RecSys 2023 -- Average Consistency

Repository for the RecSys 2023 Paper "On the Consistency of Average Embeddings for Item Recommendation" by W. Bendada, G. Salha-Galvan, R. Hennequin, T. Bouabça and T. Cazenave

Installation

The following lines of codes clone the project, download the public datasets used for our experiments and install some standard machine learning library (including torch) required to reproduce our results.

git clone https://github.com/deezer/consistency.git
cd consistency
curl https://zenodo.org/record/5121674/files/song_embeddings.parquet?download=1 --output data/song_embeddings.parquet
pip install -r requirements.txt

Experiments

Theoretical consistency

The script plot_distributions_consistency.py will reproduce the plots of Figure 2. It brings a comparison between average consistency as computed using Proposition 2 versus the one observed for a set of embeddings sampled from the same given distribution. For instance, running

python -m plot_distributions_consistency -d normal

will plot the following distribution

Empirical consistency

The script plot_real_embeddings_consistency.py will reproduce the plots of Figure 3. It brings a comparison between average consistency of a real-world set of embeddings versus the one computed for a set of i.i.d vectors of the same size and dimensions following a normal standard distribution. For instance, running

python -m plot_real_embeddings_consistency -s svd

will plot the following distribution

Optionnal : Normal Approximation

The script plot_normal_approximation.py will reproduce the plots of Figure 1. It illustrates how inner products between i.i.d vectors can be approximated by a normal law provided that the dimension of those vectors is large enough, regardless of the family of distributions that those vectors follow. For instance, running

python -m plot_normal_approximation -d normal

will plot the following distribution