We study inductive matrix completion (matrix completion with side information) under an i.i.d. subgaussian noise assumption at a low noise regime, with uniform sampling of the entries. We obtain for the first time generalization bounds with the following three properties: (1) they scale like the standard deviation of the noise and in particular approach zero in the exact recovery case; (2) even in the presence of noise, they converge to zero when the sample size approaches infinity; and (3) for a fixed dimension of the side information, they only have a logarithmic dependence on the size of the matrix. Differently from many works in approximate recovery, we present results both for bounded Lipschitz losses and for the absolute loss, with the latter relying on Talagrand-type inequalities. The proofs create a bridge between two approaches to the theoretical analysis of matrix completion, since they consist in a combination of techniques from both the exact recovery literature and the approximate recovery literature.

MOTIVATION: Atomistic models of nucleic acids (NA) fragments can be used to model the 3D structures of specific protein-NA interactions and address the problem of great NA flexibility, especially in their single-stranded regions. One way to obtain relevant NA fragments is to extract them from existing 3D structures corresponding to the targeted context (e.g. specific 2D structures, protein families, sequences) and to learn from them. Several databases exist for specific NA 3D motifs, especially in RNA, but none can handle the variety of possible contexts. RESULTS: This article presents protNAff (protein-bound Nucleic Acids filters and fragments), a new pipeline for the conception of searchable databases on the 2D and 3D structures of protein-bound NA, the selection of context-specific (regions of) NA structures by combinations of filters, and the creation of context-specific NA fragment libraries. The strength of this pipeline is its modularity, allowing users to adapt it to many specific modeling problems. As examples, the pipeline is applied to the quantitative analysis of (i) the sequence-specificity of trinucleotide conformations, (ii) the conformational diversity of RNA at several levels of resolution, (iii) the effect of protein binding on RNA local conformations and (iv) the protein-binding propensity of RNA hairpin loops of various lengths. AVAILABILITY AND IMPLEMENTATION: The source code is freely available for download at URL https://github.com/isaureCdB/protNAff. The database and the trinucleotide fragment library are downloadable at URL https://zenodo.org/record/6483823#.YmbVhFxByV4. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: The heterokonts are a particularly interesting group of eukaryotic organisms; they include many key species of planktonic and coastal algae and several important pathogens. To understand the biology of these organisms, it is necessary to be able to predict the subcellular localisation of their proteins but this is not straightforward, particularly in photosynthetic heterokonts which possess a complex chloroplast, acquired as the result of a secondary endosymbiosis. This is because the bipartite target peptides that deliver proteins to these chloroplasts can be easily confused with the signal peptides of secreted proteins, causing currently available algorithms to make erroneous predictions. HECTAR, a subcellular targeting prediction method which takes into account the specific properties of heterokont proteins, has been developed to address this problem. RESULTS: HECTAR is a statistical prediction method designed to assign proteins to five different categories of subcellular targeting: Signal peptides, type II signal anchors, chloroplast transit peptides, mitochondrion transit peptides and proteins which do not possess any N-terminal target peptide. The recognition rate of HECTAR is 96.3%, with Matthews correlation coefficients ranging from 0.67 to 0.95. The method is based on a hierarchical architecture which implements the divide and conquer approach to identify the different possible target peptides one at a time. At each node of the hierarchy, the most relevant outputs of various existing subcellular prediction methods are combined by a Support Vector Machine. CONCLUSION: The HECTAR method is able to predict the subcellular localisation of heterokont proteins with high accuracy. It also efficiently predicts the subcellular localisation of proteins from cryptophytes, a group that is phylogenetically close to the heterokonts. A variant of HECTAR, called HECTARSEC, can be used to identify signal peptide and type II signal anchor sequences in proteins from any eukaryotic organism. Both HECTAR and HECTARSEC are available as a web application at the following address: http://www.sb-roscoff.fr/hectar/.

BACKGROUND: Membrane proteins are estimated to represent about 25% of open reading frames in fully sequenced genomes. However, the experimental study of proteins remains difficult. Considerable efforts have thus been made to develop prediction methods. Most of these were conceived to detect transmembrane helices in polytopic proteins. Alternatively, a membrane protein can be monotopic and anchored via an amphipathic helix inserted in a parallel way to the membrane interface, so-called in-plane membrane (IPM) anchors. This type of membrane anchor is still poorly understood and no suitable prediction method is currently available. RESULTS: We report here the "AmphipaSeeK" method developed to predict IPM anchors. It uses a set of 21 reported examples of IPM anchored proteins. The method is based on a pattern recognition Support Vector Machine with a dedicated kernel. CONCLUSION: AmphipaSeeK was shown to be highly specific, in contrast with classically used methods (e.g. hydrophobic moment). Additionally, it has been able to retrieve IPM anchors in naively tested sets of transmembrane proteins (e.g. PagP). AmphipaSeek and the list of the 21 IPM anchored proteins is available on NPS@, our protein sequence analysis server.

We introduce a support vector machine devoted to the approximation of multi-class discriminant functions. Its training procedure consists in minimizing an expression of the guaranteed risk. This bound is significantly tighter than the former ones, which should make the implementation of the structural risk minimization inductive principle in the context of multi-class discrimination better grounded.

Starting from a direct definition of the notion of margin in the multiclass case, we study the generalization performance of multiclass discriminant systems. In the framework of statistical learning theory, we establish on this performance a bound based on covering numbers. An application to a linear ensemble method which estimates the class posterior probabilities provides us with a way to compare this bound and another one based on combinatorial dimensions, with respect to the capacity measure they incorporate. Experimental results highlight their usefulness for a real-world problem.

MOTIVATION: In many fields of pattern recognition, combination has proved efficient to increase the generalization performance of individual prediction methods. Numerous systems have been developed for protein secondary structure prediction, based on different principles. Finding better ensemble methods for this task may thus become crucial. Furthermore, efforts need to be made to help the biologist in the post-processing of the outputs. RESULTS: An ensemble method has been designed to post-process the outputs of discriminant models, in order to obtain an improvement in prediction accuracy while generating class posterior probability estimates. Experimental results establish that it can increase the recognition rate of protein secondary structure prediction methods that provide inhomogeneous scores, even though their individual prediction successes are largely different. This combination thus constitutes a help for the biologist, who can use it confidently on top of any set of prediction methods. Moreover, the resulting estimates can be used in various ways, for instance to determine which areas in the sequence are predicted with a given level of reliability. AVAILABILITY: The prediction is freely available over the Internet on the Network Protein Sequence Analysis (NPS@) WWW server at http://pbil.ibcp.fr/NPSA/npsa_server.ht ml. The source code of the combiner can be obtained on request for academic use.

Supervised classification has already been the subject of numerous studies in the fields of Statistics, Pattern Recognition and Artificial Intelligence under various appellations which include discriminant analysis, discrimination and concept learning. Many practical applications relating to this field have been developed. New methods have appeared in recent years, due to developments concerning Neural Networks and Machine Learning. These "hybrid" approaches share one common factor in that they combine symbolic and numerical aspects. The former are characterized by the representation of knowledge, the latter by the introduction of frequencies and probabilistic criteria. In the present study, we shall present a certain number of hybrid methods, conceived (or improved) by members of the SYMENU research group. These methods issue mainly from Machine Learning and from research on Classification Trees done in Statistics, and they may also be qualified as "rule-based". They shall be compared with other more classical approaches. This comparison will be based on a detailed description of each of the twelve methods envisaged, and on the results obtained concerning the "Waveform Recognition Problem" proposed by Breiman et al.,4 which is difficult for rule based approaches.