Chao Pan

Chao Pan, Jin Sima, Saurav Prakash et al.

Federated clustering (FC) is an unsupervised learning problem that arises in a number of practical applications, including personalized recommender and healthcare systems. With the adoption of recent laws ensuring the "right to be forgotten", the problem of machine unlearning for FC methods has become of significant importance. We introduce, for the first time, the problem of machine unlearning for FC, and propose an efficient unlearning mechanism for a customized secure FC framework. Our FC framework utilizes special initialization procedures that we show are well-suited for unlearning. To protect client data privacy, we develop the secure compressed multiset aggregation (SCMA) framework that addresses sparse secure federated learning (FL) problems encountered during clustering as well as more general problems. To simultaneously facilitate low communication complexity and secret sharing protocols, we integrate Reed-Solomon encoding with special evaluation points into our SCMA pipeline, and prove that the client communication cost is logarithmic in the vector dimension. Additionally, to demonstrate the benefits of our unlearning mechanism over complete retraining, we provide a theoretical analysis for the unlearning performance of our approach. Simulation results show that the new FC framework exhibits superior clustering performance compared to previously reported FC baselines when the cluster sizes are highly imbalanced. Compared to completely retraining K-means++ locally and globally for each removal request, our unlearning procedure offers an average speed-up of roughly 84x across seven datasets. Our implementation for the proposed method is available at https://github.com/thupchnsky/mufc.

Chao Pan, Eli Chien, Olgica Milenkovic

As the demand for user privacy grows, controlled data removal (machine unlearning) is becoming an important feature of machine learning models for data-sensitive Web applications such as social networks and recommender systems. Nevertheless, at this point it is still largely unknown how to perform efficient machine unlearning of graph neural networks (GNNs); this is especially the case when the number of training samples is small, in which case unlearning can seriously compromise the performance of the model. To address this issue, we initiate the study of unlearning the Graph Scattering Transform (GST), a mathematical framework that is efficient, provably stable under feature or graph topology perturbations, and offers graph classification performance comparable to that of GNNs. Our main contribution is the first known nonlinear approximate graph unlearning method based on GSTs. Our second contribution is a theoretical analysis of the computational complexity of the proposed unlearning mechanism, which is hard to replicate for deep neural networks. Our third contribution are extensive simulation results which show that, compared to complete retraining of GNNs after each removal request, the new GST-based approach offers, on average, a 10.38x speed-up and leads to a 2.6% increase in test accuracy during unlearning of 90 out of 100 training graphs from the IMDB dataset (10% training ratio). Our implementation is available online at https://doi.org/10.5281/zenodo.7613150.

Chao Pan, Eli Chien, Puoya Tabaghi et al.

Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform the required learning tasks. For hierarchical data, the space of choice is a hyperbolic space because it guarantees low-distortion embeddings for tree-like structures. The geometry of hyperbolic spaces has properties not encountered in Euclidean spaces that pose challenges when trying to rigorously analyze algorithmic solutions. We propose a unified framework for learning scalable and simple hyperbolic linear classifiers with provable performance guarantees. The gist of our approach is to focus on Poincaré ball models and formulate the classification problems using tangent space formalisms. Our results include a new hyperbolic perceptron algorithm as well as an efficient and highly accurate convex optimization setup for hyperbolic support vector machine classifiers. Furthermore, we adapt our approach to accommodate second-order perceptrons, where data is preprocessed based on second-order information (correlation) to accelerate convergence, and strategic perceptrons, where potentially manipulated data arrives in an online manner and decisions are made sequentially. The excellent performance of the Poincaré second-order and strategic perceptrons shows that the proposed framework can be extended to general machine learning problems in hyperbolic spaces. Our experimental results, pertaining to synthetic, single-cell RNA-seq expression measurements, CIFAR10, Fashion-MNIST and mini-ImageNet, establish that all algorithms provably converge and have complexity comparable to those of their Euclidean counterparts. Accompanying codes can be found at: https://github.com/thupchnsky/PoincareLinearClassification.

Eli Chien, Chao Pan, Olgica Milenkovic

Graph-structured data is ubiquitous in practice and often processed using graph neural networks (GNNs). With the adoption of recent laws ensuring the ``right to be forgotten'', the problem of graph data removal has become of significant importance. To address the problem, we introduce the first known framework for \emph{certified graph unlearning} of GNNs. In contrast to standard machine unlearning, new analytical and heuristic unlearning challenges arise when dealing with complex graph data. First, three different types of unlearning requests need to be considered, including node feature, edge and node unlearning. Second, to establish provable performance guarantees, one needs to address challenges associated with feature mixing during propagation. The underlying analysis is illustrated on the example of simple graph convolutions (SGC) and their generalized PageRank (GPR) extensions, thereby laying the theoretical foundation for certified unlearning of GNNs. Our empirical studies on six benchmark datasets demonstrate excellent performance-complexity trade-offs when compared to complete retraining methods and approaches that do not leverage graph information. For example, when unlearning $20\%$ of the nodes on the Cora dataset, our approach suffers only a $0.1\%$ loss in test accuracy while offering a $4$-fold speed-up compared to complete retraining. Our scheme also outperforms unlearning methods that do not leverage graph information with a $12\%$ increase in test accuracy for a comparable time complexity.

Eli Chien, Wei-Ning Chen, Chao Pan et al.

GNNs can inadvertently expose sensitive user information and interactions through their model predictions. To address these privacy concerns, Differential Privacy (DP) protocols are employed to control the trade-off between provable privacy protection and model utility. Applying standard DP approaches to GNNs directly is not advisable due to two main reasons. First, the prediction of node labels, which relies on neighboring node attributes through graph convolutions, can lead to privacy leakage. Second, in practical applications, the privacy requirements for node attributes and graph topology may differ. In the latter setting, existing DP-GNN models fail to provide multigranular trade-offs between graph topology privacy, node attribute privacy, and GNN utility. To address both limitations, we propose a new framework termed Graph Differential Privacy (GDP), specifically tailored to graph learning. GDP ensures both provably private model parameters as well as private predictions. Additionally, we describe a novel unified notion of graph dataset adjacency to analyze the properties of GDP for different levels of graph topology privacy. Our findings reveal that DP-GNNs, which rely on graph convolutions, not only fail to meet the requirements for multigranular graph topology privacy but also necessitate the injection of DP noise that scales at least linearly with the maximum node degree. In contrast, our proposed Differentially Private Decoupled Graph Convolutions (DPDGCs) represent a more flexible and efficient alternative to graph convolutions that still provides the necessary guarantees of GDP. To validate our approach, we conducted extensive experiments on seven node classification benchmarking and illustrative synthetic datasets. The results demonstrate that DPDGCs significantly outperform existing DP-GNNs in terms of privacy-utility trade-offs.

Saurav Prakash, Jin Sima, Chao Pan et al.

Hierarchical and tree-like data sets arise in many applications, including language processing, graph data mining, phylogeny and genomics. It is known that tree-like data cannot be embedded into Euclidean spaces of finite dimension with small distortion. This problem can be mitigated through the use of hyperbolic spaces. When such data also has to be processed in a distributed and privatized setting, it becomes necessary to work with new federated learning methods tailored to hyperbolic spaces. As an initial step towards the development of the field of federated learning in hyperbolic spaces, we propose the first known approach to federated classification in hyperbolic spaces. Our contributions are as follows. First, we develop distributed versions of convex SVM classifiers for Poincaré discs. In this setting, the information conveyed from clients to the global classifier are convex hulls of clusters present in individual client data. Second, to avoid label switching issues, we introduce a number-theoretic approach for label recovery based on the so-called integer $B_h$ sequences. Third, we compute the complexity of the convex hulls in hyperbolic spaces to assess the extent of data leakage; at the same time, in order to limit communication cost for the hulls, we propose a new quantization method for the Poincaré disc coupled with Reed-Solomon-like encoding. Fourth, at the server level, we introduce a new approach for aggregating convex hulls of the clients based on balanced graph partitioning. We test our method on a collection of diverse data sets, including hierarchical single-cell RNA-seq data from different patients distributed across different repositories that have stringent privacy constraints. The classification accuracy of our method is up to $\sim 11\%$ better than its Euclidean counterpart, demonstrating the importance of privacy-preserving learning in hyperbolic spaces.

Chao Pan, Chuanyi Zhang

As a general type of machine learning approach, artificial neural networks have established state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various kinds of neural networks architectures, polynomial neural networks (PNNs) have been recently shown to be analyzable by spectrum analysis via neural tangent kernel, and particularly effective at image generation and face recognition. However, acquiring theoretical insight into the computation and sample complexity of PNNs remains an open problem. In this paper, we extend the analysis in previous literature to PNNs and obtain novel results on sample complexity of PNNs, which provides some insights in explaining the generalization ability of PNNs.

Peizhi Niu, Chao Pan, Siheng Chen et al.

Graph neural networks (GNNs) have become instrumental in diverse real-world applications, offering powerful graph learning capabilities for tasks such as social networks and medical data analysis. Despite their successes, GNNs are vulnerable to adversarial attacks, including membership inference attacks (MIA), which threaten privacy by identifying whether a record was part of the model's training data. While existing research has explored MIA in GNNs under graph inductive learning settings, the more common and challenging graph transductive learning setting remains understudied in this context. This paper addresses this gap and proposes an effective two-stage defense, Graph Transductive Defense (GTD), tailored to graph transductive learning characteristics. The gist of our approach is a combination of a train-test alternate training schedule and flattening strategy, which successfully reduces the difference between the training and testing loss distributions. Extensive empirical results demonstrate the superior performance of our method (a decrease in attack AUROC by $9.42\%$ and an increase in utility performance by $18.08\%$ on average compared to LBP), highlighting its potential for seamless integration into various classification models with minimal overhead.

Eli Chien, Chao Pan, Jianhao Peng et al.

Hypergraphs are used to model higher-order interactions amongst agents and there exist many practically relevant instances of hypergraph datasets. To enable efficient processing of hypergraph-structured data, several hypergraph neural network platforms have been proposed for learning hypergraph properties and structure, with a special focus on node classification. However, almost all existing methods use heuristic propagation rules and offer suboptimal performance on many datasets. We propose AllSet, a new hypergraph neural network paradigm that represents a highly general framework for (hyper)graph neural networks and for the first time implements hypergraph neural network layers as compositions of two multiset functions that can be efficiently learned for each task and each dataset. Furthermore, AllSet draws on new connections between hypergraph neural networks and recent advances in deep learning of multiset functions. In particular, the proposed architecture utilizes Deep Sets and Set Transformer architectures that allow for significant modeling flexibility and offer high expressive power. To evaluate the performance of AllSet, we conduct the most extensive experiments to date involving ten known benchmarking datasets and three newly curated datasets that represent significant challenges for hypergraph node classification. The results demonstrate that AllSet has the unique ability to consistently either match or outperform all other hypergraph neural networks across the tested datasets.

Puoya Tabaghi, Chao Pan, Eli Chien et al.

Embedding methods for product spaces are powerful techniques for low-distortion and low-dimensional representation of complex data structures. Here, we address the new problem of linear classification in product space forms -- products of Euclidean, spherical, and hyperbolic spaces. First, we describe novel formulations for linear classifiers on a Riemannian manifold using geodesics and Riemannian metrics which generalize straight lines and inner products in vector spaces. Second, we prove that linear classifiers in $d$-dimensional space forms of any curvature have the same expressive power, i.e., they can shatter exactly $d+1$ points. Third, we formalize linear classifiers in product space forms, describe the first known perceptron and support vector machine classifiers for such spaces and establish rigorous convergence results for perceptrons. Moreover, we prove that the Vapnik-Chervonenkis dimension of linear classifiers in a product space form of dimension $d$ is \emph{at least} $d+1$. We support our theoretical findings with simulations on several datasets, including synthetic data, image data, and single-cell RNA sequencing (scRNA-seq) data. The results show that classification in low-dimensional product space forms for scRNA-seq data offers, on average, a performance improvement of $\sim15\%$ when compared to that in Euclidean spaces of the same dimension.

Chao Pan, Siheng Chen, Antonio Ortega

Although spatio-temporal graph neural networks have achieved great empirical success in handling multiple correlated time series, they may be impractical in some real-world scenarios due to a lack of sufficient high-quality training data. Furthermore, spatio-temporal graph neural networks lack theoretical interpretation. To address these issues, we put forth a novel mathematically designed framework to analyze spatio-temporal data. Our proposed spatio-temporal graph scattering transform (ST-GST) extends traditional scattering transforms to the spatio-temporal domain. It performs iterative applications of spatio-temporal graph wavelets and nonlinear activation functions, which can be viewed as a forward pass of spatio-temporal graph convolutional networks without training. Since all the filter coefficients in ST-GST are mathematically designed, it is promising for the real-world scenarios with limited training data, and also allows for a theoretical analysis, which shows that the proposed ST-GST is stable to small perturbations of input signals and structures. Finally, our experiments show that i) ST-GST outperforms spatio-temporal graph convolutional networks by an increase of 35% in accuracy for MSR Action3D dataset; ii) it is better and computationally more efficient to design the transform based on separable spatio-temporal graphs than the joint ones; and iii) the nonlinearity in ST-GST is critical to empirical performance.

Chao Pan, S. M. Hossein Tabatabaei Yazdi, S Kasra Tabatabaei et al.

The main obstacles for the practical deployment of DNA-based data storage platforms are the prohibitively high cost of synthetic DNA and the large number of errors introduced during synthesis. In particular, synthetic DNA products contain both individual oligo (fragment) symbol errors as well as missing DNA oligo errors, with rates that exceed those of modern storage systems by orders of magnitude. These errors can be corrected either through the use of a large number of redundant oligos or through cycles of writing, reading, and rewriting of information that eliminate the errors. Both approaches add to the overall storage cost and are hence undesirable. Here we propose the first method for storing quantized images in DNA that uses signal processing and machine learning techniques to deal with error and cost issues without resorting to the use of redundant oligos or rewriting. Our methods rely on decoupling the RGB channels of images, performing specialized quantization and compression on the individual color channels, and using new discoloration detection and image inpainting techniques. We demonstrate the performance of our approach experimentally on a collection of movie posters stored in DNA.

I Chien, Chao Pan, Olgica Milenkovic

We consider the problem of approximate $K$-means clustering with outliers and side information provided by same-cluster queries and possibly noisy answers. Our solution shows that, under some mild assumptions on the smallest cluster size, one can obtain an $(1+ε)$-approximation for the optimal potential with probability at least $1-δ$, where $ε>0$ and $δ\in(0,1)$, using an expected number of $O(\frac{K^3}{εδ})$ noiseless same-cluster queries and comparison-based clustering of complexity $O(ndK + \frac{K^3}{εδ})$, here, $n$ denotes the number of points and $d$ the dimension of space. Compared to a handful of other known approaches that perform importance sampling to account for small cluster sizes, the proposed query technique reduces the number of queries by a factor of roughly $O(\frac{K^6}{ε^3})$, at the cost of possibly missing very small clusters. We extend this settings to the case where some queries to the oracle produce erroneous information, and where certain points, termed outliers, do not belong to any clusters. Our proof techniques differ from previous methods used for $K$-means clustering analysis, as they rely on estimating the sizes of the clusters and the number of points needed for accurate centroid estimation and subsequent nontrivial generalizations of the double Dixie cup problem. We illustrate the performance of the proposed algorithm both on synthetic and real datasets, including MNIST and CIFAR $10$.