Predictive information in Gaussian processes with application to music analysis

This is the author's accepted manuscript of this article. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-40020-9.Lecture Notes in Computer ScienceLecture Notes in Computer ScienceWe describe an information-theoretic approach to the analysis of sequential data, which emphasises the predictive aspects of perception, and the dynamic process of forming and modifying expectations about an unfolding stream of data, characterising these using a set of process information measures. After reviewing the theoretical foundations and the definition of the predictive information rate, we describe how this can be computed for Gaussian processes, including how the approach can be adpated to non-stationary processes, using an online Bayesian spectral estimation method to compute the Bayesian surprise. We finish with a sample analysis of a recording of Steve Reich’s Drummin

Fast Method to Fit a C1 Piecewise-Bézier Function to Manifold-Valued Data Points: How Suboptimal is the Curve Obtained on the Sphere S2?

We propose an analysis of the quality of the fitting method proposed in Gousenbourger et al., 2017 (ESANN2017 proceedings). This method fits smooth paths to manifold-valued data points using C1 piecewise-Bézier functions. This method is based on the principle of minimizing an objective function composed of a data-attachment term and a regularization term chosen as the mean squared acceleration of the path. However, the method strikes a tradeoff between speed and accuracy by following a strategy that is guaranteed to yield the optimal curve only when the manifold is linear. In this paper, we focus on the sphere S2. We compare the quality of the path returned by the algorithms from Gousenbourger et al., 2017 (ESANN2017 proceedings) with the path obtained by minimizing, over the same search space of C1 piecewise-Bézier curves, a finite-difference approximation of the objective function by means of a derivative-free manifold-based optimization method

Inductive Means and Sequences Applied to Online Classification of EEG

The translation of brain activity into user command, through Brain-Computer Interfaces (BCI), is a very active topic in machine learning and signal processing. As commercial applications and out-of-the-lab solutions are proposed, there is an increased pressure to provide online algorithms and real-time implementations. Electroencephalography (EEG) systems offer lightweight and wearable solutions, at the expense of signal quality. Approaches based on covariance matrices have demonstrated good robustness to noise and provide a suitable representation for classification tasks, relying on advances in Riemannian geometry. We propose to equip the minimum distance to mean (MDM) classifier with a new family of means, based on the inductive mean, for block-online classification tasks and to embed the inductive mean in an incremental learning algorithm for online classification of EEG

Weakly correlated sparse components with nearly orthonormal loadings

There is already a great number of highly efficient methods producing components with sparse loadings which significantly facilitates the interpretation of principal component analysis (PCA). However, they produce either only orthonormal loadings, or only uncorrelated components, or, most frequently, neither of them. To overcome this weakness, we introduce a new approach to define sparse PCA similar to the Dantzig selector idea already employed for regression problems. In contrast to the existing methods, the new approach makes it possible to achieve simultaneously nearly uncorrelated sparse components with nearly orthonormal loadings. The performance of the new method is illustrated on real data sets. It is demonstrated that the new method outperforms one of the most popular available methods for sparse PCA in terms of preservation of principal components properties