arXiv subjects

Jesus Malo

Publications and source records attributed to Jesus Malo.

25 records · Page 2Linked to original sources

arXiv2020

Information Theory Measures via Multidimensional Gaussianization

Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle heterogeneous data types, and the measures can be interpreted in physical units. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. Here we propose an indirect way of computing information based on a multivariate Gaussianization transform. Our proposal mitigates the difficulty of multivariate density estimation by reducing it to a composition of tractable (marginal) operations and simple linear transformations, which can be interpreted as a particular deep neural network. We introduce specific Gaussianization-based methodologies to estimate total correlation, entropy, mutual information and Kullback-Leibler divergence. We compare them to recent estimators showing the accuracy on synthetic data generated from different multivariate distributions. We made the tools and datasets publicly available to provide a test-bed to analyze future methodologies. Results show that our proposal is superior to previous estimators particularly in high-dimensional scenarios; and that it leads to interesting insights in neuroscience, geoscience, computer vision, and machine learning.

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arXiv2020

Spatio-Chromatic Information available from different Neural Layers via Gaussianization

How much visual information about the retinal images can be extracted from the different layers of the visual pathway?. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested to be organized for optimal information transmission. However, the efficiency of these different layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint spatio-chromatic array of responses. In this work we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted by the system based on a recent Gaussianization technique that reduces the challenging multivariate PDF estimation problem to a set of simpler univariate estimations. Total correlation measured using the proposed estimator is consistent with predictions based on the analytical Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If the noise at certain representation is proportional to the dynamic range of the response, and one assumes sensors of equivalent noise level, transmitted information shows the following trends: (1) progressively deeper representations are better in terms of the amount of information about the input, (2) the transmitted information up to the cortical representation follows the PDF of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially bigger than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.

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arXiv2018

Derivatives and Inverse of Cascaded Linear+Nonlinear Neural Models

In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences [Carandini&Heeger12]. However, the conventional literature is usually too focused on only describing the input->output transform. Instead, here we present the maths of such cascades beyond the forward transform, namely the Jacobians and the inverse. The fundamental reason for this analytical treatment is that it offers useful insight into the psychophysics, the physiology, and the function of the visual system. For instance, we show how the trends of the sensitivity (discrimination regions) and the adaptation of the receptive fields can be seen in the expression of the Jacobian wrt the stimulus. This matrix also tells us which regions of the stimulus space are encoded more efficiently in multi-information terms. The Jacobian wrt the parameters shows which aspects of the model have bigger impact in the response, and hence bigger relevance. The analytic inverse implies conditions for the response and the model to ensure decoding. From an applied perspective, (a) the Jacobian wrt the stimulus is necessary in new experimental methods based on the synthesis of visual stimuli with interesting geometry, (b) the Jacobian matrices wrt the parameters are convenient to learn the model from classical experiments or alternative optimization goals, and (c) the inverse is a model-based alternative to blind machine-learning neural decoding that does not include meaningful biological information. The theory is checked by building a derivable and invertible vision model that actually follows the modular program suggested by Carandini&Heeger. To stress the generality of this modular setting we show examples where some of the canonical Divisive Normalization layers are substituted by equivalent layers such as the Wilson-Cowan model at V1, or a tone-mapping model at the retina.

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arXiv2018

Appropriate kernels for Divisive Normalization explained by Wilson-Cowan equations

The interaction between wavelet-like sensors in Divisive Normalization is classically described through Gaussian kernels that decay with spatial distance, angular distance and frequency distance. However, simultaneous explanation of (a) distortion perception in natural image databases and (b) contrast perception of artificial stimuli requires very specific modifications in classical Divisive Normalization. First, the wavelet response has to be high-pass filtered before the Gaussian interaction is applied. Then, distinct weights per subband are also required after the Gaussian interaction. In summary, the classical Gaussian kernel has to be left- and right-multiplied by two extra diagonal matrices. In this paper we provide a lower-level justification for this specific empirical modification required in the Gaussian kernel of Divisive Normalization. Here we assume that the psychophysical behavior described by Divisive Normalization comes from neural interactions following the Wilson-Cowan equations. In particular, we identify the Divisive Normalization response with the stationary regime of a Wilson-Cowan model. From this identification we derive an expression for the Divisive Normalization kernel in terms of the interaction kernel of the Wilson-Cowan equations. It turns out that the Wilson-Cowan kernel is left- and-right multiplied by diagonal matrices with high-pass structure. In conclusion, symmetric Gaussian inhibitory relations between wavelet-like sensors wired in the lower-level Wilson-Cowan model lead to the appropriate non-symmetric kernel that has to be empirically included in Divisive Normalization to explain a wider range of phenomena.

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arXiv2016

Derivatives and inverse of a linear-nonlinear multi-layer spatial vision model

Linear-nonlinear transforms are interesting in vision science because they are key in modeling a number of perceptual experiences such as color, motion or spatial texture. Here we first show that a number of issues in vision may be addressed through an analytic expression of the Jacobian of these linear-nonlinear transforms. The particular model analyzed afterwards (an extension of [Malo & Simoncelli SPIE 2015]) is illustrative because it consists of a cascade of standard linear-nonlinear modules. Each module roughly corresponds to a known psychophysical mechanism: (1) linear spectral integration and nonlinear brightness-from-luminance computation, (2) linear pooling of local brightness and nonlinear normalization for local contrast computation, (3) linear frequency selectivity and nonlinear normalization for spatial contrast masking, and (4) linear wavelet-like decomposition and nonlinear normalization for frequency-dependent masking. Beyond being the appropriate technical report with the missing details in [Malo & Simoncelli SPIE 2015], the interest of the presented analytic results and numerical methods transcend the particular model because of the ubiquity of the linear-nonlinear structure. Part of this material was presented at MODVIS 2016 (see slides of the conference talk in the appendix at the end of this document).

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arXiv2016

Sequential Principal Curves Analysis

This work includes all the technical details of the Sequential Principal Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear and invertible feature extraction technique. The identified curvilinear features can be interpreted as a set of nonlinear sensors: the response of each sensor is the projection onto the corresponding feature. Moreover, it can be easily tuned for different optimization criteria; e.g. infomax, error minimization, decorrelation; by choosing the right way to measure distances along each curvilinear feature. Even though proposed in [Laparra et al. Neural Comp. 12] and shown to work in multiple modalities in [Laparra and Malo Frontiers Hum. Neuro. 15], the SPCA framework has its original roots in the nonlinear ICA algorithm in [Malo and Gutierrez Network 06]. Later on, the SPCA philosophy for nonlinear generalization of PCA originated substantially faster alternatives at the cost of introducing different constraints in the model. Namely, the Principal Polynomial Analysis (PPA) [Laparra et al. IJNS 14], and the Dimensionality Reduction via Regression (DRR) [Laparra et al. IEEE TGRS 15]. This report illustrates the reasons why we developed such family and is the appropriate technical companion for the missing details in [Laparra et al., NeCo 12, Laparra and Malo, Front.Hum.Neuro. 15]. See also the data, code and examples in the dedicated sites http://isp.uv.es/spca.html and http://isp.uv.es/after effects.html

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arXiv2016

Dimensionality Reduction via Regression in Hyperspectral Imagery

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The properties of DRR enable learning a more broader class of data manifolds than the recently proposed Non-linear Principal Components Analysis (NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance of the representation in reducing the dimensionality of remote sensing data. In particular, we tackle two common problems: processing very high dimensional spectral information such as in hyperspectral image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA).

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