CoFi Rank : Maximum Margin Matrix Factorization for Collaborative Ranking Markus Weimer, Alexandros Karatzoglou, Quoc Viet Le and Alex Smola NIPS’07.

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Presentation transcript:

CoFi Rank : Maximum Margin Matrix Factorization for Collaborative Ranking Markus Weimer, Alexandros Karatzoglou, Quoc Viet Le and Alex Smola NIPS’07

Idea Maximum Margin Matrix Factorization Structured Estimation for Ranking Bundle Method Solver

Collaborative Filtering Based on partial observed matrix to predict unobserved entries

Matrix Factorization Low Rank Approximation SVD for fully observed Y Non-convex

Maximum Margin Matrix Factorization Trace norm+Hinge loss: Convex Semi-Definite Programming

Regularized Matrix Factorization Formulation Probabilistic Matrix Factorization (PMF) CoFi Rank Linear Convex Upper Bound Non-Convex Solved by linear programming Alternating optimizing

How to Compute Loss? Linear Convex Upper Bound Solved by Linear Programming Can this explain in simple way?

Useful Links CoFi Rank MMMF MF

Famous Researchers in Optimization Yurii Nesterov – “Introductory Lectures on Convex Optimization: A Basic Course” Arkadi Nemirovski – “Efficient methods in convex programming” Stephen P. Boyd – “Convex Optimization” Stephen J. Wright – “Numerical Optimization” Dimitri Bertsekas – “Nonlinear Programming”Nonlinear Programming

Questions?

Normalized Discounted Cumulative Gain (NDCG)

How to set c ? c i is set decreasing,  is maximized with respect to π for argsort(f) c i =(i+1) -0.25

Convex Upper Bound Linear Convex Upper Bound

Bundle Method General convex optimization solver with tight convergence bound O(1/  )

Bundle MethodBundle Method for CoFi Rank