insikt - Machine Learning - # Clustering-based Approximate Nearest Neighbor Search

Improving Clustering-Based Approximate Nearest Neighbor Search through Learning-to-Rank

Q: How can the learning-to-rank approach be extended to optimize for top-k accuracy directly, rather than just top-1?

To extend the learning-to-rank approach for optimizing top-k accuracy directly, we can modify the loss function and training process. Currently, the formulation focuses on optimizing for top-1 accuracy by ranking partitions based on their likelihood of containing the nearest neighbor to a query. To adapt this for top-k accuracy, we need to consider multiple relevant partitions for each query. One approach is to redefine the oracle routing function 𝜏∗(𝑞) to have 1 in the 𝑖-th component if the intersection between the set of top-k data vectors and partition 𝐶𝑖 is non-empty, and 0 otherwise. This adjustment allows us to train the routing function to rank multiple relevant partitions for each query, optimizing for top-k accuracy. The loss function would need to be updated to reflect the new objective of maximizing top-k accuracy. By considering the top-k relevant partitions for each query during training and updating the routing function based on this information, we can directly optimize for top-k accuracy using the learning-to-rank approach.

Q: What are the theoretical guarantees and limitations of the proposed learning-to-rank formulation for clustering-based ANN search?

The proposed learning-to-rank formulation for clustering-based ANN search offers several theoretical guarantees and limitations: Theoretical Guarantees: Consistency: The cross-entropy loss used in the learning-to-rank formulation is a consistent surrogate for Mean Reciprocal Rank (MRR) when each query has at most one relevant item with probability 1. This provides a theoretical guarantee that optimizing the loss function will lead to improved ranking performance. Efficiency: By learning a routing function, the search space for nearest neighbor search is reduced, leading to more efficient query processing. This efficiency can be theoretically proven through the reduction in the number of partitions evaluated for each query. Limitations: Complexity: The learning-to-rank approach may introduce additional complexity to the clustering-based ANN search system, especially in terms of training the routing function and integrating it into the existing workflow. This complexity can impact the practical implementation of the approach. Scalability: The scalability of the learning-to-rank formulation may be limited by the size of the dataset and the dimensionality of the embeddings. As the dataset grows larger or the embeddings become higher-dimensional, the computational requirements for training the routing function may increase significantly.

Q: Can the learnt routing function be used to guide the clustering algorithm itself, leading to query-aware partitioning of the data?

Yes, the learnt routing function can be leveraged to guide the clustering algorithm itself, enabling query-aware partitioning of the data. By incorporating the insights gained from learning the routing function back into the clustering process, we can adapt the partitioning strategy to better suit the characteristics of the queries and data distribution. Implementation Approach: Iterative Refinement: During the clustering phase, the cluster representatives can be iteratively refined based on the learnt routing function. By updating the cluster assignments and representatives according to the routing scores learned from the training data, the clustering algorithm can become more query-aware. Dynamic Partitioning: The learnt routing function can inform the clustering algorithm on how to dynamically adjust the partitions based on the query characteristics. This dynamic partitioning approach can lead to more effective grouping of data points, improving the accuracy of the nearest neighbor search. Benefits: Improved Accuracy: Query-aware partitioning ensures that the data is grouped in a way that aligns with the query distribution, leading to higher accuracy in identifying nearest neighbors. Adaptability: By incorporating the learnt routing function into the clustering algorithm, the system can adapt to changes in the data distribution and query patterns, making it more versatile and robust. In conclusion, integrating the insights from the learnt routing function into the clustering algorithm enables a more intelligent and adaptive partitioning strategy, enhancing the overall performance of clustering-based ANN search.

Centrala begrepp

Learning a ranking function for routing queries to the most relevant partitions can consistently improve the accuracy of clustering-based approximate nearest neighbor search.

Sammanfattning

The paper proposes a learning-to-rank (LTR) approach to improve the routing function in clustering-based approximate nearest neighbor search (ANN). In this method, the routing function, which maps a query to a set of relevant partitions, is learned using supervised LTR techniques instead of using a predefined function.

The key insights are:

The routing function in clustering-based ANN can be formulated as a ranking problem, where the goal is to rank the partitions by their likelihood of containing the nearest neighbor to the query.
The ground-truth for training the ranking function can be easily obtained by performing an exact search for each query and identifying the partition that contains the nearest neighbor.
The cross-entropy loss, which is a consistent surrogate for maximizing mean reciprocal rank (MRR), can be used as the training objective.

The authors demonstrate through experiments on various text datasets that learning a simple linear routing function can consistently improve the top-1 and top-k accuracy of clustering-based ANN compared to the baseline routing function. The gains are observed across different clustering algorithms, including standard, spherical, and shallow K-means.

The results suggest that bridging the fields of LTR and ANN can lead to significant performance improvements in practical applications. The authors also discuss potential future directions, such as incorporating LTR into the clustering algorithm itself to enable query-aware partitioning.

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Statistik

The top-1 accuracy of the learnt routing function is 0.746, 0.751, and 0.670 on the Ms Marco dataset, compared to 0.392, 0.627, and 0.517 for the baseline, when using 0.1% of the total number of partitions.
The top-10 accuracy of the learnt routing function is consistently higher than the baseline across different values of ℓ (the number of partitions probed) on all three datasets.

Citat

"A critical piece of the modern information retrieval puzzle is approximate nearest neighbor search."
"We make a simple observation: The routing function solves a ranking problem. Its quality can therefore be assessed with a ranking metric, making the function amenable to learning-to-rank."
"As we demonstrate empirically on various datasets, learning a simple linear function consistently improves the accuracy of clustering-based MIPS."

Viktiga insikter från

A Learning-to-Rank Formulation of Clustering-Based Approximate Nearest Neighbor Search

by Thomas Vecch... på arxiv.org 04-19-2024

https://arxiv.org/pdf/2404.11731.pdf

A Learning-to-Rank Formulation of Clustering-Based Approximate Nearest Neighbor Search

Djupare frågor

How can the learning-to-rank approach be extended to optimize for top-k accuracy directly, rather than just top-1?

To extend the learning-to-rank approach for optimizing top-k accuracy directly, we can modify the loss function and training process. Currently, the formulation focuses on optimizing for top-1 accuracy by ranking partitions based on their likelihood of containing the nearest neighbor to a query. To adapt this for top-k accuracy, we need to consider multiple relevant partitions for each query.
One approach is to redefine the oracle routing function 𝜏∗(𝑞) to have 1 in the 𝑖-th component if the intersection between the set of top-k data vectors and partition 𝐶𝑖 is non-empty, and 0 otherwise. This adjustment allows us to train the routing function to rank multiple relevant partitions for each query, optimizing for top-k accuracy.
The loss function would need to be updated to reflect the new objective of maximizing top-k accuracy. By considering the top-k relevant partitions for each query during training and updating the routing function based on this information, we can directly optimize for top-k accuracy using the learning-to-rank approach.

What are the theoretical guarantees and limitations of the proposed learning-to-rank formulation for clustering-based ANN search?

The proposed learning-to-rank formulation for clustering-based ANN search offers several theoretical guarantees and limitations:
Theoretical Guarantees:

Consistency: The cross-entropy loss used in the learning-to-rank formulation is a consistent surrogate for Mean Reciprocal Rank (MRR) when each query has at most one relevant item with probability 1. This provides a theoretical guarantee that optimizing the loss function will lead to improved ranking performance.

Efficiency: By learning a routing function, the search space for nearest neighbor search is reduced, leading to more efficient query processing. This efficiency can be theoretically proven through the reduction in the number of partitions evaluated for each query.

Limitations:

Complexity: The learning-to-rank approach may introduce additional complexity to the clustering-based ANN search system, especially in terms of training the routing function and integrating it into the existing workflow. This complexity can impact the practical implementation of the approach.

Scalability: The scalability of the learning-to-rank formulation may be limited by the size of the dataset and the dimensionality of the embeddings. As the dataset grows larger or the embeddings become higher-dimensional, the computational requirements for training the routing function may increase significantly.

Can the learnt routing function be used to guide the clustering algorithm itself, leading to query-aware partitioning of the data?

Yes, the learnt routing function can be leveraged to guide the clustering algorithm itself, enabling query-aware partitioning of the data. By incorporating the insights gained from learning the routing function back into the clustering process, we can adapt the partitioning strategy to better suit the characteristics of the queries and data distribution.
Implementation Approach:

Iterative Refinement: During the clustering phase, the cluster representatives can be iteratively refined based on the learnt routing function. By updating the cluster assignments and representatives according to the routing scores learned from the training data, the clustering algorithm can become more query-aware.

Dynamic Partitioning: The learnt routing function can inform the clustering algorithm on how to dynamically adjust the partitions based on the query characteristics. This dynamic partitioning approach can lead to more effective grouping of data points, improving the accuracy of the nearest neighbor search.

Benefits:

Improved Accuracy: Query-aware partitioning ensures that the data is grouped in a way that aligns with the query distribution, leading to higher accuracy in identifying nearest neighbors.

Adaptability: By incorporating the learnt routing function into the clustering algorithm, the system can adapt to changes in the data distribution and query patterns, making it more versatile and robust.

In conclusion, integrating the insights from the learnt routing function into the clustering algorithm enables a more intelligent and adaptive partitioning strategy, enhancing the overall performance of clustering-based ANN search.