Theo Crookes /stor-i-student-sites/theo-crookes Tue, 28 Nov 2023 11:40:46 +0000 en-GB hourly 1 https://wordpress.org/?v=6.9.4 /stor-i-student-sites/theo-crookes/wp-content/uploads/sites/46/2022/12/cropped-snip-removebg-preview-32x32.png Theo Crookes /stor-i-student-sites/theo-crookes 32 32 Triggered Bandits within Streaming Data Settings /stor-i-student-sites/theo-crookes/2023/11/28/triggered-bandits-within-streaming-data-settings/ /stor-i-student-sites/theo-crookes/2023/11/28/triggered-bandits-within-streaming-data-settings/#respond Tue, 28 Nov 2023 11:33:08 +0000 /stor-i-student-sites/theo-crookes/?p=276 The main aim of this project is to develop novel decision-making algorithms to integrate with current anomaly detection techniques in the streaming data setting. This project is partnered with BT; BT are a large multi-national telecommunications provider, managing around 28 million telephone lines within the UK alone, alongside providing maintenance for other areas of crucial national telecommunication infrastructure. A wide range of important telecommunications data is collected along these lines and streamed to BT.

Anomaly detection methods have been developed for streamed data; these methods can be applied to the telecommunications data. Anomalies within telecommunications data are sometimes consequences of critical incidents; therefore, fast optimal decision-making after anomalies have been detected within BT is important to ensure critical national infrastructure is maintained.

A decision-making algorithm utilising a pre-trained optimisation is not ideal because methods applying non-adaptive decision-making policies have been found to be unable to learn how to make optimal decisions in the streaming data setting where reward distributions may be non-static; therefore, a bandit approach would be more suitable for this problem. The decision-making algorithms we develop will relax unsuitable assumptions commonly made in multi-armed bandit policies to synthesise multi-armed bandit techniques with well-established anomaly detection methods. The novel decision-making algorithms we will develop will be self-optimising and adaptive. Furthermore, the algorithm will give feedback to the anomaly detection method to improve the accuracy and delay of detection.

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MMath: Master’s Project /stor-i-student-sites/theo-crookes/2022/11/15/hello-world/ /stor-i-student-sites/theo-crookes/2022/11/15/hello-world/#respond Tue, 15 Nov 2022 09:13:03 +0000 /stor-i-student-sites/theo-crookes/?p=1 My Master’s Project is on Accessibility Percolation, a term coined by Nowak and Krug [1]. In short, consider a graph on which each edge is assigned a uniform U[0,1] random variable, a path on this graph is said to be accessible if the numbers along the path are increasing. We look at the probability of such types of paths existing under certain conditions on specific types of graphs.

The project follows the proofs of the theorems found in Roberts and Zhao [2] and Berestycki, Brunet and Shi [3], which study increasing paths in regular trees and increasing paths in the irregular trees and the hypercube respectively. Please find a link to the project below:

[1] Stefan Nowak and Joachim Krug. “Accessibility percolation on n-trees”. In: EPL (Europhysics Letters) 101.6 (2013), p. 66004.

[2] Matthew Roberts and Lee Zhao. “Increasing paths in regular trees”. In: Electronic Communications in Probability 18 (2013), pp. 1–10.

[3] Julien Berestycki, Eric Brunet, and Zhan Shi. “The number of accessible paths in the hypercube”. In: Bernoulli 22.2 (2016), pp. 653–680.

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