310 research outputs found
On the Consistency of Ordinal Regression Methods
Many of the ordinal regression models that have been proposed in the
literature can be seen as methods that minimize a convex surrogate of the
zero-one, absolute, or squared loss functions. A key property that allows to
study the statistical implications of such approximations is that of Fisher
consistency. Fisher consistency is a desirable property for surrogate loss
functions and implies that in the population setting, i.e., if the probability
distribution that generates the data were available, then optimization of the
surrogate would yield the best possible model. In this paper we will
characterize the Fisher consistency of a rich family of surrogate loss
functions used in the context of ordinal regression, including support vector
ordinal regression, ORBoosting and least absolute deviation. We will see that,
for a family of surrogate loss functions that subsumes support vector ordinal
regression and ORBoosting, consistency can be fully characterized by the
derivative of a real-valued function at zero, as happens for convex
margin-based surrogates in binary classification. We also derive excess risk
bounds for a surrogate of the absolute error that generalize existing risk
bounds for binary classification. Finally, our analysis suggests a novel
surrogate of the squared error loss. We compare this novel surrogate with
competing approaches on 9 different datasets. Our method shows to be highly
competitive in practice, outperforming the least squares loss on 7 out of 9
datasets.Comment: Journal of Machine Learning Research 18 (2017
Learning to Rank: Online Learning, Statistical Theory and Applications.
Learning to rank is a supervised machine learning problem, where the output space is the special structured space of emph{permutations}. Learning to rank has diverse application areas, spanning information retrieval, recommendation systems, computational biology and others.
In this dissertation, we make contributions to some of the exciting directions of research in learning to rank. In the first part, we extend the classic, online perceptron algorithm for classification to learning to rank, giving a loss bound which is reminiscent of Novikoff's famous convergence theorem for classification. In the second part, we give strategies for learning ranking functions in an online setting, with a novel, feedback model, where feedback is restricted to labels of top ranked items. The second part of our work is divided into two sub-parts; one without side information and one with side information. In the third part, we provide novel generalization error bounds for algorithms applied to various Lipschitz and/or smooth ranking surrogates. In the last part, we apply ranking losses to learn policies for personalized advertisement recommendations, partially overcoming the problem of click sparsity. We conduct experiments on various simulated and commercial datasets, comparing our strategies with baseline strategies for online learning to rank and personalized advertisement recommendation.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133334/1/sougata_1.pd
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