Epitope prediction improved by multitask support vector machines

Motivation: In silico methods for the prediction of antigenic peptides binding to MHC class I molecules play an increasingly important role in the identification of T-cell epitopes. Statistical and machine learning methods, in particular, are widely used to score candidate epitopes based on their similarity with known epitopes and non epitopes. The genes coding for the MHC molecules, however, are highly polymorphic, and statistical methods have difficulties to build models for alleles with few known epitopes. In this case, recent works have demonstrated the utility of leveraging information across alleles to improve the performance of the prediction. Results: We design a support vector machine algorithm that is able to learn epitope models for all alleles simultaneously, by sharing information across similar alleles. The sharing of information across alleles is controlled by a user-defined measure of similarity between alleles. We show that this similarity can be defined in terms of supertypes, or more directly by comparing key residues known to play a role in the peptide-MHC binding. We illustrate the potential of this approach on various benchmark experiments where it outperforms other state-of-the-art methods

Kernel methods for in silico chemogenomics

Predicting interactions between small molecules and proteins is a crucial ingredient of the drug discovery process. In particular, accurate predictive models are increasingly used to preselect potential lead compounds from large molecule databases, or to screen for side-effects. While classical in silico approaches focus on predicting interactions with a given specific target, new chemogenomics approaches adopt cross-target views. Building on recent developments in the use of kernel methods in bio- and chemoinformatics, we present a systematic framework to screen the chemical space of small molecules for interaction with the biological space of proteins. We show that this framework allows information sharing across the targets, resulting in a dramatic improvement of ligand prediction accuracy for three important classes of drug targets: enzymes, GPCR and ion channels

Clustered Multi-Task Learning: A Convex Formulation

In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for supervised classification or regression, this can be achieved by including a priori information about the weight vectors associated with the tasks, and how they are expected to be related to each other. In this paper, we assume that tasks are clustered into groups, which are unknown beforehand, and that tasks within a group have similar weight vectors. We design a new spectral norm that encodes this a priori assumption, without the prior knowledge of the partition of tasks into groups, resulting in a new convex optimization formulation for multi-task learning. We show in simulations on synthetic examples and on the IEDB MHC-I binding dataset, that our approach outperforms well-known convex methods for multi-task learning, as well as related non convex methods dedicated to the same problem

Increasing stability and interpretability of gene expression signatures

Motivation : Molecular signatures for diagnosis or prognosis estimated from large-scale gene expression data often lack robustness and stability, rendering their biological interpretation challenging. Increasing the signature's interpretability and stability across perturbations of a given dataset and, if possible, across datasets, is urgently needed to ease the discovery of important biological processes and, eventually, new drug targets. Results : We propose a new method to construct signatures with increased stability and easier interpretability. The method uses a gene network as side interpretation and enforces a large connectivity among the genes in the signature, leading to signatures typically made of genes clustered in a few subnetworks. It combines the recently proposed graph Lasso procedure with a stability selection procedure. We evaluate its relevance for the estimation of a prognostic signature in breast cancer, and highlight in particular the increase in interpretability and stability of the signature

Wigner function negativity and contextuality in quantum computation on rebits

We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of [M. Howard et al., Nature 510, 351--355 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of $n$ rebits, and prove a corresponding discrete Hudson's theorem. We introduce contextuality witnesses for rebit states, and discuss the compatibility of our result with state-independent contextuality.Comment: 18 + 4 page

Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians

In a recent contribution [Phys. Rev. B 81, 165104 (2010)] fermionic Projected Entangled-Pair States (PEPS) were used to approximate the ground state of free and interacting spinless fermion models, as well as the $t$-$J$ model. This paper revisits these three models in the presence of an additional next-nearest hopping amplitude in the Hamiltonian. First we explain how to account for next-nearest neighbor Hamiltonian terms in the context of fermionic PEPS algorithms based on simulating time evolution. Then we present benchmark calculations for the three models of fermions, and compare our results against analytical, mean-field, and variational Monte Carlo results, respectively. Consistent with previous computations restricted to nearest-neighbor Hamiltonians, we systematically obtain more accurate (or better converged) results for gapped phases than for gapless ones.Comment: 10 pages, 11 figures, minor change

A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization

We present a general approach for collaborative filtering (CF) using spectral regularization to learn linear operators from "users" to the "objects" they rate. Recent low-rank type matrix completion approaches to CF are shown to be special cases. However, unlike existing regularization based CF methods, our approach can be used to also incorporate information such as attributes of the users or the objects -- a limitation of existing regularization based CF methods. We then provide novel representer theorems that we use to develop new estimation methods. We provide learning algorithms based on low-rank decompositions, and test them on a standard CF dataset. The experiments indicate the advantages of generalizing the existing regularization based CF methods to incorporate related information about users and objects. Finally, we show that certain multi-task learning methods can be also seen as special cases of our proposed approach

Machine Learning for In Silico Virtual Screening and Chemical Genomics: New Strategies

Support vector machines and kernel methods belong to the same class of machine learning algorithms that has recently become prominent in both computational biology and chemistry, although both fields have largely ignored each other. These methods are based on a sound mathematical and computationally efficient framework that implicitly embeds the data of interest, respectively proteins and small molecules, in high-dimensional feature spaces where various classification or regression tasks can be performed with linear algorithms. In this review, we present the main ideas underlying these approaches, survey how both the “biological” and the “chemical” spaces have been separately constructed using the same mathematical framework and tricks, and suggest different avenues to unify both spaces for the purpose of in silico chemogenomics