Fast matrix computations for functional additive models

It is common in functional data analysis to look at a set of related functions: a set of learning curves, a set of brain signals, a set of spatial maps, etc. One way to express relatedness is through an additive model, whereby each individual function $g_{i}\left(x\right)$ is assumed to be a variation around some shared mean $f(x)$. Gaussian processes provide an elegant way of constructing such additive models, but suffer from computational difficulties arising from the matrix operations that need to be performed. Recently Heersink & Furrer have shown that functional additive model give rise to covariance matrices that have a specific form they called quasi-Kronecker (QK), whose inverses are relatively tractable. We show that under additional assumptions the two-level additive model leads to a class of matrices we call restricted quasi-Kronecker, which enjoy many interesting properties. In particular, we formulate matrix factorisations whose complexity scales only linearly in the number of functions in latent field, an enormous improvement over the cubic scaling of na\"ive approaches. We describe how to leverage the properties of rQK matrices for inference in Latent Gaussian Models

Graph Tikhonov Regularization and Interpolation via Random Spanning Forests

Novel Monte Carlo estimators are proposed to solve both the Tikhonov regularization (TR) and the interpolation problems on graphs. These estimators are based on random spanning forests (RSF), the theoretical properties of which enable to analyze the estimators' theoretical mean and variance. We also show how to perform hyperparameter tuning for these RSF-based estimators. TR is a component in many well-known algorithms, and we show how the proposed estimators can be easily adapted to avoid expensive intermediate steps in generalized semi-supervised learning, label propagation, Newton's method and iteratively reweighted least squares. In the experiments, we illustrate the proposed methods on several problems and provide observations on their run time

Smoothing graph signals via random spanning forests

International audienceAnother facet of the elegant link between random processes on graphs and Laplacian-based numerical linear algebra is uncovered: based on random spanning forests, novel Monte-Carlo estimators for graph signal smoothing are proposed. These random forests are sampled efficiently via a variant of Wilson's algorithm-in time linear in the number of edges. The theoretical variance of the proposed estimators are analyzed , and their application to several problems are considered , such as Tikhonov denoising of graph signals or semi-supervised learning for node classification on graphs

Discussions on "Riemann manifold Langevin and Hamiltonian Monte Carlo methods"

This is a collection of discussions of `Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by Girolami and Calderhead, to appear in the Journal of the Royal Statistical Society, Series B.Comment: 6 pages, one figur

Estimating the inverse trace using random forests on graphs

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Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"

This report is a collection of comments on the Read Paper of Fearnhead and Prangle (2011), to appear in the Journal of the Royal Statistical Society Series B, along with a reply from the authors.Comment: 10 page

The candidate antimalarial drug MMV665909 causes oxygen-dependent mRNA mistranslation and synergises with quinoline-derived antimalarials

To cope with growing resistance to current antimalarials, new drugs with novel modes of action are urgently needed. Molecules targeting protein synthesis appear to be promising candidates. We identified a compound (MMV665909) from the MMV Malaria Box of candidate antimalarials that could produce synergistic growth inhibition with the aminoglycoside antibiotic paromomycin, suggesting a possible action of the compound in mRNA mistranslation. This mechanism of action was substantiated with the yeast cell model using available reporters of mistranslation and other genetic tools. Mistranslation induced by MMV665909 was oxygen-dependent, suggesting a role for reactive oxygen species (ROS). Overexpression of Rli1 (a ROS-sensitive, conserved FeS protein essential in mRNA translation) rescued inhibition by MMV665909, consistent with the drug’s action on translation fidelity being mediated through Rli1. The MMV drug also synergised with major quinoline-derived antimalarials which can perturb amino acid availability or promote ROS stress: chloroquine, amodiaquine and primaquine. The data collectively suggest translation-fidelity as a novel target of antimalarial action and support MMV665909 as a promising drug candidate