Francis R. Bach

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Sparse coding—that is, modelling data vectors as sparse linear combinations of basis elements—is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set in order to adapt it to specific data. Variations of this problem include(More)
Sparse coding---that is, modelling data vectors as sparse linear combinations of basis elements---is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on <i>learning</i> the basis set, also called dictionary, to adapt it to specific data, an approach that has recently proven to be very effective for signal(More)
We propose in this paper to unify two different approaches to image restoration: On the one hand, learning a basis set (dictionary) adapted to sparse signal descriptions has proven to be very effective in image reconstruction and classification tasks. On the other hand, explicitly exploiting the self-similarities of natural images has led to the successful(More)
We develop an online variational Bayes (VB) algorithm for Latent Dirichlet Allocation (LDA). Online LDA is based on online stochastic optimization with a natural gradient step, which we show converges to a local optimum of the VB objective function. It can handily analyze massive document collections, including those arriving in a stream. We study the(More)
While classical kernel-based classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimization of the coefficients of such a combination reduces to(More)
In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for composite objectives where a proximal(More)
Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context,(More)
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by(More)
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of purely reconstructive ones. This paper proposes a new step in that direction, with a novel sparse representation for(More)
Many successful models for scene or object recognition transform low-level descriptors (such as Gabor filter responses, or SIFT descriptors) into richer representations of intermediate complexity. This process can often be broken down into two steps: (1) a coding step, which performs a pointwise transformation of the descriptors into a representation better(More)