolves from normal to metastatic tumor tissue, with intra-patient normal-primary variation comparable to inter-patient variation. Significant expression changes between normal and adjacent normal tissue support the notion of a cancer field effect, but extended out to the NIS. Most differentially expressed protein-coding genes and lncRNAs were found to be associated with pattern formation, embryogenesis, and the epithelial-mesenchymal transition. We validated the protein expression changes of a novel candidate gene, C2orf88, by immunohistochemistry staining of representative tissues. Significant mutual information between epithelial ligand and NIS receptor gene expression, across primary and metastatic tissue, suggests a unidirectional model of molecular signaling between the two tissues. Furthermore, survival analyses of 827 luminal breast tumor samples demonstrated the predictive power of the NIS gene expression to inform clinical outcomes. Together, these results highlight the evolution of NIS gene expression in breast tumors and suggest novel therapeutic strategies targeting the microenvironment