Supplementary Material for Deconvolving Feedback Loops in Recommender Systems

We have used the adjusted cosine similarity relationships, S2 = (R̂ 2 obs) T R̂2obs,Strue = (R̂true) R̂true, the property of matrix transpose (AB)T = BT AT , and the property that Strue is symmetric, i.e., Strue = Strue. The base cases are now proved in equations 3, 4. Considering equation 2 to be true at the kth iteration, we wish to prove the following at the (k + 1)th iteration: R̂ obs = R̂true(I + αk+1Strue(I + αkStrue(I + αk−1Strue · · · (I + α2Strue(I + α1Strue)) · · · )3)3) (5) Using assumptions 1, 2 and 3 we have the following relationship: R̂ obs = R̂true + αk+1(R̂ k+1 obs Sk+1). (6)