Michael U. Gutmann

Learning Features by Contrasting Natural Images with Noise

Modeling the statistical structure of natural images is interesting for reasons related to neuroscience as well as engineering. Currently, this modeling relies heavily on generative probabilistic models. The estimation of such models is, however, difficult, especially when they consist of multiple layers. If the goal lies only in estimating the features, i.e. in pinpointing structure in natural images, one could also estimate instead a discriminative probabilistic model where multiple layers are more easily handled. For that purpose, we propose to estimate a classifier that can tell natural images apart from reference data which has been constructed to contain some known structure of natural images. The features of the classifier then reveal the interesting structure. Here, we use a classifier with one layer of features and reference data which contains the covariance-structure of natural images. We show that the features of the classifier are similar to those which are obtained from generative probabilistic models. Furthermore, we investigate the optimal shape of the nonlinearity that is used within the classifier.

Statistical model of natural stimuli predicts edge-like pooling of spatial frequency channels in V2

BackgroundIt has been shown that the classical receptive fields of simple and complex cells in the primary visual cortex emerge from the statistical properties of natural images by forcing the cell responses to be maximally sparse or independent. We investigate how to learn features beyond the primary visual cortex from the statistical properties of modelled complex-cell outputs. In previous work, we showed that a new model, non-negative sparse coding, led to the emergence of features which code for contours of a given spatial frequency band.ResultsWe applied ordinary independent component analysis to modelled outputs of complex cells that span different frequency bands. The analysis led to the emergence of features which pool spatially coherent across-frequency activity in the modelled primary visual cortex. Thus, the statistically optimal way of processing complex-cell outputs abandons separate frequency channels, while preserving and even enhancing orientation tuning and spatial localization. As a technical aside, we found that the non-negativity constraint is not necessary: ordinary independent component analysis produces essentially the same results as our previous work.ConclusionWe propose that the pooling that emerges allows the features to code for realistic low-level image features related to step edges. Further, the results prove the viability of statistical modelling of natural images as a framework that produces quantitative predictions of visual processing.

Likelihood-free inference via classification

Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.

Fundamentals and Recent Developments in Approximate Bayesian Computation

&NA; Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood‐free inference; phylogenetics; simulator‐based models; stochastic simulation models; tree‐based models.]

A three-layer model of natural image statistics

An important property of visual systems is to be simultaneously both selective to specific patterns found in the sensory input and invariant to possible variations. Selectivity and invariance (tolerance) are opposing requirements. It has been suggested that they could be joined by iterating a sequence of elementary selectivity and tolerance computations. It is, however, unknown what should be selected or tolerated at each level of the hierarchy. We approach this issue by learning the computations from natural images. We propose and estimate a probabilistic model of natural images that consists of three processing layers. Two natural image data sets are considered: image patches, and complete visual scenes downsampled to the size of small patches. For both data sets, we find that in the first two layers, simple and complex cell-like computations are performed. In the third layer, we mainly find selectivity to longer contours; for patch data, we further find some selectivity to texture, while for the downsampled complete scenes, some selectivity to curvature is observed.

Recombination produces coherent bacterial species clusters in both core and accessory genomes

Background: Population samples show bacterial genomes can be divided into a core of ubiquitous genes and accessory genes that are present in a fraction of isolates. The ecological significance of this variation in gene content remains unclear. However, microbiologists agree that a bacterial species should be ‘genomically coherent’, even though there is no consensus on how this should be determined. Results: We use a parsimonious model combining diversification in both the core and accessory genome, including mutation, homologous recombination (HR) and horizontal gene transfer (HGT) introducing new loci, to produce a population of interacting clusters of strains with varying genome content. New loci introduced by HGT may then be transferred on by HR. The model fits well to a systematic population sample of 616 pneumococcal genomes, capturing the major features of the population structure with parameter values that agree well with empirical estimates. Conclusions: The model does not include explicit selection on individual genes, suggesting that crude comparisons of gene content may be a poor predictor of ecological function. We identify a clearly divergent subpopulation of pneumococci that are inconsistent with the model and may be considered genomically incoherent with the rest of the population. These strains have a distinct disease tropism and may be rationally defined as a separate species. We also find deviations from the model that may be explained by recent population bottlenecks or spatial structure.

Direct learning of sparse changes in markov networks by density ratio estimation

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we directly learn the network structure change by estimating the ratio of Markov network models. This density-ratio formulation naturally allows us to introduce sparsity in the network structure change, which highly contributes to enhancing interpretability. Furthermore, computation of the normalization term, a critical bottleneck of the naive approach, can be remarkably mitigated. We also give the dual formulation of the optimization problem, which further reduces the computation cost for large-scale Markov networks. Through experiments, we demonstrate the usefulness of our method.

Frequency-dependent selection in vaccine-associated pneumococcal population dynamics

Many bacterial species are composed of multiple lineages distinguished by extensive variation in gene content. These often cocirculate in the same habitat, but the evolutionary and ecological processes that shape these complex populations are poorly understood. Addressing these questions is particularly important for Streptococcus pneumoniae, a nasopharyngeal commensal and respiratory pathogen, because the changes in population structure associated with the recent introduction of partial-coverage vaccines have substantially reduced pneumococcal disease. Here we show that pneumococcal lineages from multiple populations each have a distinct combination of intermediate-frequency genes. Functional analysis suggested that these loci may be subject to negative frequency-dependent selection (NFDS) through interactions with other bacteria, hosts or mobile elements. Correspondingly, these genes had similar frequencies in four populations with dissimilar lineage compositions. These frequencies were maintained following substantial alterations in lineage prevalences once vaccination programmes began. Fitting a multilocus NFDS model of post-vaccine population dynamics to three genomic datasets using Approximate Bayesian Computation generated reproducible estimates of the influence of NFDS on pneumococcal evolution, the strength of which varied between loci. Simulations replicated the stable frequency of lineages unperturbed by vaccination, patterns of serotype switching and clonal replacement. This framework highlights how bacterial ecology affects the impact of clinical interventions.Accessory loci are shown to have similar frequencies in diverse Streptococcus pneumoniae populations, suggesting negative frequency-dependent selection drives post-vaccination population restructuring.

Spatio-Chromatic Adaptation via Higher-Order Canonical Correlation Analysis of Natural Images

Independent component and canonical correlation analysis are two general-purpose statistical methods with wide applicability. In neuroscience, independent component analysis of chromatic natural images explains the spatio-chromatic structure of primary cortical receptive fields in terms of properties of the visual environment. Canonical correlation analysis explains similarly chromatic adaptation to different illuminations. But, as we show in this paper, neither of the two methods generalizes well to explain both spatio-chromatic processing and adaptation at the same time. We propose a statistical method which combines the desirable properties of independent component and canonical correlation analysis: It finds independent components in each data set which, across the two data sets, are related to each other via linear or higher-order correlations. The new method is as widely applicable as canonical correlation analysis, and also to more than two data sets. We call it higher-order canonical correlation analysis. When applied to chromatic natural images, we found that it provides a single (unified) statistical framework which accounts for both spatio-chromatic processing and adaptation. Filters with spatio-chromatic tuning properties as in the primary visual cortex emerged and corresponding-colors psychophysics was reproduced reasonably well. We used the new method to make a theory-driven testable prediction on how the neural response to colored patterns should change when the illumination changes. We predict shifts in the responses which are comparable to the shifts reported for chromatic contrast habituation.

Direct learning of sparse changes in Markov networks by density ratio estimation

We propose a new method for detecting changes in Markov network structure between two sets of samples. Instead of naively fitting two Markov network models separately to the two data sets and figuring out their difference, we directly learn the network structure change by estimating the ratio of Markov network models. This density-ratio formulation naturally allows us to introduce sparsity in the network structure change, which highly contributes to enhancing interpretability. Furthermore, computation of the normalization term, which is a critical computational bottleneck of the naive approach, can be remarkably mitigated. Through experiments on gene expression and Twitter data analysis, we demonstrate the usefulness of our method.