By Benjamin M. Marlin
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2 diverges from the true value of P (X1 = 1). In addition, the estimate θˆ11 is approximately equal to the true value of P (X1 = 1|R1 = 1) as claimed. Finally, the results also show that estimating all the parameters of the true data model using EM and then estimating P (X1 = 1) as cˆ + dˆ is not subject to bias as claimed. It is important to realize that in order for parameter estimation to be unbiased, it is not sufficient for missing data to be missing at random with respect to a true underlying data model.
Survey Rating Distribution Yahoo! 1 0 0 0 1 2 3 4 Rating Value 5 (a) Yahoo! Survey Rating Distribution 1 2 3 4 Rating Value 5 (b) Yahoo! 2: Distribution of rating values in the Yahoo! survey set and base set compared to several popular collaborative filtering data sets including EachMovie, and Netflix. 2 Rating Data Analysis Following the survey, users were presented with a set of ten songs to rate. The artist name and song title were given for each song, along with a thirty second audio clip, which the user could play before entering a rating.
The models and methods presented in this chapter provide a starting point for the development of novel models and methods for both unsupervised learning with non-random missing data, and classification with missing features. Experimental results using the methods described in this chapter are presented in Chapters 5 and 6. 1. We assume that the data random variables Xn are vectors of length D that are subject to random missing data. We assume that there are K mixture components. The random variables Z n are mixture component indicator variables.