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Convex learning algorithms, such as Support Vector Machines (SVMs), are often seen as highly desirable because they offer strong practical properties and are amenable to theoretical analysis. However, in this work we show how non-convexity can provide scalability advantages over convexity. We show how concave-convex programming can be applied to produce(More)
In this paper we study a new framework introduced by Vapnik (1998) and Vapnik (2006) that is an alternative capacity concept to the large margin approach. In the particular case of binary classification, we are given a set of labeled examples, and a collection of "non-examples" that do not belong to either class of interest. This collection, called the(More)
Since the work of Ramón y Cajal in the late 19th and early 20th centuries, neuroscientists have speculated that a complete understanding of neuronal cell types and their connections is key to explaining complex brain functions. However, a complete census of the constituent cell types and their wiring diagram in mature neocortex remains elusive. By combining(More)
We study a pattern classification algorithm which has recently been proposed by Vapnik and coworkers. It builds on a new inductive principle which assumes that in addition to positive and negative data, a third class of data is available, termed the Universum. We assay the behavior of the algorithm by establishing links with Fisher discriminant analysis and(More)
Neural codes are believed to have adapted to the statistical properties of the natural environment. However, the principles that govern the organization of ensemble activity in the visual cortex during natural visual input are unknown. We recorded populations of up to 500 neurons in the mouse primary visual cortex and characterized the structure of their(More)
This Chapter presents the PASCAL 1 Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a discussion with some lessons to be learnt. The Challenge was set up to evaluate the ability of Machine Learning algorithms to provide good " probabilis-tic predictions " ,(More)
Orientation selectivity is the most striking feature of simple cell coding in V1 that has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation(More)
In this paper, we introduce a new family of probability densities called L p-nested symmetric distributions. The common property, shared by all members of the new class, is the same functional form ρ(x x x) = ˜ ρ(f (x x x)), where f is a nested cascade of L p-norms x x x p = (∑ |x i | p) 1/p. L p-nested symmetric distributions thereby are a special case of(More)
We compare two approaches to the problem of estimating the depth of a point in space from observing its image position in two different cameras: 1. The classical photogrammetric approach explicitly models the two cameras and estimates their intrinsic and extrinsic parameters using a tedious calibration procedure; 2. A generic machine learning approach where(More)