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Alexander Greaves-Tunnell

Publications and source records attributed to Alexander Greaves-Tunnell.

3 recordsLinked to original sources

Quantization for Vector Search under Streaming Updates

Large-scale vector databases for approximate nearest neighbor (ANN) search typically store a quantized dataset in main memory for fast access, and full precision data on remote disk. State-of-the-art ANN quantization methods are highly data-dependent, rendering them unable to handle point insertions and deletions. This either leads to degraded search quality over time, or forces costly global rebuilds of the entire search index. In this paper, we formally study data-dependent quantization under streaming dataset updates. We formulate a computation model of limited remote disk access and define a dynamic consistency property that guarantees freshness under updates. We use it to obtain the following results: Theoretically, we prove that static data-dependent quantization can be made dynamic with bounded disk I/O per update while retaining formal accuracy guarantees for ANN search. Algorithmically, we develop a practical data-dependent quantization method which is provably dynamically consistent, adapting itself to the dataset as it evolves over time. Our experiments show that the method outperforms baselines in large-scale nearest neighbor search quantization under streaming updates.

cs.DS

A Statistical Investigation of Long Memory in Language and Music

Representation and learning of long-range dependencies is a central challenge confronted in modern applications of machine learning to sequence data. Yet despite the prominence of this issue, the basic problem of measuring long-range dependence, either in a given data source or as represented in a trained deep model, remains largely limited to heuristic tools. We contribute a statistical framework for investigating long-range dependence in current applications of deep sequence modeling, drawing on the well-developed theory of long memory stochastic processes. This framework yields testable implications concerning the relationship between long memory in real-world data and its learned representation in a deep learning architecture, which are explored through a semiparametric framework adapted to the high-dimensional setting.

stat.ML

Virus Dynamics on Starlike Graphs

The field of epidemiology has presented fascinating and relevant questions for mathematicians, primarily concerning the spread of viruses in a community. The importance of this research has greatly increased over time as its applications have expanded to also include studies of electronic and social networks and the spread of information and ideas. We study virus propagation on a non-linear hub and spoke graph (which models well many airline networks). We determine the long-term behavior as a function of the cure and infection rates, as well as the number of spokes n. For each n we prove the existence of a critical threshold relating the two rates. Below this threshold, the virus always dies out; above this threshold, all non-trivial initial conditions iterate to a unique non-trivial steady state. We end with some generalizations to other networks.

math.DS