We present a novel regularization-based Multitask Learning (MTL) formulation for Structured Output (SO) prediction for the case of hierarchical task relations. Structured output learning often results in difficult inference problems and requires large amounts of training data to obtain accurate models. We propose to use MTL to exploit information available for related structured output learning tasks by means of hierarchical regularization. Due to the combination of example sets, the cost of training models for structured output prediction can easily become infeasible for real world applications. We thus propose an efficient algorithm based on bundle methods to solve the optimization problems resulting from MTL structured output learning. We demonstrate the performance of our approach on gene finding problems from the application domain of computational biology. We show that 1) our proposed solver achieves much faster convergence than previous methods and 2) that the Hierarchical SO-MTL approach clearly outperforms considered non-MTL methods.

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations and hence support interpretability. Unfortunately, L1-norm MKL is hardly observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary Lp-norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary p>1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the traditionally used wrapper approaches. Finally, we apply Lp-norm MKL to real-world problems from computational biology, showing that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.

We have developed a new Linear Support Vector Machine (SVM) training algorithm called OCAS. Its computational effort scales linearly with the sample size. In an extensive empirical evaluation OCAS significantly outperforms current state of the art SVM solvers, like SVMlight, SVMperf and BMRM, achieving speedups of over 1,000 on some datasets over SVMlight and 20 over SVMperf, while obtaining the same precise Support Vector solution. OCAS even in the early optimization steps shows often faster convergence than the so far in this domain prevailing approximative methods SGD and Pegasos. Effectively parallelizing OCAS we were able to train on a dataset of size 15 million examples (itself about 32GB in size) in just 671 seconds --- a competing string kernel SVM required 97,484 seconds to train on 10 million examples sub-sampled from this dataset.

MOTIVATION: At the heart of many important bioinformatics problems, such as gene finding and function prediction, is the classification of biological sequences. Frequently the most accurate classifiers are obtained by training support vector machines (SVMs) with complex sequence kernels. However, a cumbersome shortcoming of SVMs is that their learned decision rules are very hard to understand for humans and cannot easily be related to biological facts. RESULTS: To make SVM-based sequence classifiers more accessible and profitable, we introduce the concept of positional oligomer importance matrices (POIMs) and propose an efficient algorithm for their computation. In contrast to the raw SVM feature weighting, POIMs take the underlying correlation structure of k-mer features induced by overlaps of related k-mers into account. POIMs can be seen as a powerful generalization of sequence logos: they allow to capture and visualize sequence patterns that are relevant for the investigated biological phenomena. AVAILABILITY: All source code, datasets, tables and figures are available at http://www.fml.tuebingen.mpg.de/raetsch/projects/POIM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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BACKGROUND: For splice site recognition, one has to solve two classification problems: discriminating true from decoy splice sites for both acceptor and donor sites. Gene finding systems typically rely on Markov Chains to solve these tasks. RESULTS: In this work we consider Support Vector Machines for splice site recognition. We employ the so-called weighted degree kernel which turns out well suited for this task, as we will illustrate in several experiments where we compare its prediction accuracy with that of recently proposed systems. We apply our method to the genome-wide recognition of splice sites in Caenorhabditis elegans, Drosophila melanogaster, Arabidopsis thaliana, Danio rerio, and Homo sapiens. Our performance estimates indicate that splice sites can be recognized very accurately in these genomes and that our method outperforms many other methods including Markov Chains, GeneSplicer and SpliceMachine. We provide genome-wide predictions of splice sites and a stand-alone prediction tool ready to be used for incorporation in a gene finder. AVAILABILITY: Data, splits, additional information on the model selection, the whole genome predictions, as well as the stand-alone prediction tool are available for download at http://www.fml.mpg.de/raetsch/projects/splice.

For modern biology, precise genome annotations are of prime importance, as they allow the accurate definition of genic regions. We employ state-of-the-art machine learning methods to assay and improve the accuracy of the genome annotation of the nematode Caenorhabditis elegans. The proposed machine learning system is trained to recognize exons and introns on the unspliced mRNA, utilizing recent advances in support vector machines and label sequence learning. In 87% (coding and untranslated regions) and 95% (coding regions only) of all genes tested in several out-of-sample evaluations, our method correctly identified all exons and introns. Notably, only 37% and 50%, respectively, of the presently unconfirmed genes in the C. elegans genome annotation agree with our predictions, thus we hypothesize that a sizable fraction of those genes are not correctly annotated. A retrospective evaluation of the Wormbase WS120 annotation [] of C. elegans reveals that splice form predictions on unconfirmed genes in WS120 are inaccurate in about 18% of the considered cases, while our predictions deviate from the truth only in 10%-13%. We experimentally analyzed 20 controversial genes on which our system and the annotation disagree, confirming the superiority of our predictions. While our method correctly predicted 75% of those cases, the standard annotation was never completely correct. The accuracy of our system is further corroborated by a comparison with two other recently proposed systems that can be used for splice form prediction: SNAP and ExonHunter. We conclude that the genome annotation of C. elegans and other organisms can be greatly enhanced using modern machine learning technology.

We describe Hidden Semi-Markov Support Vector Machines (SHM SVMs), an extension of HM SVMs to semi-Markov chains. This allows us to predict segmentations of sequences based on segment-based features measuring properties such as the length of the segment. We propose a novel technique to partition the problem into sub-problems. The independently obtained partial solutions can then be recombined in an efficient way, which allows us to solve label sequence learning problems with several thousands of labeled sequences. We have tested our algorithm for predicting gene structures, an important problem in computational biology. Results on a well-known model organism illustrate the great potential of SHM SVMs in computational biology.

We propose a generic algorithm for computation of similarity measures for se- quential data. The algorithm uses generalized suffix trees for efficient calculation of various kernel, distance and non-metric similarity functions. Its worst-case run-time is linear in the length of sequences and independent of the underlying embedding language, which can cover words, k-grams or all contained subse- quences. Experiments with network intrusion detection, DNA analysis and text processing applications demonstrate the utility of distances and similarity coeffi- cients for sequences as alternatives to classical kernel functions.

BACKGROUND: Support Vector Machines (SVMs)--using a variety of string kernels--have been successfully applied to biological sequence classification problems. While SVMs achieve high classification accuracy they lack interpretability. In many applications, it does not suffice that an algorithm just detects a biological signal in the sequence, but it should also provide means to interpret its solution in order to gain biological insight. RESULTS: We propose novel and efficient algorithms for solving the so-called Support Vector Multiple Kernel Learning problem. The developed techniques can be used to understand the obtained support vector decision function in order to extract biologically relevant knowledge about the sequence analysis problem at hand. We apply the proposed methods to the task of acceptor splice site prediction and to the problem of recognizing alternatively spliced exons. Our algorithms compute sparse weightings of substring locations, highlighting which parts of the sequence are important for discrimination. CONCLUSION: The proposed method is able to deal with thousands of examples while combining hundreds of kernels within reasonable time, and reliably identifies a few statistically significant positions.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined, and helps for automatic model selection, improving the interpretability of the learning result. In a second part we discuss general speed up mechanism for SVMs, especially when used with sparse feature maps as appear for string kernels, allowing us to train a string kernel SVM on a 10 million real-world splice data set from computational biology. We integrated multiple kernel learning in our machine learning toolbox SHOGUN for which the source code is publicly available at http://www.fml.tuebingen.mpg.de/raetsch/projects/shogun.

In genomic sequence analysis tasks like splice site recognition or promoter identification, large amounts of training sequences are available, and indeed needed to achieve sufficiently high classification performances. In this work we study two recently proposed and successfully used kernels, namely the Spectrum kernel and the Weighted Degree kernel (WD). In particular, we suggest several extensions using Suffix Trees and modifications of an SMO-like SVM training algorithm in order to accelerate the training of the SVMs and their evaluation on test sequences. Our simulations show that for the spectrum kernel and WD kernel, large scale SVM training can be accelerated by factors of 20 and 4 times, respectively, while using much less memory (e.g. no kernel caching). The evaluation on new sequences is often several thousand times faster using the new techniques (depending on the number of Support Vectors). Our method allows us to train on sets as large as one million sequences.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classi- fication, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementa- tions. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classifica- tion. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learn- ing result and works for hundred thousands of examples or hundreds of kernels to be combined. f (x) = sign N Xi=1 αiyik(xi, x) + b! ,

Recently, Jaakkola and Haussler (1999) proposed a method for constructing kernel functions from probabilistic models. Their so-called Fisher kernel has been combined with discriminative classifiers such as support vector machines and applied successfully in, for example, DNA and protein analysis. Whereas the Fisher kernel is calculated from the marginal log-likelihood, we propose the TOP kernel derived; from tangent vectors of posterior log-odds. Furthermore, we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing the TOP kernel. In experiments, our new discriminative TOP kernel compares favorably to the Fisher kernel.

Recently, Jaakkola and Haussler proposed a method for construct(cid:173) ing kernel functions from probabilistic models. Their so called "Fisher kernel" has been combined with discriminative classifiers such as SVM and applied successfully in e.g. DNA and protein analysis. Whereas the Fisher kernel (FK) is calculated from the marginal log-likelihood, we propose the TOP kernel derived from Tangent vectors Of Posterior log-odds. Furthermore we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing FK and TOP. In experiments our new discriminative TOP kernel compares favorably to the Fisher kernel.