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

BACKGROUND: It 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. RESULTS: We 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. CONCLUSION: We 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

Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

BLUES from Music: BLind Underdetermined Extraction of Sources from Music

In this paper we propose to use an instantaneous ICA method (BLUES) to separate the instruments in a real music stereo recording. We combine two strong separation techniques to segregate instruments from a mixture: ICA and binary time-frequency masking. By combining the methods, we are able to make use of the fact that the sources are differently distributed in both space, time and frequency. Our method is able to segregate an arbitrary number of instruments and the segregated sources are maintained as stereo signals. We have evaluated our method on real stereo recordings, and we can segregate instruments which are spatially different from other instruments

New permutation algorithms for causal discovery using ICA

Abstract. Causal discovery is the task of finding plausible causal relationships from statistical dat

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Unsupervised Bayesian linear unmixing of gene expression microarrays

Background: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Results: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. Conclusions: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor

Estudo da Razão de Bowen em uma Área de Floresta no Sudoeste da Amazônia

The changes mainly occurred in the hydrological cycle are associated with anthropogenic changes. In Brazil are already seen possible changes in the southwestern region that has suffered from water scarcity in their reservoirs. Understanding the Bowen ratio in the Amazon region becomes important to try to understand this ecosystem, since such information connect regional climate change. The latent heat fluxes were analyzed (λE) and sensible heat (H) in REBIO Jaru to determine the reason for Bowen and seek possible climate interactions in humid, wetdry, dry, dry-wet periods in 2009. The results observed in these periods in the Bowen ratio were 0:21; 0:24; 0:30; 0:21, and show that the forest little changes with seasonality during the year unlike the transition of biomes (Amazon - cerrado) and pasture area.As variações ocorridas principalmente no ciclo hidrológico associam-se as mudanças antrópicas. No Brasil já são vistas possíveis alterações na região sudoeste que vem sofrendo com a escassez hídrica em seus reservatórios. Compreender a razão de Bowen na região amazônica torna-se importante para tentar conhecer esse ecossistema, já que tais informações se conectam as alterações climáticas regionais. Foram analisados os fluxos de calor latente (λE) e calor sensível (H) na REBIO Jaru para determinar a razão de Bowen e buscar possíveis interações climáticas nos períodos úmido, úmido-seco, seco e seco-úmido no ano de 2009.  Os resultados observados nesses períodos na razão de Bowen foram: 0.21; 0.24; 0.30;  0.21, e mostram que a floresta pouco se altera com a sazonalidade durante o ano ao contrário dos biomas de transição (Amazônia – cerrado) e da área de pastagem

Correlated topographic analysis: estimating an ordering of correlated components

Abstract This paper describes a novel method, which we call correlated topographic analysis (CTA), to estimate non-Gaussian components and their ordering (topography). The method is inspired by a central motivation of recent variants of independent component analysis (ICA), namely, to make use of the residual statistical dependency which ICA cannot remove. We assume that components nearby on the topographic arrangement have both linear and energy correlations, while far-away components are statistically independent. We use these dependencies to fix the ordering of the components. We start by proposing the generative model for the components. Then, we derive an approximation of the likelihood based on the model. Furthermore, since gradient methods tend to get stuck in local optima, we propose a three-step optimization method which dramatically improves topographic estimation. Using simulated data, we show that CTA estimates an ordering of the components and generalizes a previous method in terms of topography estimation. Finally, to demonstrate that CTA is widely applicable, we learn topographic representations for three kinds of real data: natural images, outputs of simulated complex cells and text data

Correction for a measurement artifact of the Multi-Angle Absorption Photometer (MAAP) at high black carbon mass concentration levels

The Multi-Angle Absorption Photometer (MAAP) is a widely-used instrument for aerosol black carbon (BC) measurements. In this paper, we show correction methods for an artifact found to affect the instrument accuracy in environments characterized by high black carbon concentrations. The artifact occurs after a filter spot change – as BC mass is accumulated on a fresh filter spot, the attenuation of the light (raw signal) is weaker than anticipated. This causes a sudden decrease, followed by a gradual increase in measured BC concentration. The artifact is present in the data when the BC concentration exceeds ~3 μg m<sup>−3</sup> at the typical MAAP flow rate of 16.7 L min<sup>−1</sup> or 1 m<sup>3</sup> h<sup>−1</sup>. The artifact is caused by erroneous dark counts in the photodetector measuring the transmitted light, in combination with an instrument internal averaging procedure of the photodetector raw signals. It was found that, in addition to the erroneous temporal response of the data, concentrations higher than 9 μg m<sup>−3</sup> (at the flow rate of 16.7 L min<sup>−1</sup>) are underestimated by the MAAP. The underestimation increases with increasing BC accumulation rate. At a flow rate of 16.7 L min<sup>−1</sup> and concentration of about 24 μg m<sup>−3</sup> (BC accumulation rate ~0.4 μg min<sup>−1</sup>), the underestimation is about 30%. There are two ways of overcoming the MAAP artifact. One method is by logging the raw signal of the 165° photomultiplier measuring the reflected light from the filter spot. As this signal is not affected by the artifact, it can be converted to approximately correct absorption and BC values. However, as the typical print formats of the MAAP do not give the reflected signal as an output, a semi-empirical correction method was developed based on laboratory experiments to correct for the results in the post-processing phase. The correction function was applied to three MAAP datasets from Gual Pahari (India), Beijing (China), and Welgegund (South Africa). In Beijing, the results could also be compared against a photoacoustic spectrometer (PAS). The correction improved the quality of all three MAAP datasets substantially, even though the individual instruments operated at different flow rates and in different environments