Collaborative Filtering with Implicit Feedback

Loss, Negative Sampling and Embeddings

Challenges with Implicit Feedback

Interactions are likely very sparse

• Most of the time, only positive signals are recorded
• No interactions may mean user dislike item or not yet exposed to item

Not able to directly use common matrix factorisation algorithms

• Assumes no interactions as zeroes

Collaborative Filtering Model

Ranking

Retrieval

Embedding model

User (features)

Item (features)

User embeddings

Item embeddings

Scoring model

Loss model

Transform model

Transformed user embeddings

Transformed item embeddings

Loss Functions

Pointwise loss: generally low performance

Pairwise loss: 1 negative sample for each positive example

• Bayesian Personalised Ranking (BPR): -logsigmoid(distance_neg - distance_pos)
• Pairwise Hinge (PHL): relu(distance_pos - distance_neg + margin)

Setwise loss functions: multiple negative samples

• Cosine Contrastive Loss (CCL): distance_pos + mean(relu(m - distance_neg))
• Sampled Softmax, InfoNCE: cross_entropy(cat(score_pos, score_neg), 0)

Other loss: no negative samples

• DirectAU (DAU): distance_pos + uniformity loss

Relationship between loss functions

Cosine Contrastive Loss (CCL)

Inspired by contrastive loss in computer vision tasks

Automatically emphasises hard negatives due to hinge loss

Not straightforward to include negative labels (user thumbs down, explicit “not interested”)

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Sampled Softmax (SSM), InfoNCE

Inefficient to compute softmax over all items, hence use sampling

• Biased softmax estimation if samples are not uniformly distributed
• For example, popularity sampling means popular items are penalised more
• There is a concept of log(q) sampling bias correction for unbiased estimate

Option to include temperature factor to score to control smoothness of distribution

InfoNCE+

Mutual Information Neural Estimator + (MINE+)

Equivalent to below if 𝞊 = 0

Equivalent to InfoNCE if

𝝺 = 1, 𝞊 = 1

DirectAU

Encourages embeddings to be well distributed on the surface of a unit sphere

Negative samples not needed

Negative Sampling Strategy

Random negative sampling

• Noisy false negatives averaged out during training
• Require computing many embeddings for loss and batch update

In-batch negative sampling

• Equivalent to popularity sampling
• Efficient reuse in-batch computed embeddings
• Does not train against trivial negatives

Hard negative sampling

• Requires scoring between all pairs every few batch / epoch

In-Batch

Negative Sampling

Mixed Negative Sampling

Parameter Reduction with Bloom Embeddings

Standard (dictionary-indexed) embeddings uses a lot of parameters and memory

• Unique embeddings for each id
• Also does not allow online training

Hashing trick reduces embedding size with cost of collision

• Collision is problematic for matrix factorisation as the embedding completely defines the user / item

Bloom embeddings further reduces chance of collision

• Multiple hashes per user / item and aggregate embeddings
• Unified embeddings: use 1 set of embeddings for all user and item features

Hashing Trick

Other Embedding Issues

ID-based embeddings unable to learn embeddings for unseen entities

Solution: in addition to ID, also map user/item features to embeddings and aggregate (weighted sum/mean) together

• New user/item will get meaningful embeddings as long as there are valid features

Other Findings

Recent research articles mainly use naive matrix factorisation and LightGCN

• LightGCN is very simple, yet strong GNN model
• However, does not allow online training due to changes in graph structure

Score: dot product / l₂ distance (unbounded) vs cosine similarity (bounded)

• Cosine similarity (normalised embeddings) improves training performance significantly

Evaluation Metrics

If retrieved results are directly shown, use Normalised Discounted Cumulative Gain (NDCG) or Average Precision (AP)

• Emphasize top ranked results stronger

If retrieved results followed by reranking step, use Recall with k equal to number of candidates to be reranked

Implementation Details

ID vs feature embeddings

PHL & BPR performs very strong, MINE is underwhelming

ID + features generally performed worse: poor aggregation of embeddings

In-Batch vs Mixed Negative Sampling

Large improvements with mixed negative sampling, probably also because num negative samples effectively doubled

PHL & BPR performs best, DAU does not used negative samples effectively

In-Batch vs Mixed Negative Sampling

Even with same number of negative samples per interaction, MNS shows significant improvements

Additional random negative samples does not increase performance

Mixed Negative Sampling

ID + features improved even more with mixed negative sampling

PHL and BPR performs best in all settings

Hyperparameters Search with flaml.BlendSearch

Matrix Factorisation

Bloom embeddings

User (features)

Item (features)

User embeddings

Item embeddings

Cosine similarity

Pairwise hinge loss

Mixed negatives

Final Comments

Retrieval terminology

• Query: user context
• Candidate: item context

Retrieval query is not always user context

• For item-item recommendation, use item context

Hence, this generic model can be used for both user-item and item-item recommendation

References

Implementation: https://github.com/yxtay/matrix-factorization-pytorch

TensorFlow Recommenders: tfrs.tasks.Retrieval | TensorFlow Recommenders

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BPR: [1205.2618] BPR: Bayesian Personalized Ranking from Implicit Feedback

CCL: [2109.12613] SimpleX: A Simple and Strong Baseline for Collaborative Filtering

SSM: [2201.02327] On the Effectiveness of Sampled Softmax Loss for Item Recommendation

DirectAU: [2206.12811] Towards Representation Alignment and Uniformity in Collaborative Filtering

MAWU: [2308.06091] Toward a Better Understanding of Loss Functions for Collaborative Filtering

InfoNCE+, MINE+: [2312.08520] Revisiting Recommendation Loss Functions through Contrastive Learning (Technical Report)

References

[2101.08769] Item Recommendation from Implicit Feedback

Sampling-Bias-Corrected Neural Modeling for Large Corpus Item Recommendations

Sampling : the secret of how to train good embeddings

What is Candidate Sampling

MNS: Mixed Negative Sampling for Learning Two-tower Neural Networks in Recommendations

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Hashing Trick: [0902.2206] Feature Hashing for Large Scale Multitask Learning

Hash Embeddings: [1709.03933] Hash Embeddings for Efficient Word Representations

Unified Embeddings: [2305.12102] Unified Embedding: Battle-Tested Feature Representations for Web-Scale ML Systems

Bloom embeddings: Compact word vectors with Bloom embeddings

Alignment & Uniformity

DirectAU