## Adaptive Sparseness for Supervised Learning (2003)

Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 80 - 4 self |

### BibTeX

@ARTICLE{Figueiredo03adaptivesparseness,

author = {Mario A.T. Figueiredo and Senior Member},

title = {Adaptive Sparseness for Supervised Learning},

journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},

year = {2003},

volume = {25},

pages = {1150--1159}

}

### Years of Citing Articles

### OpenURL

### Abstract

The goal of supervised learning is to infer a functional mapping based on a set of training examples. To achieve good generalization, it is necessary to control the "complexity" of the learned function. In Bayesian approaches, this is done by adopting a prior for the parameters of the function being learned. We propose a Bayesian approach to supervised learning, which leads to sparse solutions; that is, in which irrelevant parameters are automatically set exactly to zero. Other ways to obtain sparse classifiers (such as Laplacian priors, support vector machines) involve (hyper)parameters which control the degree of sparseness of the resulting classifiers; these parameters have to be somehow adjusted/estimated from the training data. In contrast, our approach does not involve any (hyper)parameters to be adjusted or estimated. This is achieved by a hierarchical-Bayes interpretation of the Laplacian prior, which is then modified by the adoption of a Jeffreys' noninformative hyperprior. Implementation is carried out by an expectationmaximization (EM) algorithm. Experiments with several benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms SVMs and performs competitively with the best alternative techniques, although it involves no tuning or adjustment of sparseness-controlling hyperparameters.

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Citation Context ...es interpretation of the Laplacian prior as a normal/independent distribution (as proposed for robust regression in [18]); 2. a Jeffreys’ noninformative second-level hyperprior (in the same spirit a=-=s [19]-=-), which expresses scaleinvariance and, more importantly, is parameterfree [20]; 3. an expectation-maximization (EM) algorithm which yields a maximum a posteriori (MAP) estimate of (and of the observa... |

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Citation Context ...hod strongly depend on an adequate choice of these parameters, and our formulation does not contribute to the solution of this problem. ACKNOWLEDGMENTS Earlier versions of this work were presented in =-=[1]-=- and [2]. This work was supported by the Foundation for Science and Technology, Portuguese Ministry of Science and Technology, under project POSI/33143/SRI/2000. 5. Available at www.stats.ox.ac.uk/pub... |

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Citation Context ... Dashed line: Hardthreshold rule. Dotted line: Soft-threshold rule (obtained with a Laplacian prior). robust regression under Laplacian noise models [18]. A related equivalence was also considered in =-=[26]-=-. 3.4 Sparse Regression via EM The hierarchical decomposition of the Laplacian prior allows using the expectation-maximization (EM) algorithm to implement the LASSO criterion in (3). This is done simp... |

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Citation Context ...ngly depend on an adequate choice of these parameters, and our formulation does not contribute to the solution of this problem. ACKNOWLEDGMENTS Earlier versions of this work were presented in [1] and =-=[2]-=-. This work was supported by the Foundation for Science and Technology, Portuguese Ministry of Science and Technology, under project POSI/33143/SRI/2000. 5. Available at www.stats.ox.ac.uk/pub/PRNN/. ... |

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Citation Context ...an prior, which appears under different guises, like ridge regression [11], or weight decay [5], [6]. Gaussian priors are also at the heart of the nonparametric Gaussian processes approach [5], [10], =-=[12]-=-, which has roots in earlier spline models [13] and regularized radial basis functions [14]. The main disadvantage of Gaussian priors is that they do not control the structural complexity of the learn... |

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Citation Context ...tional densities, pðxjyÞ, and the probability of each class,pðyÞ, [6]. In regression, this can be done, for example, by representing the joint density using a kernel method or a Gaussian mixture (=-=see [8]-=- and references therein). From this joint probability function estimate, optimal Bayesian decision rules can be derived by the standard Bayesian decision theory machinery [6]. In the discriminative ap... |