Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Overcomplete Dictionary and Deep Learning Approaches to Image and Video Analysis

Extracting useful information while ignoring others (e.g. noise, occlusion, lighting) is an essential and challenging data analyzing step for many computer vision tasks such as facial recognition, scene reconstruction, event detection, image restoration, etc. Data analyzing of those tasks can be formulated as a form of matrix decomposition or factorization to separate useful and/or fill in missing information based on sparsity and/or low-rankness of the data. There has been an increasing number of non-convex approaches including conventional matrix norm optimizing and emerging deep learning models. However, it is hard to optimize the ideal l0-norm or learn the deep models directly and efficiently. Motivated from this challenging process, this thesis proposes two sets of approaches: conventional and deep learning based. For conventional approaches, this thesis proposes a novel online non-convex lp-norm based Robust PCA (OLP-RPCA) approach for matrix decomposition, where 0 < p < 1. OLP-RPCA is developed from the offline version LP-RPCA. A robust face recognition framework is also developed from Robust PCA and sparse coding approaches. More importantly, OLP-RPCA method can achieve real-time performance on large-scale data without parallelizing or implementing on a graphics processing unit. We mathematically and empirically show that our OLP-RPCA algorithm is linear in both the sample dimension and the number of samples. The proposed OLP-RPCA and LP-RPCA approaches are evaluated in various applications including Gaussian/non-Gaussian image denoising, face modeling, real-time background subtraction and video inpainting and compared against numerous state-of-the-art methods to demonstrate the robustness of the algorithms. In addition, this thesis proposes a novel Robust lp-norm Singular Value Decomposition (RP-SVD) method for analyzing two-way functional data. The proposed RP-SVD is formulated as an lp-norm based penalized loss minimization problem. The proposed RP-SVD method is evaluated in four applications, i.e. noise and outlier removal, estimation of missing values, structure from motion reconstruction and facial image reconstruction. For deep learning based approaches, this thesis explores the idea of matrix decomposition via Robust Deep Boltzmann Machines (RDBM), an alternative form of Robust Boltzmann Machines, which aiming at dealing with noise and occlusion for face-related applications, particularly. This thesis proposes an extension to texture modeling in the Deep Appearance Models (DAMs) by using RDBM to enhance its robustness against noise and occlusion. The extended model can cope with occlusion and extreme poses when modeling human faces in 2D image reconstruction. This thesis also introduces new fitting algorithms with occlusion awareness through the mask obtained from the RDBM reconstruction. The proposed approach is evaluated in various applications by using challenging face datasets, i.e. Labeled Face Parts in the Wild (LFPW), Helen, EURECOM and AR databases, to demonstrate its robustness and capabilities

Optimization for Probabilistic Machine Learning

We have access to great variety of datasets more than any time in the history. Everyday, more data is collected from various natural resources and digital platforms. Great advances in the area of machine learning research in the past few decades have relied strongly on availability of these datasets. However, analyzing them imposes significant challenges that are mainly due to two factors. First, the datasets have complex structures with hidden interdependencies. Second, most of the valuable datasets are high dimensional and are largely scaled. The main goal of a machine learning framework is to design a model that is a valid representative of the observations and develop a learning algorithm to make inference about unobserved or latent data based on the observations. Discovering hidden patterns and inferring latent characteristics in such datasets is one of the greatest challenges in the area of machine learning research. In this dissertation, I will investigate some of the challenges in modeling and algorithm design, and present my research results on how to overcome these obstacles. Analyzing data generally involves two main stages. The first stage is designing a model that is flexible enough to capture complex variation and latent structures in data and is robust enough to generalize well to the unseen data. Designing an expressive and interpretable model is one of crucial objectives in this stage. The second stage involves training learning algorithm on the observed data and measuring the accuracy of model and learning algorithm. This stage usually involves an optimization problem whose objective is to tune the model to the training data and learn the model parameters. Finding global optimal or sufficiently good local optimal solution is one of the main challenges in this step. Probabilistic models are one of the best known models for capturing data generating process and quantifying uncertainties in data using random variables and probability distributions. They are powerful models that are shown to be adaptive and robust and can scale well to large datasets. However, most probabilistic models have a complex structure. Training them could become challenging commonly due to the presence of intractable integrals in the calculation. To remedy this, they require approximate inference strategies that often results in non-convex optimization problems. The optimization part ensures that the model is the best representative of data or data generating process. The non-convexity of an optimization problem take away the general guarantee on finding a global optimal solution. It will be shown later in this dissertation that inference for a significant number of probabilistic models require solving a non-convex optimization problem. One of the well-known methods for approximate inference in probabilistic modeling is variational inference. In the Bayesian setting, the target is to learn the true posterior distribution for model parameters given the observations and prior distributions. The main challenge involves marginalization of all the other variables in the model except for the variable of interest. This high-dimensional integral is generally computationally hard, and for many models there is no known polynomial time algorithm for calculating them exactly. Variational inference deals with finding an approximate posterior distribution for Bayesian models where finding the true posterior distribution is analytically or numerically impossible. It assumes a family of distribution for the estimation, and finds the closest member of that family to the true posterior distribution using a distance measure. For many models though, this technique requires solving a non-convex optimization problem that has no general guarantee on reaching a global optimal solution. This dissertation presents a convex relaxation technique for dealing with hardness of the optimization involved in the inference. The proposed convex relaxation technique is based on semidefinite optimization that has a general applicability to polynomial optimization problem. I will present theoretical foundations and in-depth details of this relaxation in this work. Linear dynamical systems represent the functionality of many real-world physical systems. They can describe the dynamics of a linear time-varying observation which is controlled by a controller unit with quadratic cost function objectives. Designing distributed and decentralized controllers is the goal of many of these systems, which computationally, results in a non-convex optimization problem. In this dissertation, I will further investigate the issues arising in this area and develop a convex relaxation framework to deal with the optimization challenges. Setting the correct number of model parameters is an important aspect for a good probabilistic model. If there are only a few parameters, model may lack capturing all the essential relations and components in the observations while too many parameters may cause significant complications in learning or overfit to the observations. Non-parametric models are suitable techniques to deal with this issue. They allow the model to learn the appropriate number of parameters to describe the data and make predictions. In this dissertation, I will present my work on designing Bayesian non-parametric models as powerful tools for learning representations of data. Moreover, I will describe the algorithm that we derived to efficiently train the model on the observations and learn the number of model parameters. Later in this dissertation, I will present my works on designing probabilistic models in combination with deep learning methods for representing sequential data. Sequential datasets comprise a significant portion of resources in the area of machine learning research. Designing models to capture dependencies in sequential datasets are of great interest and have a wide variety of applications in engineering, medicine and statistics. Recent advances in deep learning research has shown exceptional promises in this area. However, they lack interpretability in their general form. To remedy this, I will present my work on mixing probabilistic models with neural network models that results in better performance and expressiveness of the results

Détection de changement par fusion d'images de télédétection de résolutions et modalités différentes

La détection de changements dans une scène est l’un des problèmes les plus complexes en télédétection. Il s’agit de détecter des modifications survenues dans une zone géographique donnée par comparaison d’images de cette zone acquises à différents instants. La comparaison est facilitée lorsque les images sont issues du même type de capteur c’est-à-dire correspondent à la même modalité (le plus souvent optique multi-bandes) et possèdent des résolutions spatiales et spectrales identiques. Les techniques de détection de changements non supervisées sont, pour la plupart, conçues spécifiquement pour ce scénario. Il est, dans ce cas, possible de comparer directement les images en calculant la différence de pixels homologues, c’est-à-dire correspondant au même emplacement au sol. Cependant, dans certains cas spécifiques tels que les situations d’urgence, les missions ponctuelles, la défense et la sécurité, il peut s’avérer nécessaire d’exploiter des images de modalités et de résolutions différentes. Cette hétérogénéité dans les images traitées introduit des problèmes supplémentaires pour la mise en œuvre de la détection de changements. Ces problèmes ne sont pas traités par la plupart des méthodes de l’état de l’art. Lorsque la modalité est identique mais les résolutions différentes, il est possible de se ramener au scénario favorable en appliquant des prétraitements tels que des opérations de rééchantillonnage destinées à atteindre les mêmes résolutions spatiales et spectrales. Néanmoins, ces prétraitements peuvent conduire à une perte d’informations pertinentes pour la détection de changements. En particulier, ils sont appliqués indépendamment sur les deux images et donc ne tiennent pas compte des relations fortes existant entre les deux images. L’objectif de cette thèse est de développer des méthodes de détection de changements qui exploitent au mieux l’information contenue dans une paire d’images observées, sans condition sur leur modalité et leurs résolutions spatiale et spectrale. Les restrictions classiquement imposées dans l’état de l’art sont levées grâce à une approche utilisant la fusion des deux images observées. La première stratégie proposée s’applique au cas d’images de modalités identiques mais de résolutions différentes. Elle se décompose en trois étapes. La première étape consiste à fusionner les deux images observées ce qui conduit à une image de la scène à haute résolution portant l’information des changements éventuels. La deuxième étape réalise la prédiction de deux images non observées possédant des résolutions identiques à celles des images observées par dégradation spatiale et spectrale de l’image fusionnée. Enfin, la troisième étape consiste en une détection de changements classique entre images observées et prédites de mêmes résolutions. Une deuxième stratégie modélise les images observées comme des versions dégradées de deux images non observées caractérisées par des résolutions spectrales et spatiales identiques et élevées. Elle met en œuvre une étape de fusion robuste qui exploite un a priori de parcimonie des changements observés. Enfin, le principe de la fusion est étendu à des images de modalités différentes. Dans ce cas où les pixels ne sont pas directement comparables, car correspondant à des grandeurs physiques différentes, la comparaison est réalisée dans un domaine transformé. Les deux images sont représentées par des combinaisons linéaires parcimonieuses des éléments de deux dictionnaires couplés, appris à partir des données. La détection de changements est réalisée à partir de l’estimation d’un code couplé sous condition de parcimonie spatiale de la différence des codes estimés pour chaque image. L’expérimentation de ces différentes méthodes, conduite sur des changements simulés de manière réaliste ou sur des changements réels, démontre les avantages des méthodes développées et plus généralement de l’apport de la fusion pour la détection de changement

Algorithms for Multiclass Classification and Regularized Regression

Multiclass classification and regularized regression problems are very common in modern statistical and machine learning applications. On the one hand, multiclass classification problems require the prediction of class labels: given observations of objects that belong to certain classes, can we predict to which class a new object belongs? On the other hand, the reg