Missing Data Problems in Machine Learning by Benjamin M. Marlin

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By Benjamin M. Marlin

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14]. We consider the prediction of ratings for both user-selected and randomly selected songs. Preparing the data set for this empirical protocol involves several steps. We begin by randomly partitioning the 5400 survey users into five blocks of 1080 users each. Each block is used as a set of test users in turn. The ratings for the test users are further divided into observed ratings, test ratings for user selected items, and test ratings for randomly selected items. The observed ratings consist of all but one of the user selected ratings for each user.

Zn is a latent variable indicating which mixture component data case n belongs to. βk are the mixture component distribution parameters. α are the parameters of the prior distribution on θ, and φ are the parameters of the prior distribution on βk . We denote the prior distribution on the mixing proportions θ with hyperparameters α by P (θ|α). We denote the prior distribution on the mixture component distributions β k with hyperparameters φ by P (βk |φ). A conjugate prior is often used for the mixture proportion parameters [59, p.

The strong generalization error for randomly selected items is computed by predicting the value of each test user’s randomly-selected test items. The novel aspect of this protocol stems from the division of the rating data into three sets of ratings. The observed ratings for each user are ratings for user-selected items. Thus, the user selected test items come from the same distribution as the observed ratings, and both rating sets are subject to the same unknown missing data mechanism. The ratings for randomly selected test items come from a known selection mechanism where missing data is missing completely at random.

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