Nick Duffield

Peiman Mohseni, Nick Duffield, Raymond K. W. Wong

Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering. Neural processes (NPs), a family of probabilistic functional models, are promising solutions -- especially when endowed with domain-specific symmetries like translation equivariance, which improve sample efficiency and generalization. Yet existing translation-equivariant NPs face two limitations: (i) they stack generic components with non-linearities, obscuring the induced function class and limiting interpretability; and (ii) convolutional designs rely on kernels with local receptive fields and require dense uniform input grids, while attention-based methods avoid these issues but scale quadratically with the number of observations. We address both with two contributions. First, using the Volterra expansion, we characterize continuous translation-equivariant operators as sums of higher-order convolutions, yielding analytical transparency while admitting efficient approximation by first-order convolutions. Second, we introduce set Fourier convolutions (SFConvs), a frequency-domain parameterization that operates directly on irregularly sampled points, achieves approximately global receptive fields, and scales linearly in the number of observations. Building on these ideas, we propose two conditional NPs (CNPs): SFConvCNPs, which stack SFConv blocks with non-linearities, and SFVConvCNPs, which integrate the Volterra formulation. Experiments on synthetic and real-world datasets demonstrate our methods' efficacy against state-of-the-art baselines.

Arman Hasanzadeh, Ehsan Hajiramezanali, Nick Duffield et al.

Multi-omics data analysis has the potential to discover hidden molecular interactions, revealing potential regulatory and/or signal transduction pathways for cellular processes of interest when studying life and disease systems. One of critical challenges when dealing with real-world multi-omics data is that they may manifest heterogeneous structures and data quality as often existing data may be collected from different subjects under different conditions for each type of omics data. We propose a novel deep Bayesian generative model to efficiently infer a multi-partite graph encoding molecular interactions across such heterogeneous views, using a fused Gromov-Wasserstein (FGW) regularization between latent representations of corresponding views for integrative analysis. With such an optimal transport regularization in the deep Bayesian generative model, it not only allows incorporating view-specific side information, either with graph-structured or unstructured data in different views, but also increases the model flexibility with the distribution-based regularization. This allows efficient alignment of heterogeneous latent variable distributions to derive reliable interaction predictions compared to the existing point-based graph embedding methods. Our experiments on several real-world datasets demonstrate enhanced performance of MoReL in inferring meaningful interactions compared to existing baselines.

Ziyi Zhang, Shaogang Ren, Xiaoning Qian et al.

In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The advancement of deep neural networks has significantly improved forecasting performance. However, a notable challenge lies in the ability of these models to generalize well to out-of-distribution (OOD) time series data. The inherent spatial heterogeneity and domain shifts across urban environments create hurdles that prevent models from adapting and performing effectively in new urban environments. To tackle this problem, we propose a solution to derive invariant representations for more robust predictions under different urban environments instead of relying on spurious correlation across urban environments for better generalizability. Through extensive experiments on both synthetic and real-world data, we demonstrate that our proposed method outperforms traditional time series forecasting models when tackling domain shifts in changing urban environments. The effectiveness and robustness of our method can be extended to diverse fields including climate modeling, urban planning, and smart city resource management.

Peiman Mohseni, Nick Duffield

Conditional Neural Processes (CNPs) constitute a family of probabilistic models that harness the flexibility of neural networks to parameterize stochastic processes. Their capability to furnish well-calibrated predictions, combined with simple maximum-likelihood training, has established them as appealing solutions for addressing various learning problems, with a particular emphasis on meta-learning. A prominent member of this family, Convolutional Conditional Neural Processes (ConvCNPs), utilizes convolution to explicitly introduce translation equivariance as an inductive bias. However, ConvCNP's reliance on local discrete kernels in its convolution layers can pose challenges in capturing long-range dependencies and complex patterns within the data, especially when dealing with limited and irregularly sampled observations from a new task. Building on the successes of Fourier neural operators (FNOs) for approximating the solution operators of parametric partial differential equations (PDEs), we propose Spectral Convolutional Conditional Neural Processes (SConvCNPs), a new addition to the NPs family that allows for more efficient representation of functions in the frequency domain.

Ziyi Zhang, Shaogang Ren, Xiaoning Qian et al.

Granger causality is widely used for causal structure discovery in complex systems from multivariate time series data. Traditional Granger causality tests based on linear models often fail to detect even mild non-linear causal relationships. Therefore, numerous recent studies have investigated non-linear Granger causality methods, achieving improved performance. However, these methods often rely on two key assumptions: causal sufficiency and known interventional targets. Causal sufficiency assumes the absence of latent confounders, yet their presence can introduce spurious correlations. Moreover, real-world time series data usually come from heterogeneous environments, without prior knowledge of interventions. Therefore, in practice, it is difficult to distinguish intervened environments from non-intervened ones, and even harder to identify which variables or timesteps are affected. To address these challenges, we propose Invariant Granger Causality (InvarGC), which leverages cross-environment heterogeneity to mitigate the effects of latent confounding and to distinguish intervened from non-intervened environments with edge-level granularity, thereby recovering invariant causal relations. In addition, we establish the identifiability under these conditions. Extensive experiments on both synthetic and real-world datasets demonstrate the competitive performance of our approach compared to state-of-the-art methods.

Ziyi Zhang, Shaogang Ren, Xiaoning Qian et al.

Granger causality, commonly used for inferring causal structures from time series data, has been adopted in widespread applications across various fields due to its intuitive explainability and high compatibility with emerging deep neural network prediction models. To alleviate challenges in better deciphering causal structures unambiguously from time series, the use of interventional data has become a practical approach. However, existing methods have yet to be explored in the context of imperfect interventions with unknown targets, which are more common and often more beneficial in a wide range of real-world applications. Additionally, the identifiability issues of Granger causality with unknown interventional targets in complex network models remain unsolved. Our work presents a theoretically-grounded method that infers Granger causal structure and identifies unknown targets by leveraging heterogeneous interventional time series data. We further illustrate that learning Granger causal structure and recovering interventional targets can mutually promote each other. Comparative experiments demonstrate that our method outperforms several robust baseline methods in learning Granger causal structure from interventional time series data.

Peiman Mohseni, Nick Duffield, Bani Mallick et al.

Neural processes are a family of probabilistic models that inherit the flexibility of neural networks to parameterize stochastic processes. Despite providing well-calibrated predictions, especially in regression problems, and quick adaptation to new tasks, the Gaussian assumption that is commonly used to represent the predictive likelihood fails to capture more complicated distributions such as multimodal ones. To overcome this limitation, we propose Conditional Quantile Neural Processes (CQNPs), a new member of the neural processes family, which exploits the attractive properties of quantile regression in modeling the distributions irrespective of their form. By introducing an extension of quantile regression where the model learns to focus on estimating informative quantiles, we show that the sampling efficiency and prediction accuracy can be further enhanced. Our experiments with real and synthetic datasets demonstrate substantial improvements in predictive performance compared to the baselines, and better modeling of heterogeneous distributions' characteristics such as multimodality.

Arman Hasanzadeh, Mohammadreza Armandpour, Ehsan Hajiramezanali et al.

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node representations or their downstream tasks, limiting their application in high-stakes domains. In this paper, we propose a novel Bayesian perspective of graph contrastive learning methods showing random augmentations leads to stochastic encoders. As a result, our proposed method represents each node by a distribution in the latent space in contrast to existing techniques which embed each node to a deterministic vector. By learning distributional representations, we provide uncertainty estimates in downstream graph analytics tasks and increase the expressive power of the predictive model. In addition, we propose a Bayesian framework to infer the probability of perturbations in each view of the contrastive model, eliminating the need for a computationally expensive search for hyperparameter tuning. We empirically show a considerable improvement in performance compared to existing state-of-the-art methods on several benchmark datasets.

Ehsan Hajiramezanali, Arman Hasanzadeh, Nick Duffield et al.

High-throughput molecular profiling technologies have produced high-dimensional multi-omics data, enabling systematic understanding of living systems at the genome scale. Studying molecular interactions across different data types helps reveal signal transduction mechanisms across different classes of molecules. In this paper, we develop a novel Bayesian representation learning method that infers the relational interactions across multi-omics data types. Our method, Bayesian Relational Learning (BayReL) for multi-omics data integration, takes advantage of a priori known relationships among the same class of molecules, modeled as a graph at each corresponding view, to learn view-specific latent variables as well as a multi-partite graph that encodes the interactions across views. Our experiments on several real-world datasets demonstrate enhanced performance of BayReL in inferring meaningful interactions compared to existing baselines.

Arman Hasanzadeh, Ehsan Hajiramezanali, Shahin Boluki et al.

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning them as model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. GNN training with adaptive connection sampling is shown to be mathematically equivalent to an efficient approximation of training Bayesian GNNs. Experimental results with ablation studies on benchmark datasets validate that adaptively learning the sampling rate given graph training data is the key to boost the performance of GNNs in semi-supervised node classification, less prone to over-smoothing and over-fitting with more robust prediction.

Ehsan Hajiramezanali, Arman Hasanzadeh, Nick Duffield et al.

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In this paper, we advocate learning implicit latent representations using semi-implicit variational inference to further increase model flexibility. Semi-implicit stochastic recurrent neural network(SIS-RNN) is developed to enrich inferred model posteriors that may have no analytic density functions, as long as independent random samples can be generated via reparameterization. Extensive experiments in different tasks on real-world datasets show that SIS-RNN outperforms the existing methods.

Nesreen K. Ahmed, Nick Duffield, Ryan A. Rossi

Temporal networks representing a stream of timestamped edges are seemingly ubiquitous in the real-world. However, the massive size and continuous nature of these networks make them fundamentally challenging to analyze and leverage for descriptive and predictive modeling tasks. In this work, we propose a general framework for temporal network sampling with unbiased estimation. We develop online, single-pass sampling algorithms and unbiased estimators for temporal network sampling. The proposed algorithms enable fast, accurate, and memory-efficient statistical estimation of temporal network patterns and properties. In addition, we propose a temporally decaying sampling algorithm with unbiased estimators for studying networks that evolve in continuous time, where the strength of links is a function of time, and the motif patterns are temporally-weighted. In contrast to the prior notion of a $\bigtriangleup t$-temporal motif, the proposed formulation and algorithms for counting temporally weighted motifs are useful for forecasting tasks in networks such as predicting future links, or a future time-series variable of nodes and links. Finally, extensive experiments on a variety of temporal networks from different domains demonstrate the effectiveness of the proposed algorithms. A detailed ablation study is provided to understand the impact of the various components of the proposed framework.

Ehsan Hajiramezanali, Arman Hasanzadeh, Nick Duffield et al.

Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph recurrent neural network (GRNN) to capture both topology and node attribute changes in dynamic graphs. We argue that the use of high-level latent random variables in this variational GRNN (VGRNN) can better capture potential variability observed in dynamic graphs as well as the uncertainty of node latent representation. With semi-implicit variational inference developed for this new VGRNN architecture (SI-VGRNN), we show that flexible non-Gaussian latent representations can further help dynamic graph analytic tasks. Our experiments with multiple real-world dynamic graph datasets demonstrate that SI-VGRNN and VGRNN consistently outperform the existing baseline and state-of-the-art methods by a significant margin in dynamic link prediction.

Arman Hasanzadeh, Ehsan Hajiramezanali, Nick Duffield et al.

Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. Compared to VGAE, the derived graph latent representations by SIG-VAE are more interpretable, due to more expressive generative model and more faithful inference enabled by the flexible semi-implicit construction. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.

Nesreen K. Ahmed, Nick Duffield

Networks are a natural representation of complex systems across the sciences, and higher-order dependencies are central to the understanding and modeling of these systems. However, in many practical applications such as online social networks, networks are massive, dynamic, and naturally streaming, where pairwise interactions among vertices become available one at a time in some arbitrary order. The massive size and streaming nature of these networks allow only partial observation, since it is infeasible to analyze the entire network. Under such scenarios, it is challenging to study the higher-order structural and connectivity patterns of streaming networks. In this work, we consider the fundamental problem of estimating the higher-order dependencies using adaptive sampling. We propose a novel adaptive, single-pass sampling framework and unbiased estimators for higher-order network analysis of large streaming networks. Our algorithms exploit adaptive techniques to identify edges that are highly informative for efficiently estimating the higher-order structure of streaming networks from small sample data. We also introduce a novel James-Stein shrinkage estimator to reduce the estimation error. Our approach is fully analytic, computationally efficient, and can be incrementally updated in a streaming setting. Numerical experiments on large networks show that our approach is superior to baseline methods.

Xi Liu, Muhe Xie, Xidao Wen et al.

As mobile devices become more and more popular, mobile gaming has emerged as a promising market with billion-dollar revenues. A variety of mobile game platforms and services have been developed around the world. A critical challenge for these platforms and services is to understand the churn behavior in mobile games, which usually involves churn at micro level (between an app and a specific user) and macro level (between an app and all its users). Accurate micro-level churn prediction and macro-level churn ranking will benefit many stakeholders such as game developers, advertisers, and platform operators. In this paper, we present the first large-scale churn analysis for mobile games that supports both micro-level churn prediction and macro-level churn ranking. For micro-level churn prediction, in view of the common limitations of the state-of-the-art methods built upon traditional machine learning models, we devise a novel semi-supervised and inductive embedding model that jointly learns the prediction function and the embedding function for user-app relationships. We model these two functions by deep neural networks with a unique edge embedding technique that is able to capture both contextual information and relationship dynamics. We also design a novel attributed random walk technique that takes into consideration both topological adjacency and attribute similarities. To address macro-level churn ranking, we propose to construct a relationship graph with estimated micro-level churn probabilities as edge weights and adapt link analysis algorithms on the graph. We devise a simple algorithm SimSum and adapt two more advanced algorithms PageRank and HITS. The performance of our solutions for the two-level churn analysis problems is evaluated on real-world data collected from the Samsung Game Launcher platform.

Xi Liu, Ping-Chun Hsieh, Nick Duffield et al.

Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become indispensable for machine learning tasks over large networks. The majority of existing literature has considered this technique under the assumption that the network is static. However, networks in many applications, nodes and edges accrue to a growing network as a streaming. A small number of very recent results have addressed the problem of embedding for dynamic networks. However, they either rely on knowledge of vertex attributes, suffer high-time complexity or need to be re-trained without closed-form expression. Thus the approach of adapting the existing methods to the streaming environment faces non-trivial technical challenges. These challenges motivate developing new approaches to the problems of streaming network embedding. In this paper, We propose a new framework that is able to generate latent features for new vertices with high efficiency and low complexity under specified iteration rounds. We formulate a constrained optimization problem for the modification of the representation resulting from a stream arrival. We show this problem has no closed-form solution and instead develop an online approximation solution. Our solution follows three steps: (1) identify vertices affected by new vertices, (2) generate latent features for new vertices, and (3) update the latent features of the most affected vertices. The generated representations are provably feasible and not far from the optimal ones in terms of expectation. Multi-class classification and clustering on five real-world networks demonstrate that our model can efficiently update vertex representations and simultaneously achieve comparable or even better performance.

Xi Liu, Muhe Xie, Xidao Wen et al.

Mobile gaming has emerged as a promising market with billion-dollar revenues. A variety of mobile game platforms and services have been developed around the world. One critical challenge for these platforms and services is to understand user churn behavior in mobile games. Accurate churn prediction will benefit many stakeholders such as game developers, advertisers, and platform operators. In this paper, we present the first large-scale churn prediction solution for mobile games. In view of the common limitations of the state-of-the-art methods built upon traditional machine learning models, we devise a novel semi-supervised and inductive embedding model that jointly learns the prediction function and the embedding function for user-app relationships. We model these two functions by deep neural networks with a unique edge embedding technique that is able to capture both contextual information and relationship dynamics. We also design a novel attributed random walk technique that takes into consideration both topological adjacency and attribute similarities. To evaluate the performance of our solution, we collect real-world data from the Samsung Game Launcher platform that includes tens of thousands of games and hundreds of millions of user-app interactions. The experimental results with this data demonstrate the superiority of our proposed model against existing state-of-the-art methods.

Nesreen K. Ahmed, Nick Duffield, Liangzhen Xia

Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as the pairwise number of common neighbors (CN) and related metrics. While the number of node pairs that share neighbors is potentially enormous, only a relatively small proportion of them have many common neighbors. This motivates finding a weighted sampling approach to preferentially sample these node pairs. This paper presents a new sampling algorithm that provides a fixed size unbiased estimate of the similarity matrix resulting from a bipartite graph stream projection. The algorithm has two components. First, it maintains a reservoir of sampled bipartite edges with sampling weights that favor selection of high similarity nodes. Second, arriving edges generate a stream of \textsl{similarity updates} based on their adjacency with the current sample. These updates are aggregated in a second reservoir sample-based stream aggregator to yield the final unbiased estimate. Experiments on real world graphs show that a 10% sample at each stage yields estimates of high similarity edges with weighted relative errors of about 1%.

Nesreen K. Ahmed, Nick Duffield, Theodore Willke et al.

We propose Graph Priority Sampling (GPS), a new paradigm for order-based reservoir sampling from massive streams of graph edges. GPS provides a general way to weight edge sampling according to auxiliary and/or size variables so as to accomplish various estimation goals of graph properties. In the context of subgraph counting, we show how edge sampling weights can be chosen so as to minimize the estimation variance of counts of specified sets of subgraphs. In distinction with many prior graph sampling schemes, GPS separates the functions of edge sampling and subgraph estimation. We propose two estimation frameworks: (1) Post-Stream estimation, to allow GPS to construct a reference sample of edges to support retrospective graph queries, and (2) In-Stream estimation, to allow GPS to obtain lower variance estimates by incrementally updating the subgraph count estimates during stream processing. Unbiasedness of subgraph estimators is established through a new Martingale formulation of graph stream order sampling, which shows that subgraph estimators, written as a product of constituent edge estimators are unbiased, even when computed at different points in the stream. The separation of estimation and sampling enables significant resource savings relative to previous work. We illustrate our framework with applications to triangle and wedge counting. We perform a large-scale experimental study on real-world graphs from various domains and types. GPS achieves high accuracy with less than 1% error for triangle and wedge counting, while storing a small fraction of the graph with average update times of a few microseconds per edge. Notably, for a large Twitter graph with more than 260M edges, GPS accurately estimates triangle counts with less than 1% error, while storing only 40K edges.

Nesreen K. Ahmed, Jennifer Neville, Ryan A. Rossi et al.

From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a tremendous success and impact in a variety of domains, there has yet to be a fast and efficient approach for computing the frequencies of these subgraph patterns. However, existing methods are not scalable to large networks with millions of nodes and edges, which impedes the application of graphlets to new problems that require large-scale network analysis. To address these problems, we propose a fast, efficient, and parallel algorithm for counting graphlets of size k={3,4}-nodes that take only a fraction of the time to compute when compared with the current methods used. The proposed graphlet counting algorithms leverages a number of proven combinatorial arguments for different graphlets. For each edge, we count a few graphlets, and with these counts along with the combinatorial arguments, we obtain the exact counts of others in constant time. On a large collection of 300+ networks from a variety of domains, our graphlet counting strategies are on average 460x faster than current methods. This brings new opportunities to investigate the use of graphlets on much larger networks and newer applications as we show in the experiments. To the best of our knowledge, this paper provides the largest graphlet computations to date as well as the largest systematic investigation on over 300+ networks from a variety of domains.