Learned indexes are a class of index data structures that enable fast search by approximating the cumulative distribution function (CDF) using machine learning models (Kraska et al., SIGMOD'18). However, recent studies have shown that learned indexes are vulnerable to poisoning attacks, where injecting a small number of poison keys into the training data can significantly degrade model accuracy and reduce index performance (Kornaropoulos et al., SIGMOD'22). In this work, we provide a rigorous theoretical analysis of poisoning attacks targeting linear regression models over CDFs, one of the most basic regression models and a core component in many learned indexes. Our main contributions are as follows: (i) We present a theoretical proof characterizing the optimal single-point poisoning attack and show that the existing method yields the optimal attack. (ii) We show that in multi-point attacks, the existing greedy approach is not always optimal, and we rigorously derive the key properties that an optimal attack should satisfy. (iii) We propose a method to compute an upper bound of the multi-point poisoning attack's impact and empirically demonstrate that the loss under the greedy approach is often close to this bound. Our study deepens the theoretical understanding of attack strategies against linear regression models on CDFs and provides a foundation for the theoretical evaluation of attacks and defenses on learned indexes.

Current exact hierarchical density-based clustering algorithms for high-dimensional data have asymptotically quadratic complexity. We present algorithms for approximate hierarchical density-based clustering, namely for single-linkage clustering and for HDBSCAN, with empirically near-linear time scalability. We explore both graph index-based incremental nearest neighbor search and an iterative exploration scheme on the graph index approximating the MST of the reachability graph similar to Kruskal. As graph index, we use both the bottom layer and a combination of all layers of an HNSW as a stand-in for connected search graphs. We provide experiments comparing the clusterings to baselines such as exact implementation and an algorithm using metric tree-based searchers. We explore the impact of the HNSW hyperparameters on the performance in terms of running time and clustering quality. For both single-linkage clustering and HDBSCAN, our algorithms yield highly accurate clusterings while being up to two orders of magnitude faster than industry-standard baselines such as scikit-learn's hdbscan.

The PGM-index (Ferragina and Vinciguerra, VLDB'20) is one of the most practical learned indexes, owing to its theoretical elegance and consistently strong empirical performance. It is built on optimal piecewise linear approximations (PLAs) that minimize the number of segments. In this paper, we ask how sensitive this optimal PLA itself is to poisoning attacks. We propose PGM-attack, an efficient poisoning attack that sequentially inserts adversarial keys to inflate the resulting number of segments, and we develop a method for deriving theoretical upper bounds on the number of segments attainable under arbitrary insertions. Our experiments show that poisoning only 10

Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure epsilon-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aumuller et al. (TODS 2022).

Approximate nearest neighbor (ANN) search is a performance-critical component of many machine learning pipelines, and rigorous benchmarking is essential for assessing the performance of vector indexes for ANN search. However, the datasets of existing benchmarks no longer represent modern ANN applications, creating a need for an up-to-date benchmark. To address this gap, we introduce Vector Index Benchmark for Embeddings (VIBE), an open-source framework for benchmarking ANN algorithms. VIBE provides a pipeline for generating benchmark datasets with dense embedding models representative of modern applications, including retrieval-augmented generation (RAG). To represent real-world workloads, we also include out-of-distribution (OOD) datasets where the queries and the corpus are drawn from different distributions. These include multimodal retrieval datasets and maximum inner product search (MIPS) datasets covering two recent use cases: approximate attention computation and reductions of multi-vector retrieval to single-vector MIPS. We use VIBE to conduct a comprehensive evaluation of 22 open-source vector-index implementations across 11 in-distribution and 8 out-of-distribution datasets. The benchmark is available at https://github.com/vector-index-bench/vibe

This paper summarizes the innovative solutions presented at the third edition of the SISAP Indexing Challenge held at SISAP 2025. The challenge featured two distinct tasks involving vector embeddings derived from a large corpus using neural encoders. It proposed the following two tasks under strict memory and computational constraints: Both tasks required solutions to operate within strict resource limits: 16 GB of RAM, 8 virtual CPUs, and a 12-h wall-clock time for the end-to-end pipeline (including data loading, pre-processing, indexing, and searching). Each task imposes different minimum quality requirements and ranking specifications. Participants developed strategies such as data compression, optimized indexing, and efficient search algorithms to meet these constraints. This paper details the challenge design, explains the evaluation framework, and provides an overview of the submitted solutions.

Current exact single-linkage clustering algorithms have asymptotically quadratic complexity. We present algorithms for approximate single-linkage clustering with empirically near-linear scalability. We explore both graph index-based incremental nearest neighbor search and an iterative exploration scheme on the graph index approximating the MST of the reachability graph similar to Kruskal. As graph index, we use both the bottom layer and a combination of all layers of an HNSW as a stand-in for connected search graphs. We provide experiments comparing the clusterings to baselines such as exact single linkage implementation and an algorithm using metric tree-based searchers. We explore the impact of the HNSW hyperparameters on the performance in terms of running time and clustering quality and evaluate the empirical asymptotic complexity.

Approximate nearest neighbor search in high-dimensional metric spaces is crucial in modern data science pipelines. Efficient search algorithms often rely on partitioning the metric space. To find the approximate nearest neighbors of a query point, a candidate set is constructed based on the points that belong to the same part in the partition, and the closest points among these candidates are identified via a bruteforce search. Hyvönen et al. (JMLR, 2024) argue that viewing this problem as a multi-class labeling problem suggests that this traditional method is not optimal. Instead, they propose a “natural classifier” search strategy that incorporates the true labels of the candidate points, demonstrating faster searches and smaller candidate sets for the same accuracy for tree-based space partitioning methods. This paper explores the natural classifier and other search strategies for partitioning based on locality-sensitive hashing. We propose a new strategy that offers more precise control over the balance between performance and quality. Our analysis highlights the trade-offs between these methods, providing insights into optimizing search efficiency in various contexts.

The 2023 Big ANN Challenge, held at NeurIPS 2023, focused on advancing the state-of-the-art in indexing data structures and search algorithms for practical variants of Approximate Nearest Neighbor (ANN) search that reflect the growing complexity and diversity of workloads. Unlike prior challenges that emphasized scaling up classical ANN search , this competition addressed filtered search, out-of-distribution data, sparse and streaming variants of ANNS. Participants developed and submitted innovative solutions that were evaluated on new standard datasets with constrained computational resources. The results showcased significant improvements in search accuracy and efficiency over industry-standard baselines, with notable contributions from both academic and industrial teams. This paper summarizes the competition tracks, datasets, evaluation metrics, and the innovative approaches of the top-performing submissions, providing insights into the current advancements and future directions in the field of approximate nearest neighbor search.

The SISAP 2024 Indexing Challenge invited replicable and competitive approximate similarity search solutions for datasets of up to 100 million real-valued vectors. Participants are evaluated on the search performance of their implementations under quality constraints. Using a subset of the deep features of a neural network model provided by the LAION-5B dataset, the challenge posed three tasks, each with its unique focus: The present paper describes the details of the challenge, the evaluation system that was developed with it, and gives an overview of the submitted solutions.

Differentially private mean estimation is an important building block in privacy-preserving algorithms for data analysis and machine learning. Though the trade-off between privacy and utility is well understood in the worst case, many datasets exhibit structure that could potentially be exploited to yield better algorithms. In this paper we present Private Limit Adopted Noise (PLAN), a family of differentially private algorithms for mean estimation in the setting where inputs are independently sampled from a distribution D over R^d, with coordinate-wise standard deviations σ in R^d. Similar to mean estimation under Mahalanobis distance, PLAN tailors the shape of the noise to the shape of the data, but unlike previous algorithms the privacy budget is spent non-uniformly over the coordinates. Under a concentration assumption on D, we show how to exploit skew in the vector σ, obtaining a (zero-concentrated) differentially private mean estimate with l_2 error proportional to ||σ||_1. Previous work has either not taken σ into account, or measured error in Mahalanobis distance --- in both cases resulting in l_2 error proportional to sqrt{d}||σ||_2, which can be up to a factor sqrt{d} larger. To verify the effectiveness of PLAN, we empirically evaluate accuracy on both synthetic and real-world data.

Efficient and reliable methods for distinguishing outliers in data remain crucial for data analysis. Although supervised methods based on neural networks have gained recent traction, unsupervised methods such as the kNN outlier method and local outlier factor (LOF) remain state-of-the-art solutions according to different standardized benchmarks. Unfortunately, exact outlier detection through nearest neighbor search queries provides a scalability bottleneck for the high-dimensional, big datasets that are routinely analyzed in data science applications. This paper explores benefits and limitations of using approximate nearest neighbor search via Hierarchical Navigable Small World graphs (HNSW) to overcome this scalability barrier. We evaluate direct implementations that compute the kNN and LOF score from approximate neighborhoods and show the robustness of the outlier detection even in settings where the approximation is far away from the exact neighborhoods. Furthermore, we design white-box methods that compute the outlier scores directly from the underlying graph. These methods show much more variability in the quality of the outlier scores and open new ground for the development of task-aware tools based on approximate nearest neighbor search techniques.

Nearest neighbor search is a computational primitive whose efficiency is paramount to many applications. As such, the literature recently blossomed with many works focusing on improving its effectiveness in an approximate setting. In this overview paper, we review recent advances of the state of the art and discuss some trends. Given the practical relevance of the problem, new approaches need to be thoroughly benchmarked. We therefore review some recent benchmarking efforts and provide advice on the benchmarking pipeline

User relevance feedback (URF) is emerging as an important component of the multimedia analytics toolbox. State-of-the-art URF systems employ high-dimensional vectors of semantic features and train linear-SVM classifiers in each round of interaction. In a round, they present the user with the most confident media items, which lie furthest from the SVM plane. Due to the scale of current media collections, URF systems must be supported by a high-dimensional index. Usually, these indexes are designed for nearest-neighbour point queries, and it is not known how well they support the URF process. In this paper, we study the performance of four state-of-the-art high-dimensional indexes in the URF context. We analyse the quality of query results, compared to a sequential analysis of the collection, over a range of classifiers, showing that result quality depends (i) heavily on the quality of the SVM classifier and (ii) the index structure itself. We also consider a search-oriented workload, where the goal is to find the first relevant item for a task. The results show that the indexes perform similarly overall, despite differences in their paths to the solution. Interestingly, worse recall can lead to better application-specific performance.

This manuscript presents the premiere SISAP 2023 Indexing Challenge, which seeks replicable and competitive solutions in the realm of approximate similarity search algorithms. Our aim is recall, all while optimizing build time, search time, and memory consumption. Using a subset of the deep features of a neural network model provided by the LAION-5B dataset, the challenge posed three tasks, each with its unique focus: Notably, an innovative and competitive binary mapping method emerged from the challenge. It also spotlighted graph methods as the preferred indexing technique for binary and real-valued high-dimensional vectors. However, these methods have little room for improvement. Enhancing memory efficiency, refining navigational strategies, and tackling the secondary memory challenge are pivotal next steps.

We investigate the k-closest pair problem in high dimensions, that is finding the k ≥ 1 closest pairs of points in a set S ⊆𝒳 in a metric space (𝒳, dist) . This is a fundamental problem in computational geometry with a wide variety of applications, including network science, data mining, databases, and recommender systems. We propose an exact algorithm with a controllable failure probability, thus allowing the user to specify the desired recall. Our algorithm has expected subquadratic running time under mild assumption on the distance distribution, relying only on the existence of a Locality Sensitive Hash family for the metric at hand. We complement our theoretical analysis with an experimental evaluation, showing that our approach can provide solutions orders of magnitude faster than current state-of-the-art data structures designed for specific metrics.

Kernel Density Estimation (KDE) is a nonparametric method for estimating the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor search, has been shown to enable fast KDE data structures. However, these approaches do not take advantage of the many other advances that have been made in algorithms for nearest neighbor algorithms. We present an algorithm called Density Estimation from Approximate Nearest Neighbors (DEANN) where we apply Approximate Nearest Neighbor (ANN) algorithms as a black box subroutine to compute an unbiased KDE. The idea is to find points that have a large contribution to the KDE using ANN, compute their contribution exactly, and approximate the remainder with Random Sampling (RS). We present a theoretical argument that supports the idea that an ANN subroutine can speed up the evaluation. Furthermore, we provide a C++ implementation with a Python interface that can make use of an arbitrary ANN implementation as a subroutine for kernel density estimation. We show empirically that our implementation outperforms state of the art implementations in all high dimensional datasets we considered, and matches the performance of RS in cases where the ANN yield no gains in performance.

Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. Given a set of points S and a radius parameter r > 0, the r -near neighbor ( r -NN) problem asks for a data structure that, given any query point q , returns a point p within distance at most r from q. In this paper, we study the r -NN problem in the light of individual fairness and providing equal opportunities: all points that are within distance r from the query should have the same probability to be returned. The problem is of special interest in high dimensions, where Locality Sensitive Hashing (LSH), the theoretically leading approach to similarity search, does not provide any fairness guarantee. In this work, we show that LSH-based algorithms can be made fair, without a significant loss in efficiency. We propose several efficient data structures for the exact and approximate variants of the fair NN problem. Our approach works more generally for sampling uniformly from a sub-collection of sets of a given collection and can be used in a few other applications. We also carried out an experimental evaluation that highlights the inherent unfairness of existing NN data structures.