SOURCE. Liang, D., Krishnan, R.G., Hoffman, M.D. and Jebara, T. (2018), "Variational Autoencoders for Collaborative Filtering", Proceedings of the 2018 World Wide Web Conference (WWW '18), pp. 689-698, doi:10.1145/3178876.3186150.
Usage
Vaecf(
R,
K = 5,
latent_dim = 2,
beta = 0.2,
n_samples = 16,
relevance = NULL,
w_scale = 1,
skip = 0
)Arguments
- R
n_users-by-n_items non-negative click matrix.
- K
Ranking cut-off in 1..n_items.
- latent_dim
Latent width.
- beta
KL annealing weight.
- n_samples
Reparameterised draws per user.
- relevance
Binary held-out relevance, or NULL for R > 0.
- w_scale
Scales the decoder weights; 0 makes pi uniform.
- skip
Offset into the shared deterministic stream.
Value
List with elbo, loglik, kl,
elbo_per_user, loglik_per_user, kl_per_user,
recall, ndcg, recall_per_user,
ndcg_per_user, ranking, mu, logvar,
n_users, n_items, k.
Details
The contribution is the MULTINOMIAL likelihood in place of the Gaussian or logistic one (Section 2.2): pi(z_u) = softmax(f(z_u)) and log p(x_u|z_u) = sum_i x_ui log pi_i(z_u), which spends a fixed probability budget on the items the model believes will be clicked. The objective is the beta-annealed bound of Eq. (5), L_beta = E_q[log p(x_u|z)] - beta KL(q(z|x_u) || p(z)), with beta < 1 the partial regularisation of Section 2.2.2.
The encoder input is the L2-normalised log(1 + x_u) transform of Section 2.2, not the raw counts.
RANKING. Recall@K and truncated NDCG@K are the Section 4.1 definitions: Recall@K = sum_{r<=K} I[w(r) in I_u] / min(K, |I_u|) and DCG@K = sum_{r<=K} (2^{I[w(r) in I_u]} - 1)/log2(r+1). Ties are broken by ascending item index in both language arms – R scans a matrix column-major and Python row-major, so an unpinned tie rule is a real parity hazard.
DETERMINISM. Untrained weights and the reparameterisation noise come
from the shared deterministic normal stream. Relevance defaults to the
input clicks, making the metrics in-sample; pass relevance for
a held-out set.