Estimation of Logistic Regression Parameter with Partially Labeled Data

• Activity Number: 318
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Keiji Takai*+
• Companies: Kansai University
• Keywords: Partially labeled data ; Labeled data ; weighted likelihood function ; EM algorithm

Abstract

We often encounter the data whose labels are partially given. The labeling methods can be divided into twofold. The first one is a feature-independent labeling mechanism in which we label some of the observations independently of the feature vector. The second one is a feature-dependent labeling mechanism in which we label some of the observations dependently of the feature vector. In the previous studies, the first one is implicitly assumed in almost all cases. In contrast, in this talk, we discuss effects of such partially labeled data on regression parameters in logistic regression models when some of the data are labeled according to the second mechanism. First, we show that imputing a value into unlabeled observations does not improve precision of the estimates, resulting in the same estimates as obtained by using only labeled observations. This means that there is no other way but to use labeled data for estimation of the parameters. In this case, we can use an ordinal likelihood function and a weighted likelihood function with the weight of the inverse labeling mechanism. We analytically and numerically compare these likelihood functions.