Gaussian Process Vine Copulas for Multivariate Dependence

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is independent from its conditioning variables. In this paper, we relax this assumption by discovering the latent functions that specify the shape of a conditional copula given its conditioning variables We learn these functions by following a Bayesian approach based on sparse Gaussian processes with expectation propagation for scalable, approximate inference. Experiments on real-world datasets show that, when modeling all conditional dependencies, we obtain better estimates of the underlying copula of the data.

In vitro recording of neural activity using carbon nanosheet microelectrodes

The advent of nanotechnology has revolutionised our ability to engineer electrode interfaces. These are particularly attractive to measure biopotentials, and to study the nervous system. In this work, we demonstrate enhanced in vitro recording of neuronal activity using electrodes decorated with carbon nanosheets (CNSs). This material comprises of vertically aligned, free standing conductive sheets of only a few graphene layers with a high surfacearea- to-volume ratio, which makes them an interesting material for biomedical electrodes. Further, compared to carbon nanotubes, CNSs can be synthesised without the need for metallic catalysts like Ni, Co or Fe, thereby reducing potential cytotoxicity risks. Electrochemical measurements show a five times higher charge storage capacity, and an almost ten times higher double layer capacitance as compared to TiN. In vitro experiments were performed by culturing primary hippocampal neurons from mice on micropatterned electrodes. Neurophysiological recordings exhibited high signal-to-noise ratios of 6.4, which is a twofold improvement over standard TiN electrodes under the same conditions. © 2013 Elsevier Ltd. All rights reserved.

Randomized nonlinear component analysis

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear re-lationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real- world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.