Quantitative probing: Validating causal models using quantitative domain knowledge

We present quantitative probing as a model-agnostic framework for validating causal models in the presence of quantitative domain knowledge. The method is constructed as an analogue of the train/test split in correlation-based machine learning and as an enhancement of current causal validation strategies that are consistent with the logic of scientific discovery. The effectiveness of the method is illustrated using Pearl's sprinkler example, before a thorough simulation-based investigation is conducted. Limits of the technique are identified by studying exemplary failing scenarios, which are furthermore used to propose a list of topics for future research and improvements of the presented version of quantitative probing. The code for integrating quantitative probing into causal analysis, as well as the code for the presented simulation-based studies of the effectiveness of quantitative probing is provided in two separate open-source Python packages.Comment: submitted to the Journal of Causal Inferenc

A Neural Network Model for the Self-Organization of Cortical Grating Cells

A neural network model with incremental Hebbian learning of afferent and lateral synaptic couplings is proposed,which simulates the activity-dependent self-organization of grating cells in upper layers of striate cortex. These cells, found in areas V1 and V2 of the visual cortex of monkeys, respond vigorously and exclusively to bar gratings of a preferred orientation and periodicity. Response behavior to varying contrast and to an increasing number of bars in the grating show threshold and saturation effects. Their location with respect to the underlying orientation map and their nonlinear response behavior are investigated. The number of emerging grating cells is controlled in the model by the range and strength of the lateral coupling structure

Linear Invariant Systems Theory for Signal Enhancement

This paper discusses a linear time invariant (LTI) systems approach to signal enhancement via projective subspace techniques. It provides closed form expressions for the frequency response of data adaptive finite impulse response eigenfilters. An illustrative example using speech enhancement is also presented.Este artigo apresenta a aplicação da teoria de sistemas lineares invariantes no tempo (LTI) na análise de técnicas de sub-espaço. A resposta em frequência dos filtros resultantes da decomposição em valores singulares é obtida aplicando as propriedades dos sistemas LTI

A Constrained ICA-EMD Model for Group Level fMRI Analysis

Independent component analysis (ICA), being a data-driven method, has been shown to be a powerful tool for functional magnetic resonance imaging (fMRI) data analysis. One drawback of this multivariate approach is that it is not, in general, compatible with the analysis of group data. Various techniques have been proposed to overcome this limitation of ICA. In this paper, a novel ICA-based workflow for extracting resting-state networks from fMRI group studies is proposed. An empirical mode decomposition (EMD) is used, in a data-driven manner, to generate reference signals that can be incorporated into a constrained version of ICA (cICA), thereby eliminating the inherent ambiguities of ICA. The results of the proposed workflow are then compared to those obtained by a widely used group ICA approach for fMRI analysis. In this study, we demonstrate that intrinsic modes, extracted by EMD, are suitable to serve as references for cICA. This approach yields typical resting-state patterns that are consistent over subjects. By introducing these reference signals into the ICA, our processing pipeline yields comparable activity patterns across subjects in a mathematically transparent manner. Our approach provides a user-friendly tool to adjust the trade-off between a high similarity across subjects and preserving individual subject features of the independent components