Tailoring Boltzmann Machines to Netflix Data

If we let p(f) ∝ e, we obtain a probability distribution over assignments of binary states to the vertices of the machine. Let A(V ) denote the set of assigments of {0, 1} values to V , i.e. A(V ) = {a | a : V → {0, 1}}. A restricted boltzmann machine(RBM), introduced in [Smo86], is a boltzmann machine where the underlying graph is a complete bipartite graph. Let V = V1∪V2 be the partition of the vertex set. If we fix an assignment a1 ∈ A(V1) (respectively a2 ∈ A(V2)), we can compute the conditional distribution over A(V2) (resp. over A(V1)). Thus using Gibbs sampling we can sample from the joint distribution over A(V1) × A(V2). This leads to a tractable way of training an RBM to produce a desired probability distribution, see [HO06]. Salakhutdinov and Mnih obtained impressive results in the netflix competition by training an RBM to reproduce ratings data encoded as categorical data([SMH07]). We have attempted to improve upon their results by encorporating the ordinal nature of the data, and by explicitly considering the error function used by Netflix to evaluate the performance of a prediction model. In section 2 we discuss non-categorical representations of the ordinal ratings data. In section 3 we discuss the error function of the RBM, how it is different from the one specified by Netflix, and how we tried to overcome this. In section 4 we present the results of our experiments obtained by altering an RBM in the methods described. Finally in section 5 we offer our conclusions and future work.