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• W2305672500 abstract "This paper 1 promotes a novel point of view on unsupervised learning. We argue that the goal of unsupervised learning is to facilitate a solution of some higher level task and it should be evaluated based on its contribution to the solution of that task. We present an example of such analysis in the case of co-clustering, which is a widely used approach in the analysis of data matrices. This paper identifies two possible high-level tasks in matrix data analysis: discriminative prediction of the missing entries and estimation of the joint probability distribution of row and column variables. For these two tasks we derive PAC-Bayesian generalization bounds for the expected out-of-sample performance of co-clustering-based solutions. The analysis yields regularization terms that were absent in the preceding formulations of co-clustering. The bounds suggest that the expected performance of co-clustering is governed by a trade-off between its empirical performance and the mutual information preserved by the cluster variables on row and column IDs. We derive an iterative projection algorithm for finding a local optimum of this trade-off. The algorithm achieved state-of-the-art performance in the MovieLens collaborative filtering task. The paper also features a number of important technical contributions: − We derive a PAC-Bayesian bound for discrete density estimation. − We introduce combinatorial priors to PAC-Bayesian analysis. They are appropriate for discrete optimization domains and lead to regularization terms in the form of mutual information. − Co-clustering can be viewed as a Stochastic-Form Matrix Factorization (SFMF) A ≈ LMR, where L and R are stochastic matrices and M is arbitrary. SFMF has a clear probabilistic interpretation. The generalization bound and the algorithm for finding a locally optimal solution derived for co-clustering are applicable to SFMF. − It is shown that PAC-Bayesian analysis of co-clustering can be extended to tree-shaped directed and undirected graphical models." @default.
• W2305672500 created "2016-06-24" @default.
• W2305672500 creator A5004273274 @default.
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• W2305672500 date "2009-01-01" @default.
• W2305672500 modified "2023-09-23" @default.
• W2305672500 title "A PAC-Bayesian Approach to Unsupervised Learning with Application to Co-clustering Analysis" @default.
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