Supplementary Material for the AISTATS 2016 Paper: Provable Tensor Methods for Learning Mixtures of Generalized Linear Models

which is a multilinear combination of the tensor mode-1 fibers. Similarly T (u, v, w) ∈ R is a multilinear combination of the tensor entries, and T (I, I, w) ∈ Rd×d is a linear combination of the tensor slices. Now, let us proceed with the proof. Proof: Let x′ := 〈u, x〉+ b. Define l(x) := y · x⊗ x. We have E[y · x⊗3] = E[l(x)⊗ x] = E[∇xl(x)], ∗Allen Institute for Artificial Intelligence. Email: hanies@allenai.org. This work was done while the author was a visiting researcher at University of California, Irvine. †University of California, Irvine. Email: mjanzami@uci.edu ‡University of California, Irvine. Email: a.anandkumar@uci.edu 1Compare with the matrix case where for M ∈ Rd×d, we have M(I, u) = Mu := ∑ j∈[d] ujM(:, j) ∈ Rd.