arXiv subjects

François Laviolette

Publications and source records attributed to François Laviolette.

33 records · Page 2Linked to original sources

arXiv2015

Risk Bounds for the Majority Vote: From a PAC-Bayesian Analysis to a Learning Algorithm

We propose an extensive analysis of the behavior of majority votes in binary classification. In particular, we introduce a risk bound for majority votes, called the C-bound, that takes into account the average quality of the voters and their average disagreement. We also propose an extensive PAC-Bayesian analysis that shows how the C-bound can be estimated from various observations contained in the training data. The analysis intends to be self-contained and can be used as introductory material to PAC-Bayesian statistical learning theory. It starts from a general PAC-Bayesian perspective and ends with uncommon PAC-Bayesian bounds. Some of these bounds contain no Kullback-Leibler divergence and others allow kernel functions to be used as voters (via the sample compression setting). Finally, out of the analysis, we propose the MinCq learning algorithm that basically minimizes the C-bound. MinCq reduces to a simple quadratic program. Aside from being theoretically grounded, MinCq achieves state-of-the-art performance, as shown in our extensive empirical comparison with both AdaBoost and the Support Vector Machine.

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arXiv2015

On the Generalization of the C-Bound to Structured Output Ensemble Methods

This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second statistical moments of the vote's margin. This bound may advantageously $(i)$ be applied on more complex outputs such as multiclass labels and multilabel, and $(ii)$ allow to consider margin relaxations. These results open the way to develop new ensemble methods for structured output prediction with PAC-Bayesian guarantees.

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arXiv2015

Greedy Biomarker Discovery in the Genome with Applications to Antimicrobial Resistance

The Set Covering Machine (SCM) is a greedy learning algorithm that produces sparse classifiers. We extend the SCM for datasets that contain a huge number of features. The whole genetic material of living organisms is an example of such a case, where the number of feature exceeds 10^7. Three human pathogens were used to evaluate the performance of the SCM at predicting antimicrobial resistance. Our results show that the SCM compares favorably in terms of sparsity and accuracy against L1 and L2 regularized Support Vector Machines and CART decision trees. Moreover, the SCM was the only algorithm that could consider the full feature space. For all other algorithms, the latter had to be filtered as a preprocessing step.

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arXiv2015

Domain-Adversarial Neural Networks

We introduce a new representation learning algorithm suited to the context of domain adaptation, in which data at training and test time come from similar but different distributions. Our algorithm is directly inspired by theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on a data representation that cannot discriminate between the training (source) and test (target) domains. We propose a training objective that implements this idea in the context of a neural network, whose hidden layer is trained to be predictive of the classification task, but uninformative as to the domain of the input. Our experiments on a sentiment analysis classification benchmark, where the target domain data available at training time is unlabeled, show that our neural network for domain adaption algorithm has better performance than either a standard neural network or an SVM, even if trained on input features extracted with the state-of-the-art marginalized stacked denoising autoencoders of Chen et al. (2012).

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arXiv2014

On the String Kernel Pre-Image Problem with Applications in Drug Discovery

The pre-image problem has to be solved during inference by most structured output predictors. For string kernels, this problem corresponds to finding the string associated to a given input. An algorithm capable of solving or finding good approximations to this problem would have many applications in computational biology and other fields. This work uses a recent result on combinatorial optimization of linear predictors based on string kernels to develop, for the pre-image, a low complexity upper bound valid for many string kernels. This upper bound is used with success in a branch and bound searching algorithm. Applications and results in the discovery of druggable peptides are presented and discussed.

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arXiv2014

Learning interpretable models of phenotypes from whole genome sequences with the Set Covering Machine

The increased affordability of whole genome sequencing has motivated its use for phenotypic studies. We address the problem of learning interpretable models for discrete phenotypes from whole genomes. We propose a general approach that relies on the Set Covering Machine and a k-mer representation of the genomes. We show results for the problem of predicting the resistance of Pseudomonas Aeruginosa, an important human pathogen, against 4 antibiotics. Our results demonstrate that extremely sparse models which are biologically relevant can be learnt using this approach.

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arXiv2014

Improved design and screening of high bioactivity peptides for drug discovery

The discovery of peptides having high biological activity is very challenging mainly because there is an enormous diversity of compounds and only a minority have the desired properties. To lower cost and reduce the time to obtain promising compounds, machine learning approaches can greatly assist in the process and even replace expensive laboratory experiments by learning a predictor with existing data. Unfortunately, selecting ligands having the greatest predicted bioactivity requires a prohibitive amount of computational time. For this combinatorial problem, heuristics and stochastic optimization methods are not guaranteed to find adequate compounds. We propose an efficient algorithm based on De Bruijn graphs, guaranteed to find the peptides of maximal predicted bioactivity. We demonstrate how this algorithm can be part of an iterative combinatorial chemistry procedure to speed up the discovery and the validation of peptide leads. Moreover, the proposed approach does not require the use of known ligands for the target protein since it can leverage recent multi-target machine learning predictors where ligands for similar targets can serve as initial training data. Finally, we validated the proposed approach in vitro with the discovery of new cationic anti-microbial peptides. Source code is freely available at http://graal.ift.ulaval.ca/peptide-design/.

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arXiv2014

Sequential Model-Based Ensemble Optimization

One of the most tedious tasks in the application of machine learning is model selection, i.e. hyperparameter selection. Fortunately, recent progress has been made in the automation of this process, through the use of sequential model-based optimization (SMBO) methods. This can be used to optimize a cross-validation performance of a learning algorithm over the value of its hyperparameters. However, it is well known that ensembles of learned models almost consistently outperform a single model, even if properly selected. In this paper, we thus propose an extension of SMBO methods that automatically constructs such ensembles. This method builds on a recently proposed ensemble construction paradigm known as agnostic Bayesian learning. In experiments on 22 regression and 39 classification data sets, we confirm the success of this proposed approach, which is able to outperform model selection with SMBO.

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arXiv2013

Assemblathon 2: evaluating de novo methods of genome assembly in three vertebrate species

Background - The process of generating raw genome sequence data continues to become cheaper, faster, and more accurate. However, assembly of such data into high-quality, finished genome sequences remains challenging. Many genome assembly tools are available, but they differ greatly in terms of their performance (speed, scalability, hardware requirements, acceptance of newer read technologies) and in their final output (composition of assembled sequence). More importantly, it remains largely unclear how to best assess the quality of assembled genome sequences. The Assemblathon competitions are intended to assess current state-of-the-art methods in genome assembly. Results - In Assemblathon 2, we provided a variety of sequence data to be assembled for three vertebrate species (a bird, a fish, and snake). This resulted in a total of 43 submitted assemblies from 21 participating teams. We evaluated these assemblies using a combination of optical map data, Fosmid sequences, and several statistical methods. From over 100 different metrics, we chose ten key measures by which to assess the overall quality of the assemblies. Conclusions - Many current genome assemblers produced useful assemblies, containing a significant representation of their genes, regulatory sequences, and overall genome structure. However, the high degree of variability between the entries suggests that there is still much room for improvement in the field of genome assembly and that approaches which work well in assembling the genome of one species may not necessarily work well for another.

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arXiv2012

PAC-Bayesian Learning and Domain Adaptation

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a ρ-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the ρ-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.

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arXiv2012

Learning a peptide-protein binding affinity predictor with kernel ridge regression

We propose a specialized string kernel for small bio-molecules, peptides and pseudo-sequences of binding interfaces. The kernel incorporates physico-chemical properties of amino acids and elegantly generalize eight kernels, such as the Oligo, the Weighted Degree, the Blended Spectrum, and the Radial Basis Function. We provide a low complexity dynamic programming algorithm for the exact computation of the kernel and a linear time algorithm for it's approximation. Combined with kernel ridge regression and SupCK, a novel binding pocket kernel, the proposed kernel yields biologically relevant and good prediction accuracy on the PepX database. For the first time, a machine learning predictor is capable of accurately predicting the binding affinity of any peptide to any protein. The method was also applied to both single-target and pan-specific Major Histocompatibility Complex class II benchmark datasets and three Quantitative Structure Affinity Model benchmark datasets. On all benchmarks, our method significantly (p-value < 0.057) outperforms the current state-of-the-art methods at predicting peptide-protein binding affinities. The proposed approach is flexible and can be applied to predict any quantitative biological activity. The method should be of value to a large segment of the research community with the potential to accelerate peptide-based drug and vaccine development.

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arXiv2012

PAC-Bayesian Inequalities for Martingales

We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expectation of a convex function of a martingale difference sequence shifted to the [0,1] interval by the expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma's inequality.

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arXiv2012

PAC-Bayes-Bernstein Inequality for Martingales and its Application to Multiarmed Bandits

We develop a new tool for data-dependent analysis of the exploration-exploitation trade-off in learning under limited feedback. Our tool is based on two main ingredients. The first ingredient is a new concentration inequality that makes it possible to control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. The second ingredient is an application of this inequality to the exploration-exploitation trade-off via importance weighted sampling. We apply the new tool to the stochastic multiarmed bandit problem, however, the main importance of this paper is the development and understanding of the new tool rather than improvement of existing algorithms for stochastic multiarmed bandits. In the follow-up work we demonstrate that the new tool can improve over state-of-the-art in structurally richer problems, such as stochastic multiarmed bandits with side information (Seldin et al., 2011a).

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arXiv2011

PAC-Bayesian Analysis of the Exploration-Exploitation Trade-off

We develop a coherent framework for integrative simultaneous analysis of the exploration-exploitation and model order selection trade-offs. We improve over our preceding results on the same subject (Seldin et al., 2011) by combining PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a combination is also of independent interest for studies of multiple simultaneously evolving martingales.

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arXiv2011

PAC-Bayesian Analysis of Martingales and Multiarmed Bandits

We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered.

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