Low-Rank Graph Contrastive Learning for Node Classification

Graph Neural Networks (GNNs) have been widely used to learn node representations and with outstanding performance on various tasks such as node classification. However, noise, which inevitably exists in real-world graph data, would considerably degrade the performance of GNNs revealed by recent studies. In this work, we propose a novel and robust GNN encoder, Low-Rank Graph Contrastive Learning (LR-GCL). Our method performs transductive node classification in two steps. First, a low-rank GCL encoder named LR-GCL is trained by prototypical contrastive learning with low-rank regularization. Next, using the features produced by LR-GCL, a linear transductive classification algorithm is used to classify the unlabeled nodes in the graph. Our LR-GCL is inspired by the low frequency property of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. To the best of our knowledge, our theoretical result is among the first to theoretically demonstrate the advantage of low-rank learning in graph contrastive learning supported by strong empirical performance. Extensive experiments on public benchmarks demonstrate the superior performance of LR-GCL and the robustness of the learned node representations. The code of LR-GCL is available at \url{https://anonymous.4open.science/r/Low-Rank_Graph_Contrastive_Learning-64A6/}.

A Learning-based Declarative Privacy-Preserving Framework for Federated Data Management

It is challenging to balance the privacy and accuracy for federated query processing over multiple private data silos. In this work, we will demonstrate an end-to-end workflow for automating an emerging privacy-preserving technique that uses a deep learning model trained using the Differentially-Private Stochastic Gradient Descent (DP-SGD) algorithm to replace portions of actual data to answer a query. Our proposed novel declarative privacy-preserving workflow allows users to specify "what private information to protect" rather than "how to protect". Under the hood, the system automatically chooses query-model transformation plans as well as hyper-parameters. At the same time, the proposed workflow also allows human experts to review and tune the selected privacy-preserving mechanism for audit/compliance, and optimization purposes.

Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guarantees

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for Regularized Optimization (SRO). Our SRO algorithm first generates a sketch of the original data matrix, then solves the sketched problem. Different from existing randomized algorithms, our algorithm handles general Frechet subdifferentiable regularization functions in an unified framework. We present general theoretical result for the approximation error between the optimization results of the original problem and the sketched problem for regularized least square problems which can be convex or nonconvex. For arbitrary convex regularizer, relative-error bound is proved for the approximation error. Importantly, minimax rates for sparse signal estimation by solving the sketched sparse convex or nonconvex learning problems are also obtained using our general theoretical result under mild conditions. To the best of our knowledge, our results are among the first to demonstrate minimax rates for convex or nonconvex sparse learning problem by sketching under a unified theoretical framework. We further propose an iterative sketching algorithm which reduces the approximation error exponentially by iteratively invoking the sketching algorithm. Experimental results demonstrate the effectiveness of the proposed SRO and Iterative SRO algorithms.

Sharp Generalization of Transductive Learning: A Transductive Local Rademacher Complexity Approach

We introduce a new tool, Transductive Local Rademacher Complexity (TLRC), to analyze the generalization performance of transductive learning methods and motivate new transductive learning algorithms. Our work extends the idea of the popular Local Rademacher Complexity (LRC) to the transductive setting with considerable changes compared to the analysis of typical LRC methods in the inductive setting. We present a localized version of Rademacher complexity based tool wihch can be applied to various transductive learning problems and gain sharp bounds under proper conditions. Similar to the development of LRC, we build TLRC by starting from a sharp concentration inequality for independent variables with variance information. The prediction function class of a transductive learning model is then divided into pieces with a sub-root function being the upper bound for the Rademacher complexity of each piece, and the variance of all the functions in each piece is limited. A carefully designed variance operator is used to ensure that the bound for the test loss on unlabeled test data in the transductive setting enjoys a remarkable similarity to that of the classical LRC bound in the inductive setting. We use the new TLRC tool to analyze the Transductive Kernel Learning (TKL) model, where the labels of test data are generated by a kernel function. The result of TKL lays the foundation for generalization bounds for two types of transductive learning tasks, Graph Transductive Learning (GTL) and Transductive Nonparametric Kernel Regression (TNKR). When the target function is low-dimensional or approximately low-dimensional, we design low rank methods for both GTL and TNKR, which enjoy particularly sharper generalization bounds by TLRC which cannot be achieved by existing learning theory methods, to the best of our knowledge.

RecMind: Large Language Model Powered Agent For Recommendation

Recent advancements in instructing Large Language Models (LLMs) to utilize external tools and execute multi-step plans have significantly enhanced their ability to solve intricate tasks, ranging from mathematical problems to creative writing. Yet, there remains a notable gap in studying the capacity of LLMs in responding to personalized queries such as a recommendation request. To bridge this gap, we have designed an LLM-powered autonomous recommender agent, RecMind, which is capable of providing precise personalized recommendations through careful planning, utilizing tools for obtaining external knowledge, and leveraging individual data. We propose a novel algorithm, Self-Inspiring, to improve the planning ability of the LLM agent. At each intermediate planning step, the LLM 'self-inspires' to consider all previously explored states to plan for next step. This mechanism greatly improves the model's ability to comprehend and utilize historical planning information for recommendation. We evaluate RecMind's performance in various recommendation scenarios, including rating prediction, sequential recommendation, direct recommendation, explanation generation, and review summarization. Our experiment shows that RecMind outperforms existing zero/few-shot LLM-based recommendation methods in different recommendation tasks and achieves competitive performance to a recent model P5, which requires fully pre-train for the recommendation tasks.

Projective Proximal Gradient Descent for A Class of Nonconvex Nonsmooth Optimization Problems: Fast Convergence Without Kurdyka-Lojasiewicz (KL) Property

Nonconvex and nonsmooth optimization problems are important and challenging for statistics and machine learning. In this paper, we propose Projected Proximal Gradient Descent (PPGD) which solves a class of nonconvex and nonsmooth optimization problems, where the nonconvexity and nonsmoothness come from a nonsmooth regularization term which is nonconvex but piecewise convex. In contrast with existing convergence analysis of accelerated PGD methods for nonconvex and nonsmooth problems based on the Kurdyka-\L{}ojasiewicz (K\L{}) property, we provide a new theoretical analysis showing local fast convergence of PPGD. It is proved that PPGD achieves a fast convergence rate of $\cO(1/k^2)$ when the iteration number $k \ge k_0$ for a finite $k_0$ on a class of nonconvex and nonsmooth problems under mild assumptions, which is locally Nesterov's optimal convergence rate of first-order methods on smooth and convex objective function with Lipschitz continuous gradient. Experimental results demonstrate the effectiveness of PPGD.

RNAS-CL: Robust Neural Architecture Search by Cross-Layer Knowledge Distillation

Deep Neural Networks are vulnerable to adversarial attacks. Neural Architecture Search (NAS), one of the driving tools of deep neural networks, demonstrates superior performance in prediction accuracy in various machine learning applications. However, it is unclear how it performs against adversarial attacks. Given the presence of a robust teacher, it would be interesting to investigate if NAS would produce robust neural architecture by inheriting robustness from the teacher. In this paper, we propose Robust Neural Architecture Search by Cross-Layer Knowledge Distillation (RNAS-CL), a novel NAS algorithm that improves the robustness of NAS by learning from a robust teacher through cross-layer knowledge distillation. Unlike previous knowledge distillation methods that encourage close student/teacher output only in the last layer, RNAS-CL automatically searches for the best teacher layer to supervise each student layer. Experimental result evidences the effectiveness of RNAS-CL and shows that RNAS-CL produces small and robust neural architecture.

Noisy $\ell^{0}$-Sparse Subspace Clustering on Dimensionality Reduced Data

Sparse subspace clustering methods with sparsity induced by $\ell^{0}$-norm, such as $\ell^{0}$-Sparse Subspace Clustering ($\ell^{0}$-SSC)~\citep{YangFJYH16-L0SSC-ijcv}, are demonstrated to be more effective than its $\ell^{1}$ counterpart such as Sparse Subspace Clustering (SSC)~\citep{ElhamifarV13}. However, the theoretical analysis of $\ell^{0}$-SSC is restricted to clean data that lie exactly in subspaces. Real data often suffer from noise and they may lie close to subspaces. In this paper, we show that an optimal solution to the optimization problem of noisy $\ell^{0}$-SSC achieves subspace detection property (SDP), a key element with which data from different subspaces are separated, under deterministic and semi-random model. Our results provide theoretical guarantee on the correctness of noisy $\ell^{0}$-SSC in terms of SDP on noisy data for the first time, which reveals the advantage of noisy $\ell^{0}$-SSC in terms of much less restrictive condition on subspace affinity. In order to improve the efficiency of noisy $\ell^{0}$-SSC, we propose Noisy-DR-$\ell^{0}$-SSC which provably recovers the subspaces on dimensionality reduced data. Noisy-DR-$\ell^{0}$-SSC first projects the data onto a lower dimensional space by random projection, then performs noisy $\ell^{0}$-SSC on the projected data for improved efficiency. Experimental results demonstrate the effectiveness of Noisy-DR-$\ell^{0}$-SSC.

Bayesian Robust Graph Contrastive Learning

Graph Neural Networks (GNNs) have been widely used to learn node representations and with outstanding performance on various tasks such as node classification. However, noise, which inevitably exists in real-world graph data, would considerably degrade the performance of GNNs as the noise is easily propagated via the graph structure. In this work, we propose a novel and robust method, Bayesian Robust Graph Contrastive Learning (BRGCL), which trains a GNN encoder to learn robust node representations. The BRGCL encoder is a completely unsupervised encoder. Two steps are iteratively executed at each epoch of training the BRGCL encoder: (1) estimating confident nodes and computing robust cluster prototypes of node representations through a novel Bayesian nonparametric method; (2) prototypical contrastive learning between the node representations and the robust cluster prototypes. Experiments on public and large-scale benchmarks demonstrate the superior performance of BRGCL and the robustness of the learned node representations. The code of BRGCL is available at \url{https://github.com/BRGCL-code/BRGCL-code}.