Restricted Boltzmann Machines for Collaborative Filtering

The durable contribution for GTK is the categorical RBM conditional. For movie $i$ and rating category $k$, the visible group is one-hot. Given hidden state $h$, the probability of category $k$ is a softmax over the $K$ ratings for that movie, while hidden units remain Bernoulli conditionals over all observed movie-rating indicators.

Mechanism #

Each user activates only the visible groups for movies that user rated. Weights and biases are shared across users, so the construction behaves like differently masked instances of one model rather than an independently trained RBM per user. Missing ratings do not become zeros or negative observations; their visible groups are absent from that user's training case.

The energy implies

$$p(v_i^k=1\mid h)= \frac{\exp(c_i^k+\sum_j h_jW_{ij}^k)} {\sum_{\ell=1}^{K}\exp(c_i^\ell+\sum_j h_jW_{ij}^\ell)}.$$

The model was trained with contrastive divergence, so its reported predictive performance is evidence about that application, not proof that CD estimates likelihood accurately or that an RBM is a current default recommender architecture.

Applied results and limits #

The experiments used the Netflix Prize data and compared RBM variants with tuned SVD baselines. The historical result established that an undirected latent model could scale to sparse tabular ratings and contribute complementary errors to matrix-factorization models. The benchmark, hardware, and competitive landscape are dated; GTK retains the representation and conditional derivation, not the paper's ranking as a present-day recommendation.

Visual audit #

All eight physical pages were rendered and read. Figure 1's user-specific RBM topology, the softmax-unit drawing, the conditional equations, training schematic, RMSE plots, and unrolled conditional-RBM diagram were inspected. None is retained: the categorical conditional is clearer as a typed derivation, and the benchmark plots are historical rather than current evidence.