The spikes highlighted in red are part of a repeating motif.

We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the out-of-sample performance. A classical cross validation strategy is the leave-one-out cross validation (LOOCV) where one sample is left out for validation and training is done on the rest of the samples that are presented to the learner, and this process is repeated on all of the samples. LOOCV is rarely used in practice due to the high computational complexity. In this paper, we first develop a computationally efficient approximate LOOCV (ALOOCV) and provide theoretical guarantees for its performance. Then we use ALOOCV to provide an optimization algorithm for finding the regularizer in the empirical risk minimization framework. In our numerical experiments, we illustrate the accuracy and efficiency of ALOOCV as well as our proposed framework for the optimization of the regularizer.

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space X and the goal is to order all possible observations x in X by means of a scoring function s: X R so that s(X) and Y tend to increase or decrease together with highest probability. This problem generalizes bi/multi-partite ranking to a certain extent and the task of finding optimal scoring functions s( x) can be naturally cast as optimization of a dedicated functional criterion, called the IROC curve here, or as maximization of the Kendall τ related to the pair (s(X),Y). From the theoretical side, we describe the optimal elements of this problem and provide statistical guarantees for empirical Kendall τ maximization under appropriate conditions for the class of scoring function candidates. We also propose a recursive statistical learning algorithm tailored to empirical IROC curve optimization and producing a piecewise constant scoring function that is fully described by an oriented binary tree. Preliminary numerical experiments highlight the difference in nature between regression and continuous ranking and provide strong empirical evidence of the performance of empirical optimizers of the criteria proposed.

Here, we apply instantaneous and lag-based measures of conditional linear dependence, based on Granger-Geweke causality (GC), to infer network connections at distinct timescales from functional magnetic resonance imaging (fMRI) data.

Neural Information Processing Systems http://nips.cc/

We introduce Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced model selection and estimation.

Neural Information Processing Systems http://nips.cc/

We enourage readers to consult the more complete manuscript on the arXiv.

Both tasks take as input the raw image and a binary mask representing a candidate object.