In this paper, we propose a way to combine two acceleration techniques for the @math -regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms, and the use of fast structured approximations of the dictionary matrix. To do so, we introduce a new family of screening tests, termed stable screening, which can cope with approximation errors on the dictionary atoms while keeping the safety of the test (i.e. zero risk of rejecting atoms belonging to the solution support). Some of the main existing screening tests are extended to this new framework. The proposed algorithm consists in using a coarser (but faster) approximation of the dictionary at the initial iterations and then switching to better approximations until eventually adopting the original dictionary. A systematic switching criterion based on the duality gap saturation and the screening ratio is derived.Simulation results show significant reductions in both computational complexity and execution times for a wide range of tested scenarios.
Apart from the aforementioned structured dictionaries and safe screening tests --as well as other preceding correlation-based feature selection heuristics @cite_34 @cite_37 -- some related acceleration strategies for sparsity-inducing optimization problems (or more specifically for problem ) are worth citing.
@cite_37 @cite_34
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Convex sparsity-inducing regularizations are ubiquitous in high-dimensional machine learning, but solving the resulting optimization problems can be slow. To accelerate solvers, state-of-the-art approaches consist in reducing the size of the optimization problem at hand. In the context of regression, this can be achieved either by discarding irrelevant features (screening techniques) or by prioritizing features likely to be included in the support of the solution (working set techniques). Duality comes into play at several steps in these techniques. Here, we propose an extrapolation technique starting from a sequence of iterates in the dual that leads to the construction of improved dual points. This enables a tighter control of op-timality as used in stopping criterion, as well as better screening performance of Gap Safe rules. Finally, we propose a working set strategy based on an aggressive use of Gap Safe screening rules. Thanks to our new dual point construction, we show significant computational speedups on multiple real-world problems. We address the problem of learning structured unsupervised models with moment sparsity typical in many natural language induction tasks. For example, in unsupervised part-of-speech (POS) induction using hidden Markov models, we introduce a bias for words to be labeled by a small number of tags. In order to express this bias of posterior sparsity as opposed to parametric sparsity, we extend the posterior regularization framework [7]. We evaluate our methods on three languages — English, Bulgarian and Portuguese — showing consistent and significant accuracy improvement over EM-trained HMMs, and HMMs with sparsity-inducing Dirichlet priors trained by variational EM. We increase accuracy with respect to EM by 2.3 -6.5 in a purely unsupervised setting as well as in a weakly-supervised setting where the closed-class words are provided. Finally, we show improvements using our method when using the induced clusters as features of a discriminative model in a semi-supervised setting. Today's compilers offer a huge number of transformation options to choose among and this choice can significantly impact on the performance of the code being optimized. Not only the selection of compiler options represents a hard problem to be solved, but also the ordering of the phases is adding further complexity, making it a long standing problem in compilation research. This paper presents an innovative approach for tackling the compiler phase-ordering problem by using predictive modeling. The proposed methodology enables i) to efficiently explore compiler exploration space including optimization permutations and repetitions and ii) to extract the application dynamic features to predict the next-best optimization to be applied to maximize the performance given the current status. Experimental results are done by assessing the proposed methodology with utilizing two different search heuristics on the compiler optimization space and it demonstrates the effectiveness of the methodology on the selected set of applications. Using the proposed methodology on average we observed up to 4 execution speedup with respect to LLVM standard baseline. This paper considers a sparse signal recovery task in time-varying (time-adaptive) environments. The contribution of the paper to sparsity-aware online learning is threefold; first, a generalized thresholding (GT) operator, which relates to both convex and non-convex penalty functions, is introduced. This operator embodies, in a unified way, the majority of well-known thresholding rules which promote sparsity. Second, a non-convexly constrained, sparsity-promoting, online learning scheme, namely the adaptive projection-based generalized thresholding (APGT), is developed that incorporates the GT operator with a computational complexity that scales linearly to the number of unknowns. Third, the novel family of partially quasi-nonexpansive mappings is introduced as a functional analytic tool for treating the GT operator. By building upon the rich fixed point theory, the previous class of mappings establishes also a link between the GT operator and a union of linear subspaces; a non-convex object which lies at the heart of any sparsity promoting technique, batch or online. Based on this functional analytic framework, a convergence analysis of the APGT is provided. Extensive experiments suggest that the APGT exhibits competitive performance when compared to computationally more demanding alternatives, such as the sparsity-promoting affine projection algorithm (APA)- and recursive least-squares (RLS)-based techniques.