Structural Minimax Probability Machine

Minimax probability machine (MPM) is an interesting discriminative classifier based on generative prior knowledge. It can directly estimate the probabilistic accuracy bound by minimizing the maximum probability of misclassification. The structural information of data is an effective way to represent...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2017-07, Vol.28 (7), p.1646-1656
Main Authors: Bin Gu, Xingming Sun, Sheng, Victor S.
Format: Article
Language:English
Subjects:
Accuracy
Algorithm design and analysis
Bayes learning
Classification
Classifiers
Covariance matrices
Covariance matrix
Datasets
Economic models
Error analysis
finite mixture models
Hidden Markov models
kernel methods
Minimax technique
Mixture models
Nonlinearity
Probabilistic methods
Probability theory
second-order cone programming (SOCP)
structural learning
Support vector machines
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Summary:Minimax probability machine (MPM) is an interesting discriminative classifier based on generative prior knowledge. It can directly estimate the probabilistic accuracy bound by minimizing the maximum probability of misclassification. The structural information of data is an effective way to represent prior knowledge, and has been found to be vital for designing classifiers in real-world problems. However, MPM only considers the prior probability distribution of each class with a given mean and covariance matrix, which does not efficiently exploit the structural information of data. In this paper, we use two finite mixture models to capture the structural information of the data from binary classification. For each subdistribution in a finite mixture model, only its mean and covariance matrix are assumed to be known. Based on the finite mixture models, we propose a structural MPM (SMPM). SMPM can be solved effectively by a sequence of the second-order cone programming problems. Moreover, we extend a linear model of SMPM to a nonlinear model by exploiting kernelization techniques. We also show that the SMPM can be interpreted as a large margin classifier and can be transformed to support vector machine and maxi-min margin machine under certain special conditions. Experimental results on both synthetic and real-world data sets demonstrate the effectiveness of SMPM.
ISSN:2162-237X
2162-2388
DOI:10.1109/TNNLS.2016.2544779