Probabilistic Pair Recommendations & IRGAN: Boosting E‑commerce Click‑Through

1. Probabilistic Latent‑Class Model for Shopping‑Pair Push

In e‑commerce marketing push scenarios, click‑through rate (CTR) is heavily influenced by copy and limited to a single display slot. To improve CTR, the authors propose a “shopping‑pair” recommendation that pushes a complementary item together with a previously purchased product, increasing user attachment and opening rates.

Two metrics are defined for pairing items:

Co‑Purchase Graph (simultaneous purchase score)

View‑and‑then‑Purchase Graph (substitutivity score)

The pairing score combines high complementarity and low substitutivity, serving as an important feature in the recommendation model.

User behavior is represented by embeddings learned via a probabilistic latent‑class model. The model consists of two layers: a hidden layer that captures user segmentation using multidimensional logistic regression, and a click‑through prediction layer (a two‑dimensional logistic regression, extendable to deep neural networks).

Parameters are estimated with the Expectation‑Maximization (EM) algorithm. The Q‑function is derived and optimized via gradient descent.

Online experiments show a ~50% CTR improvement for shopping‑pair push recommendations, and the approach can be generalized to other targets such as items, news, or videos.

2. GAN for Information Retrieval – IRGAN

IRGAN integrates generative and discriminative IR models using a minimax game. The discriminator p_φ(r|q,d) learns to predict relevance from labeled data, while the generator p_θ(d|q,r) produces challenging document samples for the discriminator.

The discriminator is trained via logistic regression to maximize its objective, and the generator outputs a probability distribution over documents using a softmax function.

Training alternates between updating D (gradient descent) and G (policy gradient for discrete outputs).

Experiments on three IR tasks—Web Search, Item Recommendation, and Question Answering—demonstrate that IRGAN outperforms strong baselines.

Source code is available at https://github.com/geek-ai/irgan .