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Hierarchical learning algorithms have enjoyed tremendous growth in recent years, with many new algorithms being proposed and applied to a wide range of applications. However, despite the apparent success of hierarchical ...

This paper explores the theoretical consequences of a simple assumption: the computational goal of the feedforward path in the ventral stream -- from V1, V2, V4 and to IT -- is to discount image transformations, after ...

Understanding invariance and discrimination properties of hierarchical models is arguably the key to understanding how and why such models, of which the the mammalian visual system is one instance, can lead to good ...

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a ...

Invariance to various transformations is key to object recognition but existing definitions of invariance are somewhat confusing while discussions of invariance are often confused. In this report, we provide an operational ...

Neurons in inferotemporal cortex that respond similarly to many pairs of mirror-symmetric images -- for example, 45 degree and -45 degree views of the same face -- have often been reported. The phenomenon seemed to be an ...

In this paper, we study the stability and generalization properties of penalized empirical-risk minimization algorithms. We propose a set of properties of the penalty term that is sufficient to ensure uniform ?-stability: ...

We propose a natural image representation, the neural response, motivated by the neuroscience of the visual cortex. The inner product defined by the neural response leads to a similarity measure between functions which we ...

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie ["Regularization and variable selection via the elastic net" J. R. Stat. ...

A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a ...