Sparseness vs Estimating Conditional Probabilities: Some Asymptotic Results Export

@article{citeulike:5923264, abstract = {One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.}, author = {Bartlett, Peter L. and Tewari, Ambuj}, citeulike-article-id = {5923264}, citeulike-linkout-0 = {http://www.jmlr.org/papers/volume8/bartlett07a/bartlett07a.pdf}, journal = {Journal of Machine Learning Research}, keywords = {asymptotic\_results, consistency, estimation, probability, sparse}, month = {April}, pages = {775--790}, posted-at = {2009-10-12 02:25:17}, priority = {5}, title = {Sparseness vs Estimating Conditional Probabilities: Some Asymptotic Results}, url = {http://www.jmlr.org/papers/volume8/bartlett07a/bartlett07a.pdf}, volume = {8}, year = {2007} }

TY - JOUR ID - citeulike:5923264 L3 - citeulike-article-id:5923264 N2 - One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions. JF - Journal of Machine Learning Research EP - 790 TI - Sparseness vs Estimating Conditional Probabilities: Some Asymptotic Results VL - 8 SP - 775 KW - asymptotic_results KW - consistency KW - estimation KW - probability KW - sparse AU - Bartlett, Peter AU - Tewari, Ambuj PY - 2007/04// UR - http://www.jmlr.org/papers/volume8/bartlett07a/bartlett07a.pdf ER -