Publications (283)
Convex Sparse Matrix Factorizations
Francis Bach, Julien Mairal, Jean Ponce
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by…
Sum-of-Squares Relaxations for Information Theory and Variational Inference
Francis Bach
We consider extensions of the Shannon relative entropy, referred to as -divergences.Three classical related computational problems are typically associated with these divergence…
Two-stage stochastic algorithm for solving large-scale (non)-convex separable optimization problems under affine constraints
Benjamin Dubois-Taine, Laurent Pfeiffer, Nadia Oudjane +2
We consider nonsmooth optimization problems under affine constraints, where the objective consists of the average of the component functions of a large number of agents, and we…
Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergence
Clémentine Chazal, Anna Korba, Francis Bach
In this paper, we study the statistical and geometrical properties of the Kullback-Leibler divergence with kernel covariance operators (KKL) introduced by Bach [2022]. Unlike the c…
Domain adaptation for sequence labeling using hidden Markov models
Edouard Grave, Guillaume Obozinski, Francis Bach
Most natural language processing systems based on machine learning are not robust to domain shift. For example, a state-of-the-art syntactic dependency parser trained on Wall Stree…
Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization
Mark Schmidt, Nicolas Le Roux, Francis Bach
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calcula…