An asymptotic analysis of generative, discriminative, and pseudolikelihood estimators

Statistical and computational concerns have motivated parameter estimators based on various forms of likelihood, e.g., joint, conditional, and pseudolikelihood. In this paper, we present a unified framework for studying these estimators, which allows us to compare their relative (statistical) efficiencies. Our asymptotic analysis suggests that modeling more of the data tends to reduce variance, but at the cost of being more sensitive to model misspecification. We present experiments validating our analysis.

[1]  J. Besag Statistical Analysis of Non-Lattice Data , 1975 .

[2]  A. V. D. Vaart Asymptotic Statistics: Delta Method , 1998 .

[3]  Michael I. Jordan,et al.  On Discriminative vs. Generative Classifiers: A comparison of logistic regression and naive Bayes , 2001, NIPS.

[4]  Andrew McCallum,et al.  Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data , 2001, ICML.

[5]  Martin J. Wainwright,et al.  Tree-reweighted belief propagation algorithms and approximate ML estimation by pseudo-moment matching , 2003, AISTATS.

[6]  Guillaume Bouchard,et al.  The Tradeoff Between Generative and Discriminative Classifiers , 2004 .

[7]  Andrew McCallum,et al.  Piecewise Training for Undirected Models , 2005, UAI.

[8]  Christopher Joseph Pal,et al.  Multi-Conditional Learning: Generative/Discriminative Training for Clustering and Classification , 2006, AAAI.

[9]  Carlo Gaetan,et al.  Composite likelihood methods for space-time data , 2006 .

[10]  Martin J. Wainwright,et al.  Estimating the "Wrong" Graphical Model: Benefits in the Computation-Limited Setting , 2006, J. Mach. Learn. Res..

[11]  Tom Minka,et al.  Principled Hybrids of Generative and Discriminative Models , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[12]  Dan Klein,et al.  Agreement-Based Learning , 2007, NIPS.

[13]  Andrew Zisserman,et al.  Advances in Neural Information Processing Systems (NIPS) , 2007 .

[14]  C. Varin On composite marginal likelihoods , 2008 .

[15]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..