Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true velocity field of the corresponding differential equation, approximated by a pre-trained neural network. In contrast, the latter uses a single-sample Monte Carlo estimate of this velocity field. The related estimation error induces a discrepancy between consistency distillation and training that, we show, still holds in the continuous-time limit. To alleviate this issue, we propose a novel flow that transports noisy data towards their corresponding outputs derived from a consistency model. We prove that this flow reduces the previously identified discrepancy and the noise-data transport cost. Consequently, our method not only accelerates consistency training convergence but also enhances its overall performance. The code is available at https://github.com/thibautissenhuth/consistency_GC.

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients whilst a central entity/server orchestrates the computations (again, without having access to the samples). To achieve this feat, we take advantage of the geometric properties of the Wasserstein distance -- in particular, the triangle inequality -- and that of the associated {\em geodesics}: our algorithm, FedWad (for Federated Wasserstein Distance), iteratively approximates the Wasserstein distance by manipulating and exchanging distributions from the space of geodesics in lieu of the input samples. In addition to establishing the convergence properties of FedWad, we provide empirical results on federated coresets and federate optimal transport dataset distance, that we respectively exploit for building a novel federated model and for boosting performance of popular federated learning algorithms.

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires the usage of Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices, and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this discrepancy to brain-age prediction from MEG data, and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties – or, more accurately, its generalization properties – with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

Particle-based deep generative models, such as gradient flows and score-based diffusion models, have recently gained traction thanks to their striking performance. Their principle of displacing particle distributions using differential equations is conventionally seen as opposed to the previously widespread generative adversarial networks (GANs), which involve training a pushforward generator network. In this paper we challenge this interpretation, and propose a novel framework that unifies particle and adversarial generative models by framing generator training as a generalization of particle models. This suggests that a generator is an optional addition to any such generative model. Consequently, integrating a generator into a score-based diffusion model and training a GAN without a generator naturally emerge from our framework. We empirically test the viability of these original models as proofs of concepts of potential applications of our framework.

Non-convex sparse regularizers are common tools for learning with high-dimensional data. For accelerating convergence for Lasso problem involving those regularizers, a working set strategy addresses the optimization problem through an iterative algorithm by gradually incrementing the number of variables to optimize until the identification of the solution support. We propose in this paper the first Lasso working set algorithm for non-convex sparse regularizers with convergence guarantees. The algorithm, named FireWorks, is based on a non-convex reformulation of a recent duality-based approach and leverages on the geometry of the residuals. We provide theoretical guarantees showing that convergence is preserved even when the inner solver is inexact, under sufficient decay of the error across iterations. Experimental results demonstrate strong computational gain when using our working set strategy compared to full problem solvers for both block-coordinate descent or a proximal gradient solver.

Data-driven approaches to modeling physical systems fail to generalize to unseen systems that share the same general dynamics with the learning domain, but correspond to different physical contexts. We propose a new framework for this key problem, context-informed dynamics adaptation (CoDA), which takes into account the distributional shift across systems for fast and efficient adaptation to new dynamics. CoDA leverages multiple environments, each associated to a different dynamic, and learns to condition the dynamics model on contextual parameters, specific to each environment. The conditioning is performed via a hypernetwork, learned jointly with a context vector from observed data. The proposed formulation constrains the search hypothesis space for fast adaptation and better generalization across environments with few samples. We theoretically motivate our approach and show state-of-the-art generalization results on a set of nonlinear dynamics, representative of a variety of application domains. We also show, on these systems, that new system parameters can be inferred from context vectors with minimal supervision.

Numerical validation is at the core of machine learning research as it allows us to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automatize, publish and reproduce optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard ML tasks: $\ell_2$-regularized logistic regression, Lasso and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details.

Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA) strategies were shown to perform best on the competitive DomainBed benchmark; they directly average the weights of multiple networks despite their nonlinearities. In this paper, we propose Diverse Weight Averaging (DiWA), a new WA strategy whose main motivation is to increase the functional diversity across averaged models. To this end, DiWA averages weights obtained from several independent training runs: indeed, models obtained from different runs are more diverse than those collected along a single run thanks to differences in hyperparameters and training procedures. We motivate the need for diversity by a new bias-variance-covariance-locality decomposition of the expected error, exploiting similarities between WA and standard functional ensembling. Moreover, this decomposition highlights that WA succeeds when the variance term dominates, which we show occurs when the marginal distribution changes at test time. Experimentally, DiWA consistently improves the state of the art on DomainBed without inference overhead.

This work addresses the problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets. Most current approaches tackle this problem by searching for an embedding that is invariant across source and target domains, which corresponds to searching for a universal classifier that works well on all domains. In this paper, we address this problem from a new perspective: instead of crushing diversity of the source distributions, we exploit it to adapt better to the target distribution. Our method, named Multi-Source Domain Adaptation via Weighted Joint Distribution Optimal Transport (MSDA-WJDOT), aims at finding simultaneously an Optimal Transport-based alignment between the source and target distributions and a re-weighting of the sources distributions. We discuss the theoret- ical aspects of the method and propose a conceptually simple algorithm. Numerical experiments indicate that the proposed method achieves state-of- the-art performance on simulated and real datasets.

We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we consider a method allowing to embed the metric measure spaces in a common Euclidean space and compute an optimal transport (OT) on the embedded distributions. This leads to what we call a sub-embedding robust Wasserstein (SERW) distance. Under some conditions, SERW is a distance that considers an OT distance of the (low-distorted) embedded distributions using a common metric. In addition to this novel proposal that generalizes several recent OT works, our contributions stand on several theoretical analyses: (i) we characterize the embedding spaces to define SERW distance for distribution alignment; (ii) we prove that SERW mimics almost the same properties of GW distance, and we give a cost relation between GW and SERW. The paper also provides some numerical illustrations of how SERW behaves on matching problems.

Developing machine learning methods that are privacy preserving is today a central topic of research, with huge practical impacts. Among the numerous ways to address privacy-preserving learning, we here take the perspective of computing the divergences between distributions under the Differential Privacy (DP) framework — being able to compute divergences between distributions is pivotal for many machine learning problems, such as learning generative models or domain adaptation problems. Instead of resorting to the popular gradient-based sanitization method for DP, we tackle the problem at its roots by focusing on the Sliced Wasserstein Distance and seamlessly making it differentially private. Our main contribution is as follows: we analyze the property of adding a Gaussian perturbation to the intrinsic randomized mechanism of the Sliced Wasserstein Distance, and we establish the sensitivity of the resulting differentially private mechanism. One of our important findings is that this DP mechanism transforms the Sliced Wasserstein distance into another distance, that we call the Smoothed Sliced Wasserstein Distance. This new differentially private distribution distance can be plugged into generative models and domain adaptation algorithms in a transparent way, and we empirically show that it yields highly competitive performance compared with gradient-based DP approaches from the literature, with almost no loss in accuracy for the domain adaptation problems that we consider.

Optical Processing Units (OPUs) -- low-power photonic chips dedicated to large scale random projections -- have been used in previous work to train deep neural networks using Direct Feedback Alignment (DFA), an effective alternative to backpropagation. Here, we demonstrate how to leverage the intrinsic noise of optical random projections to build a differentially private DFA mechanism, making OPUs a solution of choice to provide a \emph{private-by-design} training. We provide a theoretical analysis of our adaptive privacy mechanism, carefully measuring how the noise of optical random projections propagates in the process and gives rise to provable Differential Privacy. Finally, we conduct experiments demonstrating the ability of our learning procedure to achieve solid end-task performance.

Optimal transport has recently been reintroduced to the machine learning community thanks in part to novel efficient optimization procedures allowing for medium to large scale applications. We propose a Python toolbox that implements several key optimal transport ideas for the machine learning community. The toolbox contains implementations of a number of founding works of OT for machine learning such as Sinkhorn algorithm and Wasserstein barycenters, but also provides generic solvers that can be used for conducting novel fundamental research. This toolbox, named POT for Python Optimal Transport, is open source with an MIT license.

The trace regression model, a direct extension of the well-studied linear regression model, allows one to map matrices to real-valued outputs. We here introduce an even more general model, namely the partial-trace regression model, a family of linear mappings from matrix-valued inputs to matrix-valued outputs; this model subsumes the trace regression model and thus the linear regression model. Borrowing tools from quantum information theory, where partial trace operators have been extensively studied, we propose a framework for learning partial trace regression models from data by taking advantage of the so-called low-rank Kraus representation of completely positive maps. We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semidefinite matrix completion, two tasks which can be formulated as partial trace regression problems.

Leveraging on the convexity of the Lasso problem, screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been proposed in the literature. This work is the first that introduces a screening rule strategy into a non-convex Lasso solver. The approach we propose is based on a iterative majorization-minimization (MM) strategy that includes a screening rule in the inner solver and a condition for propagating screened variables between iterations of MM. In addition to improve efficiency of solvers, we also provide guarantees that the inner solver is able to identify the zeros components of its critical point in finite time. Our experimental analysis illustrates the significant computational gain brought by the new screening rule compared to classical coordinate-descent or proximal gradient descent methods.

We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering the Sinkhorn problem. This allows us to solve a smaller Sinkhorn problem while ensuring approximation with provable guarantees. More formally, the approach is based on a new formulation of dual of Sinkhorn divergence problem and on the KKT optimality conditions of this problem, which enable identification of dual components to be screened. This new analysis leads to the Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn on complex tasks such as dimensionality reduction and domain adaptation involving regularized optimal transport.

This paper introduces a new approach for the scalable Tucker decomposition problem. Given a tensor X , the method proposed allows to infer the latent factors by processing one subtensor drawn from X at a time. The key principle of our approach is based on the recursive computations of gradient and on cyclic update of factors involving only one single step of gradient descent. We further improve the computational efficiency of this algorithm by proposing an inexact gradient version. These two algorithms are backed with theoretical guarantees of convergence and convergence rate under mild conditions. The scalabilty of the proposed approaches which can be easily extended to handle some common constraints encountered in tensor decomposition (e.g non-negativity), is proven via numerical experiments on both synthetic and real data sets.

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computations, that are key for developing generic dictionary learning algorithms applicable to smooth and nonsmooth losses. In order to improve identification of outliers, we introduce an initialization heuristic based on undercom-plete dictionary learning. Experimental results using synthetic and real data demonstrate that our method is able to better detect outliers, and thus capable of generating better dictionaries, outperforming state-of-the-art methods such as K-SVD and LC-KSVD.

This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function $f$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linear transformation between the joint feature/label space distributions of the two domain $\ps$ and $\pt$. We propose a solution of this problem with optimal transport, that allows to recover an estimated target $\pt^f=(X,f(X))$ by optimizing simultaneously the optimal coupling and $f$. We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results.

Domain adaptation is one of the most challenging tasks of modern data analytics. If the adaptation is done correctly, models built on a specific data representation become more robust when confronted to data depicting the same classes, but described by another observation system. Among the many strategies proposed, finding domain-invariant representations has shown excellent properties, in particular since it allows to train a unique classifier effective in all domains. In this paper, we propose a regularized unsupervised optimal transportation model to perform the alignment of the representations in the source and target domains. We learn a transportation plan matching both PDFs, which constrains labeled samples of the same class in the source domain to remain close during transport. This way, we exploit at the same time the labeled samples in the source and the distributions observed in both domains. Experiments on toy and challenging real visual adaptation examples show the interest of the method, that consistently outperforms state of the art approaches. In addition, numerical experiments show that our approach leads to better performances on domain invariant deep learning features and can be easily adapted to the semi-supervised case where few labeled samples are available in the target domain.

This paper investigates the use of supervised feature learning approaches for extracting relevant and discriminative features from acoustic scene recordings. Owing to the recent release of open datasets for acoustic scene classification problems, representation learning techniques can now be envisioned for solving the problem of feature extraction. This paper makes a step toward this goal by first introducing a supervised nonnegative matrix factorization (SNMF). Our goal through this SNMF is to induce the matrix decomposition to carry out discriminative information in addition to the usual generative ones. We achieve this objective by augmenting the nonnegative matrix factorization optimization problem with a novel loss function related to class labels of each column of the matrix to decompose. While the scale of the datasets available is still small compared to those available in computer vision, we have studied models based on convolutional neural networks. We have analyzed the performances of these models on the DCASE-16 dataset and a corrected version of the LITIS Rouen one. Our experiments show that despite the small-scale setting, supervised feature learning is favorably competitive compared to the current state-of-the-art features. We also point out that for smaller scale dataset, SNMF is indeed slightly less prone to overfitting than convolutional neural networks. While the performances of these learned features are interesting per se, a deeper analysis of their behavior in the acoustic scene problem context raises open and difficult questions that we believe, need to be addressed for further performance breakthroughs.

This issue marks the first anniversary issue since I was honored to serve as the Editor-in-Chief (EiC) of the IEEE Transactions on Neural Networks and Learning Systems (TNNLS). I am happy to report that we had a very successful year and here are a few highlights that I would like to share with the community.•The latest impact factor of TNNLS is 4.854 according to the Journal Citation Reports. This marks a record high impact factor for our journal and places TNNLS as the number one scholarly publication in Computer Science (Hardware & Architecture), number three in Computer Science (Theory & Methods), and number ten in Electrical and Electronic Engineering journals.

Several sparsity-constrained algorithms, such as orthogonal matching pursuit (OMP) or the Frank-Wolfe (FW) algorithm, with sparsity constraints work by iteratively selecting a novel atom to add to the current nonzero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this paper, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient's top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best-arm identification in a multiarmed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact FW or OMP algorithms act, with high probability, similar to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms, such as OMP, FW, or CoSaMP.

Let us consider a specific action or situation (called event) that takes place within a time series. The objective in early detection is to build a decision function that is able to go off as soon as possible from the onset of an occurrence of this event. This implies making a decision with an incomplete information. This paper proposes a novel framework that i) guarantees that a detection made with a partial observation will also occur at full observation of the time-series; ii) incorporates in a consistent manner the lack of knowledge about the minimal amount of information needed to make a decision. The proposed detector is based on mapping the temporal sequences to a landmarking space thanks to appropriately designed similarity functions. As a by-product, the framework benefits from a scalable training algorithm and a theoretical guarantee concerning its generalization ability. We also discuss an important improvement of our framework in which decision function can still be made reliable while being more expressive. Our experimental studies provide compelling results on toy data, presenting the trade-off that occurs when aiming at accuracy, earliness and reliability. Results on real physiological and video datasets show that our proposed approach is as accurate and early as state-of-the-art algorithm, while ensuring reliability and being far more efficient to learn.

In this paper (This is a combined and expanded version of previous conference papers Kadri et al., 2010, 2011c) we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are nonconvex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consists in obtaining a descent direction from an approximation of the loss function and then in performing a line search to ensure a sufficient descent. A theoretical analysis is provided showing that the iterates of the proposed algorithm admit as limit points stationary points of the DC objective function. Numerical experiments show that our approach is more efficient than the current state of the art for a problem with a convex loss function and a nonconvex regularizer. We have also illustrated the benefit of our algorithm in high-dimensional transductive learning problem where both the loss function and regularizers are nonconvex.

Presents our entry to the Detection and Classification of Acoustic Scenes challenge. The approach we propose for classifying acoustic scenes is based on transforming the audio signal into a time-frequency representation and then in extracting relevant features about shapes and evolutions of time-frequency structures. These features are based on histogram of gradients that are subsequently fed to a multi-class linear support vector machines.

The use of non-convex sparse regularization has attracted much interest when estimating a very sparse model on high dimensional data. In this work we express the optimality conditions of the optimization problem for a large class of non-convex regularizers. From those conditions, we derive an efficient active set strategy that avoids the computing of unnecessary gradients. Numerical experiments on both generated and real life datasets show a clear gain in computational cost w.r.t. the state of the art when using our method to obtain very sparse solutions.

We propose a new computer-aided detection scheme for prostate cancer screening on multiparametric magnetic resonance (mp-MR) images. Based on an annotated training database of mp-MR images from thirty patients, we train a novel support vector machine (SVM)-inspired classifier which simultaneously learns an optimal linear discriminant and a subset of predictor variables (or features) that are most relevant to the classification task, while promoting spatial smoothness of the malignancy prediction maps. The approach uses a ℓ1-norm in the regularization term of the optimization problem that rewards sparsity. Spatial smoothness is promoted via an additional cost term that encodes the spatial neighborhood of the voxels, to avoid noisy prediction maps. Experimental comparisons of the proposed ℓ1-Smooth SVM scheme to the regular ℓ2-SVM scheme demonstrate a clear visual and numerical gain on our clinical dataset.

Including spatial information is a key step for successful remote sensing image classification. In particular, when dealing with high spatial resolution, if local variability is strongly reduced by spatial filtering, the classification performance results are boosted. In this paper, we consider the triple objective of designing a spatial/spectral classifier, which is compact (uses as few features as possible), discriminative (enhances class separation), and robust (works well in small sample situations). We achieve this triple objective by discovering the relevant features in the (possibly infinite) space of spatial filters by optimizing a margin-maximization criterion. Instead of imposing a filter bank with predefined filter types and parameters, we let the model figure out which set of filters is optimal for class separation. To do so, we randomly generate spatial filter banks and use an active-set criterion to rank the candidate features according to their benefits to margin maximization (and, thus, to generalization) if added to the model. Experiments on multispectral very high spatial resolution (VHR) and hyperspectral VHR data show that the proposed algorithm, which is sparse and linear, finds discriminative features and achieves at least the same performances as models using a large filter bank defined in advance by prior knowledge.

This paper addresses the problem of automatic feature extraction for signal classification. In order to handle non-stationarity, features are designed in the time-frequency domain using a Filter Bank as the mapping function, which enables an easy interpretation for practitioners. The strategy adopted is to jointly learn a Filter Bank with a Support Vector Machine by casting the optimization program as a Multiple Kernel Learning problem. This solves the program for a finite set of filters. Thus, in order to handle an infinite number of filters, a novel active constraint algorithm is proposed based on the latest breakthroughs. Our method has been tested on a toy dataset and compared to classical methods with competitive results.

Inclusion of spatial information is known to be beneficial to the classification of hyperspectral images. However, given the high dimensionality of the data, it is difficult to know before hand which are the bands to filter or what are the filters to be applied. In this paper, we propose an active set algorithm based on a l1 support vector machine that explores the (possibily infinite) space of spatial filters and retrieves automatically the filters that maximize class separation. Experiments on hyperspectral imagery confirms the power of the method, that reaches state of the art performance with small feature sets generated automatically and without prior knowledge.

This paper addresses the problem of principal subspace tracking in presence of a colored noise. We propose to extend the YAST algorithm to handle such a case. We also propose a Riemannian framework that could benefit to other classical trackers. Finally, as a proof of concept, our method is compared to the only oblique tracker of the literature on a toy dataset.

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending functional data analysis methods to nonlinear contexts. We study this problem in the case of kernel ridge regression for functional responses with an lr-norm constraint on the combination coefficients. The resulting optimization problem is more involved than those of multiple scalar-valued kernel learning since operator-valued kernels pose more technical and theoretical issues. We propose a multiple operator-valued kernel learning algorithm based on solving a system of linear operator equations by using a block coordinate-descent procedure. We experimentally validate our approach on a functional regression task in the context of finger movement prediction in brain-computer interfaces.

Recently, there has been much interest around multitask learning (MTL) problem with the constraints that tasks should share a common sparsity profile. Such a problem can be addressed through a regularization framework where the regularizer induces a joint-sparsity pattern between task decision functions. We follow this principled framework and focus on l(p)-l(q) (with 0 ≤ p ≤ 1 and 1 ≤ q ≤ 2) mixed norms as sparsity-inducing penalties. Our motivation for addressing such a larger class of penalty is to adapt the penalty to a problem at hand leading thus to better performances and better sparsity pattern. For solving the problem in the general multiple kernel case, we first derive a variational formulation of the l(1)-l(q) penalty which helps us in proposing an alternate optimization algorithm. Although very simple, the latter algorithm provably converges to the global minimum of the l(1)-l(q) penalized problem. For the linear case, we extend existing works considering accelerated proximal gradient to this penalty. Our contribution in this context is to provide an efficient scheme for computing the l(1)-l(q) proximal operator. Then, for the more general case, when , we solve the resulting nonconvex problem through a majorization-minimization approach. The resulting algorithm is an iterative scheme which, at each iteration, solves a weighted l(1)-l(q) sparse MTL problem. Empirical evidences from toy dataset and real-word datasets dealing with brain-computer interface single-trial electroencephalogram classification and protein subcellular localization show the benefit of the proposed approaches and algorithms.

Signal Sequence Labeling consists in predicting a sequence of labels given an observed sequence of samples. A naive way is to filter the signal in order to reduce the noise and to apply a classification algorithm on the filtered samples. We propose in this paper to jointly learn the filter with the classifier leading to a large margin filtering for classification. This method allows to learn the optimal cutoff frequency and phase of the filter that may be different from zero. Two methods are proposed and tested on a toy dataset and on a real life BCI dataset from BCI Competition III.

This paper addresses the problem of automatic wavelet feature extraction for signal classication. We propose to jointly learn wavelet-based features (including scale and translation of the wavelet as well as its shape) and a decision function by casting the problem as a Multi-Kernel Learning problem. A novel active constraints algorithm is then proposed. Our method has been tested on a toy dataset and compared to classical methods with competitive results.

The Support Vector Machine (SVM) is an acknowledged powerful tool for building classifiers, but it lacks flexibility, in the sense that the kernel is chosen prior to learning. Multiple Kernel Learning (MKL) enables to learn the kernel, from an ensemble of basis kernels, whose combination is optimized in the learning process. Here, we propose Composite Kernel Learning to address the situation where distinct components give rise to a group structure among kernels. Our formulation of the learning problem encompasses several setups, putting more or less emphasis on the group structure. We characterize the convexity of the learning problem, and provide a general wrapper algorithm for computing solutions. Finally, we illustrate the behavior of our method on multi-channel data where groups correpond to channels.

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently. We finally provide preliminary experimental results illustrating the interest of our constructive approach to devising loss functions.

An efficient and general multiple kernel learning (MKL) algorithm has been recently proposed by Sonnenburg et al. (2006). This approach has opened new perspectives since it makes the MKL approach tractable for large-scale problems, by iteratively using existing support vector machine code. However, it turns out that this iterative algorithm needs several iterations before converging towards a reasonable solution. In this paper, we address the MKL problem through an adaptive 2-norm regularization formulation. Weights on each kernel matrix are included in the standard SVM empirical risk minimization problem with a l1 constraint to encourage sparsity. We propose an algorithm for solving this problem and provide an new insight on MKL algorithms based on block 1-norm regularization by showing that the two approaches are equivalent. Experimental results show that the resulting algorithm converges rapidly and its efficiency compares favorably to other MKL algorithms.

This work deals with a method for building a reproducing kernel Hilbert space (RKHS) from a Hilbert space with frame elements having special properties. Conditions on existence and a method of construction are given. Then, these RKHS are used within the framework of regularization theory for function approximation. Implications on semiparametric estimation are discussed and a multiscale scheme of regularization is also proposed. Results on toy and real-world approximation problems illustrate the effectiveness of such methods.