Efficient Learning of Sparse Conditional Random Fields for Supervised Sequence Labelling

Conditional Random Fields (CRFs) constitute a popular and efficient approach for supervised sequence labelling. CRFs can cope with large description spaces and can integrate some form of structural dependency between labels. In this contribution, we address the issue of efficient feature selection for CRFs based on imposing sparsity through an L1 penalty. We first show how sparsity of the parameter set can be exploited to significantly speed up training and labelling. We then introduce coordinate descent parameter update schemes for CRFs with L1 regularization. We finally provide some empirical comparisons of the proposed approach with state-of-the-art CRF training strategies. In particular, it is shown that the proposed approach is able to take profit of the sparsity to speed up processing and hence potentially handle larger dimensional models

Optimization with Sparsity-Inducing Penalties

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 regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

Steered mixture-of-experts for light field images and video : representation and coding

Research in light field (LF) processing has heavily increased over the last decade. This is largely driven by the desire to achieve the same level of immersion and navigational freedom for camera-captured scenes as it is currently available for CGI content. Standardization organizations such as MPEG and JPEG continue to follow conventional coding paradigms in which viewpoints are discretely represented on 2-D regular grids. These grids are then further decorrelated through hybrid DPCM/transform techniques. However, these 2-D regular grids are less suited for high-dimensional data, such as LFs. We propose a novel coding framework for higher-dimensional image modalities, called Steered Mixture-of-Experts (SMoE). Coherent areas in the higher-dimensional space are represented by single higher-dimensional entities, called kernels. These kernels hold spatially localized information about light rays at any angle arriving at a certain region. The global model consists thus of a set of kernels which define a continuous approximation of the underlying plenoptic function. We introduce the theory of SMoE and illustrate its application for 2-D images, 4-D LF images, and 5-D LF video. We also propose an efficient coding strategy to convert the model parameters into a bitstream. Even without provisions for high-frequency information, the proposed method performs comparable to the state of the art for low-to-mid range bitrates with respect to subjective visual quality of 4-D LF images. In case of 5-D LF video, we observe superior decorrelation and coding performance with coding gains of a factor of 4x in bitrate for the same quality. At least equally important is the fact that our method inherently has desired functionality for LF rendering which is lacking in other state-of-the-art techniques: (1) full zero-delay random access, (2) light-weight pixel-parallel view reconstruction, and (3) intrinsic view interpolation and super-resolution

Iterative Projection Methods for Structured Sparsity Regularization

In this paper we propose a general framework to characterize and solve the optimization problems underlying a large class of sparsity based regularization algorithms. More precisely, we study the minimization of learning functionals that are sums of a differentiable data term and a convex non differentiable penalty. These latter penalties have recently become popular in machine learning since they allow to enforce various kinds of sparsity properties in the solution. Leveraging on the theory of Fenchel duality and subdifferential calculus, we derive explicit optimality conditions for the regularized solution and propose a general iterative projection algorithm whose convergence to the optimal solution can be proved. The generality of the framework is illustrated, considering several examples of regularization schemes, including l1 regularization (and several variants), multiple kernel learning and multi-task learning. Finally, some features of the proposed framework are empirically studied

Convex Banding of the Covariance Matrix

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings