arXiv subjects

Shaojie Tang

Publications and source records attributed to Shaojie Tang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Efficient Over-parameterized Matrix Sensing from Noisy Measurements via Alternating Preconditioned Gradient Descent

We consider the noisy matrix sensing problem in the over-parameterization setting, where the estimated rank $r$ is larger than the true rank $r_\star$ of the target matrix $X_\star$. Specifically, our main objective is to recover a matrix $ X_\star \in \mathbb{R}^{n_1 \times n_2} $ with rank $ r_\star $ from noisy measurements using an over-parameterized factorization $ LR^\top $, where $ L \in \mathbb{R}^{n_1 \times r}, \, R \in \mathbb{R}^{n_2 \times r} $ and $ \min\{n_1, n_2\} \ge r > r_\star $, with $ r_\star $ being unknown. Recently, preconditioning methods have been proposed to accelerate the convergence of matrix sensing problem compared to vanilla gradient descent, incorporating preconditioning terms $ (L^\top L + λI)^{-1} $ and $ (R^\top R + λI)^{-1} $ into the original gradient. However, these methods require careful tuning of the damping parameter $λ$ and are sensitive to step size. To address these limitations, we propose the alternating preconditioned gradient descent (APGD) algorithm, which alternately updates the two factor matrices, eliminating the need for the damping parameter $λ$ and enabling faster convergence with larger step sizes. We theoretically prove that APGD convergences to a near-optimal error at a linear rate. We further show that APGD can be extended to deal with other low-rank matrix estimation tasks, also with a theoretical guarantee of linear convergence. To validate the effectiveness and scalability of the proposed APGD, we conduct simulated and real-world experiments on a wide range of low-rank estimation problems, including noisy matrix sensing, weighted PCA, 1-bit matrix completion, and matrix completion. The extensive results demonstrate that APGD consistently achieves the fastest convergence and the lowest computation time compared to the existing alternatives.

cs.LG↗

arXiv2025

DualFed: Enjoying both Generalization and Personalization in Federated Learning via Hierachical Representations

In personalized federated learning (PFL), it is widely recognized that achieving both high model generalization and effective personalization poses a significant challenge due to their conflicting nature. As a result, existing PFL methods can only manage a trade-off between these two objectives. This raises an interesting question: Is it feasible to develop a model capable of achieving both objectives simultaneously? Our paper presents an affirmative answer, and the key lies in the observation that deep models inherently exhibit hierarchical architectures, which produce representations with various levels of generalization and personalization at different stages. A straightforward approach stemming from this observation is to select multiple representations from these layers and combine them to concurrently achieve generalization and personalization. However, the number of candidate representations is commonly huge, which makes this method infeasible due to high computational costs.To address this problem, we propose DualFed, a new method that can directly yield dual representations correspond to generalization and personalization respectively, thereby simplifying the optimization task. Specifically, DualFed inserts a personalized projection network between the encoder and classifier. The pre-projection representations are able to capture generalized information shareable across clients, and the post-projection representations are effective to capture task-specific information on local clients. This design minimizes the mutual interference between generalization and personalization, thereby achieving a win-win situation. Extensive experiments show that DualFed can outperform other FL methods. Code is available at https://github.com/GuogangZhu/DualFed.

cs.LG↗

arXiv2025

A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper a generalized linear tensor bandits algorithm designed to tackle these challenges by incorporating low-dimensional tensor structures, and further derive a unified analytical framework of the proposed algorithm. Specifically, our framework introduces a convex optimization approach with the weakly decomposable regularizers, enabling it to not only achieve better results based on the tensor low-rankness structure assumption but also extend to cases involving other low-dimensional structures such as slice sparsity and low-rankness. The theoretical analysis shows that, compared to existing low-rankness tensor result, our framework not only provides better bounds but also has a broader applicability. Notably, in the special case of degenerating to low-rank matrices, our bounds still offer advantages in certain scenarios.

cs.LG↗

arXiv2024

The Power of Adaptation: Boosting In-Context Learning through Adaptive Prompting

Large Language Models (LLMs) have demonstrated exceptional abilities across a broad range of language-related tasks, including generating solutions to complex reasoning problems. An effective technique to enhance LLM performance is in-context learning, which encourages a step-by-step reasoning process by including explanatory examples to guide the model's responses. However, selecting appropriate exemplars for the model poses a challenge, as each dataset demands a distinct set of exemplars to enable the LLM to learn effectively and perform well on the test set. Current studies often rely on uncertainty- or diversity-based selection strategies to select exemplars for annotation and to improve model learning. However, these studies typically employ a non-adaptive approach, selecting a set of exemplars all at once. We argue that this non-adaptive strategy may result in a set of exemplars with high redundancy in terms of the knowledge covered, ultimately reducing their overall informativeness. To address this limitation, we propose \textsc{Adaptive-Prompt}, a novel method that adaptively selects exemplars by leveraging model feedback from previously chosen exemplars. Experimental results show that \textsc{Adaptive-Prompt} significantly enhances LLM performance across a variety of reasoning tasks.

cs.CL↗

arXiv2024

Why Go Full? Elevating Federated Learning Through Partial Network Updates

Federated learning is a distributed machine learning paradigm designed to protect user data privacy, which has been successfully implemented across various scenarios. In traditional federated learning, the entire parameter set of local models is updated and averaged in each training round. Although this full network update method maximizes knowledge acquisition and sharing for each model layer, it prevents the layers of the global model from cooperating effectively to complete the tasks of each client, a challenge we refer to as layer mismatch. This mismatch problem recurs after every parameter averaging, consequently slowing down model convergence and degrading overall performance. To address the layer mismatch issue, we introduce the FedPart method, which restricts model updates to either a single layer or a few layers during each communication round. Furthermore, to maintain the efficiency of knowledge acquisition and sharing, we develop several strategies to select trainable layers in each round, including sequential updating and multi-round cycle training. Through both theoretical analysis and experiments, our findings demonstrate that the FedPart method significantly surpasses conventional full network update strategies in terms of convergence speed and accuracy, while also reducing communication and computational overheads.

cs.LG↗

arXiv2024

Shall We Team Up: Exploring Spontaneous Cooperation of Competing LLM Agents

Large Language Models (LLMs) have increasingly been utilized in social simulations, where they are often guided by carefully crafted instructions to stably exhibit human-like behaviors during simulations. Nevertheless, we doubt the necessity of shaping agents' behaviors for accurate social simulations. Instead, this paper emphasizes the importance of spontaneous phenomena, wherein agents deeply engage in contexts and make adaptive decisions without explicit directions. We explored spontaneous cooperation across three competitive scenarios and successfully simulated the gradual emergence of cooperation, findings that align closely with human behavioral data. This approach not only aids the computational social science community in bridging the gap between simulations and real-world dynamics but also offers the AI community a novel method to assess LLMs' capability of deliberate reasoning.

cs.AI↗

arXiv2024

Decoupling General and Personalized Knowledge in Federated Learning via Additive and Low-Rank Decomposition

To address data heterogeneity, the key strategy of Personalized Federated Learning (PFL) is to decouple general knowledge (shared among clients) and client-specific knowledge, as the latter can have a negative impact on collaboration if not removed. Existing PFL methods primarily adopt a parameter partitioning approach, where the parameters of a model are designated as one of two types: parameters shared with other clients to extract general knowledge and parameters retained locally to learn client-specific knowledge. However, as these two types of parameters are put together like a jigsaw puzzle into a single model during the training process, each parameter may simultaneously absorb both general and client-specific knowledge, thus struggling to separate the two types of knowledge effectively. In this paper, we introduce FedDecomp, a simple but effective PFL paradigm that employs parameter additive decomposition to address this issue. Instead of assigning each parameter of a model as either a shared or personalized one, FedDecomp decomposes each parameter into the sum of two parameters: a shared one and a personalized one, thus achieving a more thorough decoupling of shared and personalized knowledge compared to the parameter partitioning method. In addition, as we find that retaining local knowledge of specific clients requires much lower model capacity compared with general knowledge across all clients, we let the matrix containing personalized parameters be low rank during the training process. Moreover, a new alternating training strategy is proposed to further improve the performance. Experimental results across multiple datasets and varying degrees of data heterogeneity demonstrate that FedDecomp outperforms state-of-the-art methods up to 4.9\%. The code is available at https://github.com/XinghaoWu/FedDecomp.

cs.LG↗

arXiv2024

Learning Submodular Sequencing from Samples

This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility function, we assume that we are given only a set of samples. Each sample includes a random sequence of items and its associated utility. We present an algorithm that, given polynomially many samples drawn from a two-stage uniform distribution, achieves an approximation ratio dependent on the curvature of individual submodular functions. Our results apply in a wide variety of real-world scenarios, such as ranking products in online retail platforms, where complete knowledge of the utility function is often impossible to obtain. Our algorithm gives an empirically useful solution in such contexts, thus proving that limited data can be of great use in sequencing tasks. From a technical perspective, our results extend prior work on ``optimization from samples'' by generalizing from optimizing a set function to a sequence-dependent function.

cs.LG↗

arXiv2024

The Power of Second Chance: Personalized Submodular Maximization with Two Candidates

Most of existing studies on submodular maximization focus on selecting a subset of items that maximizes a \emph{single} submodular function. However, in many real-world scenarios, we might have multiple user-specific functions, each of which models the utility of a particular type of user. In these settings, our goal would be to choose a set of items that performs well across all the user-specific functions. One way to tackle this problem is to select a single subset that maximizes the sum of all of the user-specific functions. Although this aggregate approach is efficient in the sense that it avoids computation of sets for individual functions, it really misses the power of personalization - for it does not allow to choose different sets for different functions. In this paper, we introduce the problem of personalized submodular maximization with two candidate solutions. For any two candidate solutions, the utility of each user-specific function is defined as the better of these two candidates. Our objective is, therefore, to select the best set of two candidates that maximize the sum of utilities of all the user-specific functions. We have designed effective algorithms for this problem. We also discuss how our approach generalizes to multiple candidate solutions, increasing flexibility and personalization in our solution.

cs.LG↗

arXiv2024

A Constant-Approximation Algorithm for Budgeted Sweep Coverage with Mobile Sensors

In this paper, we present the first constant-approximation algorithm for {\em budgeted sweep coverage problem} (BSC). The BSC involves designing routes for a number of mobile sensors (a.k.a. robots) to periodically collect information as much as possible from points of interest (PoIs). To approach this problem, we propose to first examine the {\em multi-orienteering problem} (MOP). The MOP aims to find a set of $m$ vertex-disjoint paths that cover as many vertices as possible while adhering to a budget constraint $B$. We develop a constant-approximation algorithm for MOP and utilize it to achieve a constant-approximation for BSC. Our findings open new possibilities for optimizing mobile sensor deployments and related combinatorial optimization tasks.

cs.DM↗

arXiv2024

The Diversity Bonus: Learning from Dissimilar Distributed Clients in Personalized Federated Learning

Personalized Federated Learning (PFL) is a commonly used framework that allows clients to collaboratively train their personalized models. PFL is particularly useful for handling situations where data from different clients are not independent and identically distributed (non-IID). Previous research in PFL implicitly assumes that clients can gain more benefits from those with similar data distributions. Correspondingly, methods such as personalized weight aggregation are developed to assign higher weights to similar clients during training. We pose a question: can a client benefit from other clients with dissimilar data distributions and if so, how? This question is particularly relevant in scenarios with a high degree of non-IID, where clients have widely different data distributions, and learning from only similar clients will lose knowledge from many other clients. We note that when dealing with clients with similar data distributions, methods such as personalized weight aggregation tend to enforce their models to be close in the parameter space. It is reasonable to conjecture that a client can benefit from dissimilar clients if we allow their models to depart from each other. Based on this idea, we propose DiversiFed which allows each client to learn from clients with diversified data distribution in personalized federated learning. DiversiFed pushes personalized models of clients with dissimilar data distributions apart in the parameter space while pulling together those with similar distributions. In addition, to achieve the above effect without using prior knowledge of data distribution, we design a loss function that leverages the model similarity to determine the degree of attraction and repulsion between any two models. Experiments on several datasets show that DiversiFed can benefit from dissimilar clients and thus outperform the state-of-the-art methods.

cs.LG↗

arXiv2024

Submodular Participatory Budgeting

Participatory budgeting refers to the practice of allocating public resources by collecting and aggregating individual preferences. Most existing studies in this field often assume an additive utility function, where each individual holds a private utility for each candidate project, and the total utility of a set of funded projects is simply the sum of the utilities of all projects. We argue that this assumption does not always hold in reality. For example, building two playgrounds in the same neighborhood does not necessarily lead to twice the utility of building a single playground. To address this, we extend the existing study by proposing a submodular participatory budgeting problem, assuming that the utility function of each individual is a monotone and submodular function over funded projects. We propose and examine three preference elicitation methods, including \emph{ranking-by-marginal-values}, \emph{ranking-by-values} and \emph{threshold approval votes}, and analyze their performances in terms of distortion. Notably, if the utility function is addicative, our aggregation rule designed for threshold approval votes achieves a better distortion than the state-of-the-art approach.

cs.GT↗

arXiv2024

Estimating before Debiasing: A Bayesian Approach to Detaching Prior Bias in Federated Semi-Supervised Learning

Federated Semi-Supervised Learning (FSSL) leverages both labeled and unlabeled data on clients to collaboratively train a model.In FSSL, the heterogeneous data can introduce prediction bias into the model, causing the model's prediction to skew towards some certain classes. Existing FSSL methods primarily tackle this issue by enhancing consistency in model parameters or outputs. However, as the models themselves are biased, merely constraining their consistency is not sufficient to alleviate prediction bias. In this paper, we explore this bias from a Bayesian perspective and demonstrate that it principally originates from label prior bias within the training data. Building upon this insight, we propose a debiasing method for FSSL named FedDB. FedDB utilizes the Average Prediction Probability of Unlabeled Data (APP-U) to approximate the biased prior.During local training, FedDB employs APP-U to refine pseudo-labeling through Bayes' theorem, thereby significantly reducing the label prior bias. Concurrently, during the model aggregation, FedDB uses APP-U from participating clients to formulate unbiased aggregate weights, thereby effectively diminishing bias in the global model. Experimental results show that FedDB can surpass existing FSSL methods. The code is available at https://github.com/GuogangZhu/FedDB.

cs.LG↗

arXiv2024

Point cloud-based registration and image fusion between cardiac SPECT MPI and CTA

A method was proposed for the point cloud-based registration and image fusion between cardiac single photon emission computed tomography (SPECT) myocardial perfusion images (MPI) and cardiac computed tomography angiograms (CTA). Firstly, the left ventricle (LV) epicardial regions (LVERs) in SPECT and CTA images were segmented by using different U-Net neural networks trained to generate the point clouds of the LV epicardial contours (LVECs). Secondly, according to the characteristics of cardiac anatomy, the special points of anterior and posterior interventricular grooves (APIGs) were manually marked in both SPECT and CTA image volumes. Thirdly, we developed an in-house program for coarsely registering the special points of APIGs to ensure a correct cardiac orientation alignment between SPECT and CTA images. Fourthly, we employed ICP, SICP or CPD algorithm to achieve a fine registration for the point clouds (together with the special points of APIGs) of the LV epicardial surfaces (LVERs) in SPECT and CTA images. Finally, the image fusion between SPECT and CTA was realized after the fine registration. The experimental results showed that the cardiac orientation was aligned well and the mean distance error of the optimal registration method (CPD with affine transform) was consistently less than 3 mm. The proposed method could effectively fuse the structures from cardiac CTA and SPECT functional images, and demonstrated a potential in assisting in accurate diagnosis of cardiac diseases by combining complementary advantages of the two imaging modalities.

eess.IV↗

arXiv2024

Efficient Generalized Low-Rank Tensor Contextual Bandits

In this paper, we aim to build a novel bandits algorithm that is capable of fully harnessing the power of multi-dimensional data and the inherent non-linearity of reward functions to provide high-usable and accountable decision-making services. To this end, we introduce a generalized low-rank tensor contextual bandits model in which an action is formed from three feature vectors, and thus can be represented by a tensor. In this formulation, the reward is determined through a generalized linear function applied to the inner product of the action's feature tensor and a fixed but unknown parameter tensor with a low tubal rank. To effectively achieve the trade-off between exploration and exploitation, we introduce a novel algorithm called "Generalized Low-Rank Tensor Exploration Subspace then Refine" (G-LowTESTR). This algorithm first collects raw data to explore the intrinsic low-rank tensor subspace information embedded in the decision-making scenario, and then converts the original problem into an almost lower-dimensional generalized linear contextual bandits problem. Rigorous theoretical analysis shows that the regret bound of G-LowTESTR is superior to those in vectorization and matricization cases. We conduct a series of simulations and real data experiments to further highlight the effectiveness of G-LowTESTR, leveraging its ability to capitalize on the low-rank tensor structure for enhanced learning.

cs.LG↗

arXiv2023

Non-monotone Sequential Submodular Maximization

In this paper, we study a fundamental problem in submodular optimization, which is called sequential submodular maximization. Specifically, we aim to select and rank a group of $k$ items from a ground set $V$ such that the weighted summation of $k$ (possibly non-monotone) submodular functions $f_1, \cdots ,f_k: 2^V \rightarrow \mathbb{R}^+$ is maximized, here each function $f_j$ takes the first $j$ items from this sequence as input. The existing research on sequential submodular maximization has predominantly concentrated on the monotone setting, assuming that the submodular functions are non-decreasing. However, in various real-world scenarios, like diversity-aware recommendation systems, adding items to an existing set might negatively impact the overall utility. In response, this paper pioneers the examination of the aforementioned problem with non-monotone submodular functions and offers effective solutions for both flexible and fixed length constraints, as well as a special case with identical utility functions. The empirical evaluations further validate the effectiveness of our proposed algorithms in the domain of video recommendations. The results of this research have implications in various fields, including recommendation systems and assortment optimization, where the ordering of items significantly impacts the overall value obtained.

cs.LG↗

arXiv2023

Data Summarization beyond Monotonicity: Non-monotone Two-Stage Submodular Maximization

The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set yields results comparable to those obtained over the original ground set. This problem has applications in various domains including data summarization. Existing studies often assume the monotonicity of the objective function, whereas our work pioneers the extension of this research to accommodate non-monotone submodular functions. We have introduced the first constant-factor approximation algorithms for this more general case.

cs.DS↗

arXiv2023

Approximation Algorithm for Unrooted Prize-Collecting Forest with Multiple Components and Its Application on Prize-Collecting Sweep Coverage

In this paper, we introduce a polynomial-time 2-approximation algorithm for the Unrooted Prize-Collecting Forest with $K$ Components (URPCF$_K$) problem. URPCF$_K$ aims to find a forest with exactly $K$ connected components while minimizing both the forest's weight and the penalties incurred by unspanned vertices. Unlike the rooted version RPCF$_K$, where a 2-approximation algorithm exists, solving the unrooted version by guessing roots leads to exponential time complexity for non-constant $K$. To address this challenge, we propose a rootless growing and rootless pruning algorithm. We also apply this algorithm to improve the approximation ratio for the Prize-Collecting Min-Sensor Sweep Cover problem (PCMinSSC) from 8 to 5. Keywords: approximation algorithm, prize-collecting Steiner forest, sweep cover.

cs.DS↗