1 code implementation • 11 Feb 2019 • Dmitry Babichev, Dmitrii Ostrovskii, Francis Bach
We develop efficient algorithms to train $\ell_1$-regularized linear classifiers with large dimensionality $d$ of the feature space, number of classes $k$, and sample size $n$.
no code implementations • 8 Feb 2019 • Ulysse Marteau-Ferey, Dmitrii Ostrovskii, Francis Bach, Alessandro Rudi
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels.
no code implementations • 8 Feb 2019 • Dmitrii Ostrovskii, Alessandro Rudi
Denoting $\text{cond}(\mathbf{S})$ the condition number of $\mathbf{S}$, the computational cost of the novel estimator is $O(d^2 n + d^3\log(\text{cond}(\mathbf{S})))$, which is comparable to the cost of the sample covariance estimator in the statistically interesing regime $n \ge d$.
1 code implementation • 16 Oct 2018 • Dmitrii Ostrovskii, Francis Bach
We demonstrate how self-concordance of the loss allows to characterize the critical sample size sufficient to guarantee a chi-square type in-probability bound for the excess risk.
no code implementations • 11 Jun 2018 • Zaid Harchaoui, Anatoli Juditsky, Arkadi Nemirovski, Dmitrii Ostrovskii
We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a time-invariant filter.
1 code implementation • ICML 2018 • Dmitrii Ostrovskii, Zaid Harchaoui
Our second contribution is a computational complexity analysis of the proposed procedures, which takes into account their statistical nature and the related notion of statistical accuracy.