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- W928803265 abstract "This poster presents novel algorithms for learning a linear regression model whose parameter is a real fixed-rank matrix. The focus is on the non linear nature of the search space. Because the set of fixed-rank matrices enjoys a rich Riemannian manifold structure, the theory of line-search algorithms on matrix manifolds can be applied [1]. The resulting algorithms scale to high-dimensional problems, enjoy local convergence properties, and connect with the recent contributions on learning fixed-rank matrices [3,4,5,6,10]. The proposed algorithms generalize our recent work on learning fixed-rank symmetric positive semidefinite matrices [2]. Problem formulation Given data matrix instances X ∈ R21, observations y ∈ R, and a linear regression model ŷ = Tr(WX), solve min W∈Rd1×d2 EX,y{l(ŷ, y)}, subject to rank(W) = r. The loss function is the quadratic loss l(ŷ, y) = 12(ŷ − y) . In practice, a surrogate cost function for the expectation above is" @default.
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- W928803265 date "2010-12-01" @default.
- W928803265 modified "2023-09-27" @default.
- W928803265 title "Rank-constrained linear regression: a Riemannian approach" @default.
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