Compass students at AISTATS 2023

Congratulations to Compass students Josh Givens, Hannah Sansford and Alex Modell who, along with their supervisors have had their papers accepted to be published at AISTATS 2023.

 

‘Implications of sparsity and high triangle density for graph representation learning’

Hannah Sansford, Alexander Modell, Nick Whiteley, Patrick Rubin-Delanchy

Hannah: In this paper we explore the implications of two common characteristics of real-world networks, sparsity and triangle-density, for graph representation learning. An example of where these properties arise in the real-world is in social networks, where, although the number of connections each individual has compared to the size of the network is small (sparsity), often a friend of a friend is also a friend (triangle-density). Our result counters a recent influential paper that shows the impossibility of simultaneously recovering these properties with finite-dimensional representations of the nodes, when the probability of connection is modelled by the inner-product. We, by contrast, show that it is possible to recover these properties using an infinite-dimensional inner-product model, where representations lie on a low-dimensional manifold. One of the implications of this work is that we can ‘zoom-in’ to local neighbourhoods of the network, where a lower-dimensional representation is possible.

The paper has been selected for oral presentation at the conference in Valencia (<2% of submissions). 

 

Density Ratio Estimation and Neyman Pearson Classification with Missing Data

Josh Givens, Song Liu, Henry W J Reeve

Josh: In our paper we adapt the popular density ratio estimation procedure KLIEP to make it robust to missing not at random (MNAR) data and demonstrate its efficacy in Neyman-Pearson (NP) classification. Density ratio estimation (DRE) aims to characterise the difference between two classes of data by estimating the ratio between their probability densities. The density ratio is a fundamental quantity in statistics appearing in many settings such as classification, GANs, and covariate shift making its estimation a valuable goal. To our knowledge there is no prior research into DRE with MNAR data, a missing data paradigm where the likelihood of an observation being missing depends on its underlying value. We propose the estimator M-KLIEP and provide finite sample bounds on its accuracy which we show to be minimax optimal for MNAR data. To demonstrate the utility of this estimator we apply it the the field of NP classification. In NP classification we aim to create a classifier which strictly controls the probability of incorrectly classifying points from one class. This is useful in any setting where misclassification for one class is much worse than the other such as fault detection on a production line where you would want to strictly control the probability of classifying a faulty item as non-faulty. In addition to showing the efficacy of our new estimator in this setting we also provide an adaptation to NP classification which allows it to still control this misclassification probability even when fit using MNAR data.

Student perspectives: Discovering the true positions of objects from pairwise similarities

A post by Annie Gray, PhD student on the Compass programme.

Introduction

Initially, my Compass mini-project aimed to explore what we can discover about objects given a matrix of similarities between them. More specifically, how to appropriately measure the distance between objects if we represent each as a point in \mathbb{R}^p (the embedding), and what this can tell us about the objects themselves. This led to discovering that the geodesic distances in the embedding relate to the Euclidean distance between the original positions of the objects, meaning we can recover the original positions of the objects. This work has applications in fields that work with relational data for example: genetics, Natural Language Processing and cyber-security.

This work resulted in a paper [3] written with my supervisors (Nick Whiteley and Patrick Rubin-Delanchy), which has been accepted at NeurIPS this year. The following gives an overview of the paper and how the ideas can be used in practice.

(more…)

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