Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select such a model based on the domain knowledge or using some exemplar signals. This paper presents a new exemplar based approach for the linear model (called the dictionary) selection, for such sparse inverse problems. The problem of dictionary selection, which has also been called the dictionary learning in this setting, is first reformulated as a joint sparsity model. The joint sparsity model here differs from the standard joint sparsity model as it considers an overcompleteness in the representation of each signal, within the range of selected subspaces. The new dictionary selection paradigm is examined with some synthetic and realistic simulations.

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convexity, for which all previously known algorithms achieve a convergence rate for function values of O(1/n^{1/2}). We consider and analyze two algorithms that achieve a rate of O(1/n) for classical supervised learning problems. For least-squares regression, we show that averaged stochastic gradient descent with constant step-size achieves the desired rate. For logistic regression, this is achieved by a simple novel stochastic gradient algorithm that (a) constructs successive local quadratic approximations of the loss functions, while (b) preserving the same running time complexity as stochastic gradient descent. For these algorithms, we provide a non-asymptotic analysis of the generalization error (in expectation, and also in high probability for least-squares), and run extensive experiments on standard machine learning benchmarks showing that they often outperform existing approaches.

The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular {\it $k$-means} is not suitable in this case. In this paper, we propose a noisy $k$-means minimization, which is based on the $k$-means loss function and a deconvolution estimator of the density $f$. In particular, this approach suffers from the dependence on a bandwidth involved in the deconvolution kernel. Fast rates of convergence for the excess risk are proposed for a particular choice of the bandwidth, which depends on the smoothness of the density $f$. Then, we turn out into the main issue of the paper: the data-driven choice of the bandwidth. We state an adaptive upper bound for a new selection rule, called ERC (Empirical Risk Comparison). This selection rule is based on the Lepski's principle, where empirical risks associated with different bandwidths are compared. Finally, we illustrate that this adaptive rule can be used in many statistical problems of $M$-estimation where the empirical risk depends on a nuisance parameter.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.

She has (which includes a human user), while planning determines equipped the apartment with a series of service robots, the concrete actions that should be carried out in order to sensors and actuators which help her manage some of best support the perceived context. The domain description the physical and cognitive difficulties she has due to formalism used by SAM is based on metric temporal constraints; her age. Her home alerts her if she appears to be overcooking such domains model both the criteria for context inference her meals, and autonomously organizes when and the planning operators used for plan synthesis. The of the user and to contextually synthesize action plans for home recognizes when Malin is sleeping, eating and actuators in the intelligent environment. The knowledge representation scheme used in SAM is based State of the art robotic and sensor systems can be leveraged on Allen's Interval Relations (Allen 1984), augmented with to achieve intelligent functionalities that are useful in a number temporal bounds.