84 research outputs found
Beyond L1: Faster and Better Sparse Models with skglm
We propose a new fast algorithm to estimate any sparse generalized linear
model with convex or non-convex separable penalties. Our algorithm is able to
solve problems with millions of samples and features in seconds, by relying on
coordinate descent, working sets and Anderson acceleration. It handles
previously unaddressed models, and is extensively shown to improve state-of-art
algorithms. We provide a flexible, scikit-learn compatible package, which
easily handles customized datafits and penalties
Celer: a Fast Solver for the Lasso with Dual Extrapolation
International audienceConvex 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
ν-SVM solutions of constrained lasso and elastic net
Many important linear sparse models have at its core the Lasso problem, for which the GLMNet algorithm is often considered as the current state of the art. Recently M. Jaggi has observed that Constrained Lasso (CL) can be reduced to an SVM-like problem, for which the LIBSVM library provides very efficient algorithms. This suggests that it could also be used advantageously to solve CL. In this work we will refine Jaggi’s arguments to reduce CL as well as constrained Elastic Net to a Nearest Point Problem, which in turn can be rewritten as an appropriate ν-SVM problem solvable by LIBSVM. We will also show experimentally that the well-known LIBSVM library results in a faster convergence than GLMNet for small problems and also, if properly adapted, for larger ones. Screening is another ingredient to speed up solving Lasso. Shrinking can be seen as the simpler alternative of SVM to screening and we will discuss how it also may in some cases reduce the cost of an SVM-based CL solutionWith partial support from Spanish government grants TIN2013-42351-P, TIN2016-76406-P, TIN2015-70308-REDT and S2013/ICE-2845 CASI-CAM-CM; work also supported by project FACIL–Ayudas FundaciĂłn BBVA a Equipos de InvestigaciĂłn CientĂfica 2016 and the UAM–ADIC Chair for Data Science and Machine Learning. The first author is also supported by the FPU–MEC grant AP-2012-5163. We gratefully acknowledge the use of the facilities of Centro de ComputaciĂłn CientĂfica (CCC) at UAM and thank Red ElĂ©ctrica de España for kindly supplying wind energy dat
Extrapolation Duale pour les Modèles Linéaires Généralisés Parcimonieux
International audienceGeneralized Linear Models (GLM) form a wide class of regression and classification models, where prediction is a function of a linear combination of the input variables. For statistical inference in high dimension, sparsity inducing regularizations have proven to be useful while offering statistical guarantees. However, solving the resulting optimization problems can be challenging: even for popular iterative algorithms such as coordinate descent, one needs to loop over a large number of variables. To mitigate this, techniques known as screening rules and working sets diminish the size of the optimization problem at hand, either by progressively removing variables, or by solving a growing sequence of smaller problems. For both techniques, significant variables are identified thanks to convex duality arguments. In this paper, we show that the dual iterates of a GLM exhibit a Vector AutoRegressive (VAR) behavior after sign identification, when the primal problem is solved with proximal gradient descent or cyclic coordinate descent. Exploiting this regularity, one can construct dual points that offer tighter certificates of optimality, enhancing the performance of screening rules and helping to design competitive working set algorithms
Benchopt: Reproducible, efficient and collaborative optimization benchmarks
Numerical validation is at the core of machine learning research as it allows
to assess the actual impact of new methods, and to confirm the agreement
between theory and practice. Yet, the rapid development of the field poses
several challenges: researchers are confronted with a profusion of methods to
compare, limited transparency and consensus on best practices, as well as
tedious re-implementation work. As a result, validation is often very partial,
which can lead to wrong conclusions that slow down the progress of research. We
propose Benchopt, a collaborative framework to automate, reproduce and publish
optimization benchmarks in machine learning across programming languages and
hardware architectures. Benchopt simplifies benchmarking for the community by
providing an off-the-shelf tool for running, sharing and extending experiments.
To demonstrate its broad usability, we showcase benchmarks on three standard
learning tasks: -regularized logistic regression, Lasso, and ResNet18
training for image classification. These benchmarks highlight key practical
findings that give a more nuanced view of the state-of-the-art for these
problems, showing that for practical evaluation, the devil is in the details.
We hope that Benchopt will foster collaborative work in the community hence
improving the reproducibility of research findings.Comment: Accepted in proceedings of NeurIPS 22; Benchopt library documentation
is available at https://benchopt.github.io
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