Pseudo-Relevance Feedback (PRF)

PRF is a blind technique because it eliminates the human-in-the-loop. Unlike explicit relevance feedback where a user marks documents as relevant, PRF automatically treats the top-k results (typically k=10 to 50) from an initial BM25 or dense retrieval pass as pseudo-relevant. This assumption is high-risk, high-reward: it works brilliantly when the initial retrieval is precise, but a single outlier in the top-k can cause query drift, poisoning the expansion terms and degrading the final results.

After identifying the pseudo-relevant set, PRF extracts candidate expansion terms using statistical measures. Common scoring functions include:

• Robertson Selection Value (RSV): Weighs term frequency in the pseudo-relevant set against the collection background.
• Kullback-Leibler Divergence: Measures the divergence between the term distribution in the feedback set and the entire corpus.
• Chi-Square: Tests the statistical dependence between a term and the pseudo-relevant class. The top-n scoring terms are then appended to the original query, often with a weighting coefficient to balance the original intent with the expanded context.

PRF fundamentally operates as a two-pass retrieval pipeline:

• Pass 1 (Initial Retrieval): The raw user query is executed against the index to fetch the top-k documents. This pass prioritizes high recall.
• Term Extraction: The content of the top-k documents is analyzed to build a statistical model of the most salient terms.
• Pass 2 (Expanded Retrieval): The original query is augmented with the extracted terms and re-executed. This pass leverages the expanded context to improve precision. This architecture introduces a latency trade-off, as it requires two sequential retrieval operations.

While classically applied to sparse bag-of-words models, PRF has been adapted for dense vector search. Techniques include:

• Vector Averaging: Computing the centroid of the embeddings of the top-k pseudo-relevant documents and using it as the new query vector.
• Generative PRF: Using a language model to read the top-k documents and generate a synthetic expanded query or a hypothetical document embedding.
• ColBERT-style PRF: Aggregating the fine-grained token-level embeddings from the pseudo-relevant set to create a richer, multi-vector query representation. These adaptations allow PRF to bridge the vocabulary gap in semantic spaces.

The primary risk of PRF is query drift, where the expanded query shifts focus away from the user's original information need. This occurs when:

• The initial retrieval fails catastrophically, returning a top-k set that is entirely non-relevant.
• The corpus contains a dominant, off-topic theme that contaminates the pseudo-relevant set.
• The original query is highly ambiguous, and the top-k converges on the wrong sense. Mitigation strategies include selective PRF, where a Query Performance Predictor (QPP) scores the clarity of the initial query and disables expansion if the initial retrieval is predicted to be weak.

PRF is often implemented using Relevance Models (RM), a formal probabilistic framework. While classic PRF heuristically selects terms, RM estimates a multinomial distribution over the vocabulary given the pseudo-relevant set. The key distinction:

• RM1: Estimates the relevance model directly from the top-k documents.
• RM3: Interpolates the relevance model with the original query model to control the influence of the expansion terms.
• RM4: Uses a web-scale corpus as an external expansion source. RM3 is the de facto standard, providing a principled smoothing mechanism to prevent the expanded query from diverging too far from the original intent.