We describe a general framework --compressive statistical learning-- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized moments) that captures the information relevant to the considered learning task. A near-minimizer of the risk is computed from the sketch through the solution of a nonlinear least squares problem. We investigate sufficient sketch sizes to control the generalization error of this procedure. The framework is illustrated on compressive PCA, compressive clustering, and compressive Gaussian mixture Modeling with fixed known variance. The latter two are further developed in a companion paper.
- Pub Date:
- June 2017
- Statistics - Machine Learning;
- Computer Science - Information Theory;
- Computer Science - Machine Learning;
- Mathematics - Statistics Theory
- Main novelties between version 1 and version 2: improved concentration bounds, improved sketch sizes for compressive k-means and compressive GMM that now scale linearly with the ambient dimensionMain novelties of version 3: all content on compressive clustering and compressive GMM is now developed in the companion paper hal-02536818