Image Restoration using Plug-and-Play CNN MAP Denoisers

Plug-and-play denoisers can be used to perform generic image restoration tasks independent of the degradation type. These methods build on the fact that the Maximum a Posteriori (MAP) optimization can be solved using smaller sub-problems, including a MAP denoising optimization. We present the first end-to-end approach to MAP estimation for image denoising using deep neural networks. We show that our method is guaranteed to minimize the MAP denoising objective, which is then used in an optimization algorithm for generic image restoration. We provide theoretical analysis of our approach and show the quantitative performance of our method in several experiments. Our experimental results show that the proposed method can achieve 70x faster performance compared to the state-of-the-art, while maintaining the theoretical perspective of MAP.

Multivariate Boosting with Look-Up Tables for Face Processing

Cosmin Atanasoaei

This thesis proposes a novel unified boosting framework. We apply this framework to the several face processing tasks, face detection, facial feature localisation, and pose classification, and use the same boosting algorithm and the same pool of features (local binary features). This is in contrast with the standard approaches that make use of a variety of features and models, for example AdaBoost, cascades of boosted classifiers and Active Appearance Models. The unified boosting framework covers multivariate classification and regression problems and it is achieved by interpreting boosting as optimization in the functional space of the weak learners. Thus a wide range of smooth loss functions can be optimized with the same algorithm. There are two general optimization strategies we propose that extend recent works on TaylorBoost and Variational AdaBoost. The first proposition is an empirical expectation formulation that minimizes the average loss and the second is a variational formulation that includes an additional penalty for large variations between predictions. These two boosting formulations are used to train real-time models using local binary features. This is achieved using look-up-tables as weak learners and multi-block Local Binary Patterns as features. The resulting boosting algorithms are simple, efficient and easily scalable with the available resources. Furthermore, we introduce a novel coarse-to-fine feature selection method to handle high resolution models and a bootstrapping algorithm to sample representative training data from very large pools of data. The proposed approach is evaluated for several face processing tasks. These tasks include frontal face detection (binary classification), facial feature localization (multivariate regression) and pose estimation (multivariate classification). Several studies are performed to assess different optimization algorithms, bootstrapping parametrizations and feature sharing methods (for the multivariate case). The results show good performance for all of these tasks. In addition to this, two other contributions are presented. First, we propose a context-based model for removing the false alarms generated by a given generic face detector. Second, we propose a new face detector that predicts the Jaccard distance between the current location and the ground truth. This allows us to formulate the face detection problem as a regression task.

EPFL2012

Viability evolutionary algorithms and applications to neuroscience and biology

Andrea Maesani

Evolutionary algorithms are heuristic methods that operate on a population of individuals, which represent candidate solutions to optimization problems. Individuals with better quality, or fitness, are reproduced at a higher rate than less fit individuals by recombination and mutation. This process of selection and reproduction, based on fitness, models competition between individuals and leads to survival-of-the-fittest. Although this process lays at the foundation of evolutionary algorithms, the simplistic assumption that a single criterion can describe the quality of individuals is often unmet in real world problems, where multiple objectives or constraints have to be combined in the same fitness function. Furthermore, in nature, survival-of-the-fittest does not derive uniquely from competition, but is better seen as the outcome of an ongoing process of competition in parallel to a process of elimination of non-fit individuals. To resolve this mismatch and model different criteria for individuals separately, the Viability Evolution paradigm has been proposed in the literature. While the idea was previously introduced at a conceptual level, it had not yet been put to the test and lacks experimental validation. Here, we bridged this gap and tested whether viability-inspired evolutionary algorithms could confer advantages over the traditional evolutionary computation paradigm based on fitness. We started by investigating the evolutionary dynamics of a simple viability evolutionary method, and we analyzed the diversity of evolving populations. We also showed that the additional information available to a viability-based algorithm, such as the number of non-viable individuals for each viability criteria, can be exploited during the search for achieving better performance on optimization problems. In particular, we devised viability algorithms for constrained optimization, which outperformed current state-of-the-art methods on a well-known set of constrained optimization benchmarks. Furthermore, we embedded one of our algorithms into a novel framework for predicting structures of protein assemblies at atomic resolution. Finally, we used evolutionary methods to optimize neural networks in the context of a neuroscience investigation on the role of noise in animal behaviors. Noise is a ubiquitous feature of neural systems, but how it affects behaviors is far from being fully understood. After collecting large-scale measurements of Drosophila walking, we used evolutionary algorithms to search for neural networks that could match observed patterns of Drosophila spontaneous and odor-induced walking. By combining dynamical systems analysis and simulations, we showed how a noise-mediated memory of odor exposure accounts for the observed responses. In conclusion, this thesis contributes to evolutionary computation by testing the Viability Evolution paradigm and by proposing efficient viability evolutionary algorithms for constrained optimization. Furthermore, this thesis contributes to biology, by providing a new viability-based framework for predicting protein assemblies and by elucidating a mechanism through which neural noise may shape animal behaviors.

EPFL2015

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016