arXiv subjects

Benjamin Paul Chamberlain

Publications and source records attributed to Benjamin Paul Chamberlain.

At least 19 recordsLinked to original sources

arXiv2023

Graph Neural Networks for Link Prediction with Subgraph Sketching

Many Graph Neural Networks (GNNs) perform poorly compared to simple heuristics on Link Prediction (LP) tasks. This is due to limitations in expressive power such as the inability to count triangles (the backbone of most LP heuristics) and because they can not distinguish automorphic nodes (those having identical structural roles). Both expressiveness issues can be alleviated by learning link (rather than node) representations and incorporating structural features such as triangle counts. Since explicit link representations are often prohibitively expensive, recent works resorted to subgraph-based methods, which have achieved state-of-the-art performance for LP, but suffer from poor efficiency due to high levels of redundancy between subgraphs. We analyze the components of subgraph GNN (SGNN) methods for link prediction. Based on our analysis, we propose a novel full-graph GNN called ELPH (Efficient Link Prediction with Hashing) that passes subgraph sketches as messages to approximate the key components of SGNNs without explicit subgraph construction. ELPH is provably more expressive than Message Passing GNNs (MPNNs). It outperforms existing SGNN models on many standard LP benchmarks while being orders of magnitude faster. However, it shares the common GNN limitation that it is only efficient when the dataset fits in GPU memory. Accordingly, we develop a highly scalable model, called BUDDY, which uses feature precomputation to circumvent this limitation without sacrificing predictive performance. Our experiments show that BUDDY also outperforms SGNNs on standard LP benchmarks while being highly scalable and faster than ELPH.

cs.LG↗

arXiv2023

Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs

Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their oversmoothing behaviour. By considering a hierarchy of increasingly general sheaves, we study how the ability of the sheaf diffusion process to achieve linear separation of the classes in the infinite time limit expands. At the same time, we prove that when the sheaf is non-trivial, discretised parametric diffusion processes have greater control than GNNs over their asymptotic behaviour. On the practical side, we study how sheaves can be learned from data. The resulting sheaf diffusion models have many desirable properties that address the limitations of classical graph diffusion equations (and corresponding GNN models) and obtain competitive results in heterophilic settings. Overall, our work provides new connections between GNNs and algebraic topology and would be of interest to both fields.

cs.LG↗

arXiv2022

Understanding over-squashing and bottlenecks on graphs via curvature

Most graph neural networks (GNNs) use the message passing paradigm, in which node features are propagated on the input graph. Recent works pointed to the distortion of information flowing from distant nodes as a factor limiting the efficiency of message passing for tasks relying on long-distance interactions. This phenomenon, referred to as 'over-squashing', has been heuristically attributed to graph bottlenecks where the number of $k$-hop neighbors grows rapidly with $k$. We provide a precise description of the over-squashing phenomenon in GNNs and analyze how it arises from bottlenecks in the graph. For this purpose, we introduce a new edge-based combinatorial curvature and prove that negatively curved edges are responsible for the over-squashing issue. We also propose and experimentally test a curvature-based graph rewiring method to alleviate the over-squashing.

stat.ML↗

arXiv2022

On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features

While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications, however, features are only partially available; for example, in social networks, age and gender are available only for a small subset of users. We present a general approach for handling missing features in graph machine learning applications that is based on minimization of the Dirichlet energy and leads to a diffusion-type differential equation on the graph. The discretization of this equation produces a simple, fast and scalable algorithm which we call Feature Propagation. We experimentally show that the proposed approach outperforms previous methods on seven common node-classification benchmarks and can withstand surprisingly high rates of missing features: on average we observe only around 4% relative accuracy drop when 99% of the features are missing. Moreover, it takes only 10 seconds to run on a graph with $\sim$2.5M nodes and $\sim$123M edges on a single GPU.

cs.LG↗

arXiv2021

Beltrami Flow and Neural Diffusion on Graphs

We propose a novel class of graph neural networks based on the discretised Beltrami flow, a non-Euclidean diffusion PDE. In our model, node features are supplemented with positional encodings derived from the graph topology and jointly evolved by the Beltrami flow, producing simultaneously continuous feature learning and topology evolution. The resulting model generalises many popular graph neural networks and achieves state-of-the-art results on several benchmarks.

cs.LG↗

arXiv2021

GRAND: Graph Neural Diffusion

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.

cs.LG↗

arXiv2021

Online Controlled Experiments for Personalised e-Commerce Strategies: Design, Challenges, and Pitfalls

Online controlled experiments are the primary tool for measuring the causal impact of product changes in digital businesses. It is increasingly common for digital products and services to interact with customers in a personalised way. Using online controlled experiments to optimise personalised interaction strategies is challenging because the usual assumption of statistically equivalent user groups is violated. Additionally, challenges are introduced by users qualifying for strategies based on dynamic, stochastic attributes. Traditional A/B tests can salvage statistical equivalence by pre-allocating users to control and exposed groups, but this dilutes the experimental metrics and reduces the test power. We present a stacked incrementality test framework that addresses problems with running online experiments for personalised user strategies. We derive bounds that show that our framework is superior to the best simple A/B test given enough users and that this condition is easily met for large scale online experiments. In addition, we provide a test power calculator and describe a selection of pitfalls and lessons learnt from our experience using it.

stat.ME↗

arXiv2019

What is the value of experimentation & measurement?

Experimentation and Measurement (E&M) capabilities allow organizations to accurately assess the impact of new propositions and to experiment with many variants of existing products. However, until now, the question of measuring the measurer, or valuing the contribution of an E&M capability to organizational success has not been addressed. We tackle this problem by analyzing how, by decreasing estimation uncertainty, E&M platforms allow for better prioritization. We quantify this benefit in terms of expected relative improvement in the performance of all new propositions and provide guidance for how much an E&M capability is worth and when organizations should invest in one.

stat.ME↗

arXiv2019

Fashion Outfit Generation for E-commerce

Combining items of clothing into an outfit is a major task in fashion retail. Recommending sets of items that are compatible with a particular seed item is useful for providing users with guidance and inspiration, but is currently a manual process that requires expert stylists and is therefore not scalable or easy to personalise. We use a multilayer neural network fed by visual and textual features to learn embeddings of items in a latent style space such that compatible items of different types are embedded close to one another. We train our model using the ASOS outfits dataset, which consists of a large number of outfits created by professional stylists and which we release to the research community. Our model shows strong performance in an offline outfit compatibility prediction task. We use our model to generate outfits and for the first time in this field perform an AB test, comparing our generated outfits to those produced by a baseline model which matches appropriate product types but uses no information on style. Users approved of outfits generated by our model 21% and 34% more frequently than those generated by the baseline model for womenswear and menswear respectively.

cs.CV↗

arXiv2019

Scalable Hyperbolic Recommender Systems

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its development. In doing so, we demonstrate the viability of hyperbolic geometry for recommender systems, showing that they significantly outperform Euclidean models on datasets with the properties of complex networks. Key to the success of our approach are the novel choice of underlying hyperbolic model and the use of the Einstein midpoint to define an asymmetric recommender system in hyperbolic space. These choices allow us to scale to millions of users and hundreds of thousands of items.

cs.IR↗

arXiv2018

Speeding Up BigClam Implementation on SNAP

We perform a detailed analysis of the C++ implementation of the Cluster Affiliation Model for Big Networks (BigClam) on the Stanford Network Analysis Project (SNAP). BigClam is a popular graph mining algorithm that is capable of finding overlapping communities in networks containing millions of nodes. Our analysis shows a key stage of the algorithm - determining if a node belongs to a community - dominates the runtime of the implementation, yet the computation is not parallelized. We show that by parallelizing computations across multiple threads using OpenMP we can speed up the algorithm by 5.3 times when solving large networks for communities, while preserving the integrity of the program and the result.

cs.SI↗

arXiv2018

Designing Experiments to Measure Incrementality on Facebook

The importance of Facebook advertising has risen dramatically in recent years, with the platform accounting for almost 20% of the global online ad spend in 2017. An important consideration in advertising is incrementality: how much of the change in an experimental metric is an advertising campaign responsible for. To measure incrementality, Facebook provide lift studies. As Facebook lift studies differ from standard A/B tests, the online experimentation literature does not describe how to calculate parameters such as power and minimum sample size. Facebook also offer multi-cell lift tests, which can be used to compare campaigns that don't have statistically identical audiences. In this case, there is no literature describing how to measure the significance of the difference in incrementality between cells, or how to estimate the power or minimum sample size. We fill these gaps in the literature by providing the statistical power and required sample size calculation for Facebook lift studies. We then generalise the statistical significance, power, and required sample size calculation to multi-cell lift studies. We represent our results theoretically in terms of the distributions of test metrics and in practical terms relating to the metrics used by practitioners, making all of our code publicly available.

stat.ME↗

arXiv2018

A Recurrent Neural Network Survival Model: Predicting Web User Return Time

The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorporate aggregate representations of users instead of automatically learning a representation directly from a raw time series of user actions. RNNs can automatically learn features, but can not be directly trained with examples of non-returning users who have no target value for their return time. We develop a novel RNN survival model that removes the limitations of the state of the art methods. We demonstrate that this model can successfully be applied to return time prediction on a large e-commerce dataset with a superior ability to discriminate between returning and non-returning users than either method applied in isolation.

cs.LG↗

arXiv2018

Predicting Twitter User Socioeconomic Attributes with Network and Language Information

Inferring socioeconomic attributes of social media users such as occupation and income is an important problem in computational social science. Automated inference of such characteristics has applications in personalised recommender systems, targeted computational advertising and online political campaigning. While previous work has shown that language features can reliably predict socioeconomic attributes on Twitter, employing information coming from users' social networks has not yet been explored for such complex user characteristics. In this paper, we describe a method for predicting the occupational class and the income of Twitter users given information extracted from their extended networks by learning a low-dimensional vector representation of users, i.e. graph embeddings. We use this representation to train predictive models for occupational class and income. Results on two publicly available datasets show that our method consistently outperforms the state-of-the-art methods in both tasks. We also obtain further significant improvements when we combine graph embeddings with textual features, demonstrating that social network and language information are complementary.

cs.CL↗

arXiv2017

Generalising Random Forest Parameter Optimisation to Include Stability and Cost

Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is only one of several metrics that must be considered when optimizing random forest parameters for commercial applications. We propose a novel metric that captures the stability of random forests predictions, which we argue is key for scenarios that require successive predictions. We motivate the need for multi-criteria optimization by showing that in practical applications, simply choosing the parameters that lead to the lowest error can introduce unnecessary costs and produce predictions that are not stable across independent runs. To optimize this multi-criteria trade-off, we present a new framework that efficiently finds a principled balance between these three considerations using Bayesian optimisation. The pitfalls of optimising forest parameters purely for error reduction are demonstrated using two publicly available real world datasets. We show that our framework leads to parameter settings that are markedly different from the values discovered by error reduction metrics.

stat.ML↗

arXiv2017

Customer Lifetime Value Prediction Using Embeddings

We describe the Customer LifeTime Value (CLTV) prediction system deployed at ASOS.com, a global online fashion retailer. CLTV prediction is an important problem in e-commerce where an accurate estimate of future value allows retailers to effectively allocate marketing spend, identify and nurture high value customers and mitigate exposure to losses. The system at ASOS provides daily estimates of the future value of every customer and is one of the cornerstones of the personalised shopping experience. The state of the art in this domain uses large numbers of handcrafted features and ensemble regressors to forecast value, predict churn and evaluate customer loyalty. Recently, domains including language, vision and speech have shown dramatic advances by replacing handcrafted features with features that are learned automatically from data. We detail the system deployed at ASOS and show that learning feature representations is a promising extension to the state of the art in CLTV modelling. We propose a novel way to generate embeddings of customers, which addresses the issue of the ever changing product catalogue and obtain a significant improvement over an exhaustive set of handcrafted features.

cs.LG↗

arXiv2017

Neural Embeddings of Graphs in Hyperbolic Space

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into applications in domains other than language. One such domain is graph-structured data, where embeddings of vertices can be learned that encapsulate vertex similarity and improve performance on tasks including edge prediction and vertex labelling. For both NLP and graph based tasks, embeddings have been learned in high-dimensional Euclidean spaces. However, recent work has shown that the appropriate isometric space for embedding complex networks is not the flat Euclidean space, but negatively curved, hyperbolic space. We present a new concept that exploits these recent insights and propose learning neural embeddings of graphs in hyperbolic space. We provide experimental evidence that embedding graphs in their natural geometry significantly improves performance on downstream tasks for several real-world public datasets.

stat.ML↗

arXiv2017

Probabilistic Inference of Twitter Users' Age based on What They Follow

Twitter provides an open and rich source of data for studying human behaviour at scale and is widely used in social and network sciences. However, a major criticism of Twitter data is that demographic information is largely absent. Enhancing Twitter data with user ages would advance our ability to study social network structures, information flows and the spread of contagions. Approaches toward age detection of Twitter users typically focus on specific properties of tweets, e.g., linguistic features, which are language dependent. In this paper, we devise a language-independent methodology for determining the age of Twitter users from data that is native to the Twitter ecosystem. The key idea is to use a Bayesian framework to generalise ground-truth age information from a few Twitter users to the entire network based on what/whom they follow. Our approach scales to inferring the age of 700 million Twitter accounts with high accuracy.

cs.SI↗