Reverse Engineering Gene Networks with ANN: Variability in Network Inference Algorithms

Motivation :Reconstructing the topology of a gene regulatory network is one of the key tasks in systems biology. Despite of the wide variety of proposed methods, very little work has been dedicated to the assessment of their stability properties. Here we present a methodical comparison of the performance of a novel method (RegnANN) for gene network inference based on multilayer perceptrons with three reference algorithms (ARACNE, CLR, KELLER), focussing our analysis on the prediction variability induced by both the network intrinsic structure and the available data. Results: The extensive evaluation on both synthetic data and a selection of gene modules of "Escherichia coli" indicates that all the algorithms suffer of instability and variability issues with regards to the reconstruction of the topology of the network. This instability makes objectively very hard the task of establishing which method performs best. Nevertheless, RegnANN shows MCC scores that compare very favorably with all the other inference methods tested. Availability: The software for the RegnANN inference algorithm is distributed under GPL3 and it is available at the corresponding author home page (http://mpba.fbk.eu/grimaldi/regnann-supmat

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-