Xiangyu Chang

Zhihong Liu, Hoang Anh Just, Xiangyu Chang et al.

Data valuation -- quantifying the contribution of individual data sources to certain predictive behaviors of a model -- is of great importance to enhancing the transparency of machine learning and designing incentive systems for data sharing. Existing work has focused on evaluating data sources with the shared feature or sample space. How to valuate fragmented data sources of which each only contains partial features and samples remains an open question. We start by presenting a method to calculate the counterfactual of removing a fragment from the aggregated data matrix. Based on the counterfactual calculation, we further propose 2D-Shapley, a theoretical framework for fragmented data valuation that uniquely satisfies some appealing axioms in the fragmented data context. 2D-Shapley empowers a range of new use cases, such as selecting useful data fragments, providing interpretation for sample-wise data values, and fine-grained data issue diagnosis.

Xiangyu Chang, Xi Chen, Zehua Lai et al.

With the fast development of big data, learning the optimal decision rule by recursively updating it and making online decisions has been easier than before. We study the online statistical inference of model parameters in a contextual bandit framework of sequential decision-making. We propose a general framework for an online and adaptive data collection environment that can update decision rules via weighted stochastic gradient descent. We allow different weighting schemes of the stochastic gradient and establish the asymptotic normality of the parameter estimator. Our proposed estimator significantly improves the asymptotic efficiency over the previous averaged SGD approach via inverse probability weights. We also conduct an optimality analysis on the weights in a linear regression setting. We provide a Bahadur representation of the proposed estimator and show that the remainder term in the Bahadur representation entails a slower convergence rate compared to classical SGD due to the adaptive data collection.

Xuechen Zhang, Mingchen Li, Xiangyu Chang et al.

The growth and diversity of machine learning applications motivate a rethinking of learning with mobile and edge devices. How can we address diverse client goals and learn with scarce heterogeneous data? While federated learning aims to address these issues, it has challenges hindering a unified solution. Large transformer models have been shown to work across a variety of tasks achieving remarkable few-shot adaptation. This raises the question: Can clients use a single general-purpose model, rather than custom models for each task, while obeying device and network constraints? In this work, we investigate pretrained transformers (PTF) to achieve these on-device learning goals and thoroughly explore the roles of model size and modularity, where the latter refers to adaptation through modules such as prompts or adapters. Focusing on federated learning, we demonstrate that: (1) Larger scale shrinks the accuracy gaps between alternative approaches and improves heterogeneity robustness. Scale allows clients to run more local SGD epochs which can significantly reduce the number of communication rounds. At the extreme, clients can achieve respectable accuracy locally highlighting the potential of fully-local learning. (2) Modularity, by design, enables $>$100$\times$ less communication in bits. Surprisingly, it also boosts the generalization capability of local adaptation methods and the robustness of smaller PTFs. Finally, it enables clients to solve multiple unrelated tasks simultaneously using a single PTF, whereas full updates are prone to catastrophic forgetting. These insights on scale and modularity motivate a new federated learning approach we call "You Only Load Once" (FedYolo): The clients load a full PTF model once and all future updates are accomplished through communication-efficient modules with limited catastrophic-forgetting, where each task is assigned to its own module.

Shuai Liu, Xiao Guo, Shun Qi et al.

Identifying functional connectivity biomarkers of major depressive disorder (MDD) patients is essential to advance understanding of the disorder mechanisms and early intervention. However, due to the small sample size and the high dimension of available neuroimaging data, the performance of existing methods is often limited. Multi-site data could enhance the statistical power and sample size, while they are often subject to inter-site heterogeneity and data-sharing policies. In this paper, we propose a federated joint estimator, NOTEARS-PFL, for simultaneous learning of multiple Bayesian networks (BNs) with continuous optimization, to identify disease-induced alterations in MDD patients. We incorporate information shared between sites and site-specific information into the proposed federated learning framework to learn personalized BN structures by introducing the group fused lasso penalty. We develop the alternating direction method of multipliers, where in the local update step, the neuroimaging data is processed at each local site. Then the learned network structures are transmitted to the center for the global update. In particular, we derive a closed-form expression for the local update step and use the iterative proximal projection method to deal with the group fused lasso penalty in the global update step. We evaluate the performance of the proposed method on both synthetic and real-world multi-site rs-fMRI datasets. The results suggest that the proposed NOTEARS-PFL yields superior effectiveness and accuracy than the comparable methods.

Mengmeng Wu, Ruoxi Jia, Changle Lin et al.

Data valuation, especially quantifying data value in algorithmic prediction and decision-making, is a fundamental problem in data trading scenarios. The most widely used method is to define the data Shapley and approximate it by means of the permutation sampling algorithm. To make up for the large estimation variance of the permutation sampling that hinders the development of the data marketplace, we propose a more robust data valuation method using stratified sampling, named variance reduced data Shapley (VRDS for short). We theoretically show how to stratify, how many samples are taken at each stratum, and the sample complexity analysis of VRDS. Finally, the effectiveness of VRDS is illustrated in different types of datasets and data removal applications.

Shuai Liu, Yixuan Qiu, Baojuan Li et al.

Major depressive disorder (MDD) requires study of brain functional connectivity alterations for patients, which can be uncovered by resting-state functional magnetic resonance imaging (rs-fMRI) data. We consider the problem of identifying alterations of brain functional connectivity for a single MDD patient. This is particularly difficult since the amount of data collected during an fMRI scan is too limited to provide sufficient information for individual analysis. Additionally, rs-fMRI data usually has the characteristics of incompleteness, sparsity, variability, high dimensionality and high noise. To address these problems, we proposed a multitask Gaussian Bayesian network (MTGBN) framework capable for identifying individual disease-induced alterations for MDD patients. We assume that such disease-induced alterations show some degrees of similarity with the tool to learn such network structures from observations to understanding of how system are structured jointly from related tasks. First, we treat each patient in a class of observation as a task and then learn the Gaussian Bayesian networks (GBNs) of this data class by learning from all tasks that share a default covariance matrix that encodes prior knowledge. This setting can help us to learn more information from limited data. Next, we derive a closed-form formula of the complete likelihood function and use the Monte-Carlo Expectation-Maximization(MCEM) algorithm to search for the approximately best Bayesian network structures efficiently. Finally, we assess the performance of our methods with simulated and real-world rs-fMRI data.

Xiao Guo, Xiang Li, Xiangyu Chang et al.

Modern multi-layer networks are commonly stored and analyzed in a local and distributed fashion because of the privacy, ownership, and communication costs. The literature on the model-based statistical methods for community detection based on these data is still limited. This paper proposes a new method for consensus community detection and estimation in a multi-layer stochastic block model using locally stored and computed network data with privacy protection. A novel algorithm named privacy-preserving Distributed Spectral Clustering (ppDSC) is developed. To preserve the edges' privacy, we adopt the randomized response (RR) mechanism to perturb the network edges, which satisfies the strong notion of differential privacy. The ppDSC algorithm is performed on the squared RR-perturbed adjacency matrices to prevent possible cancellation of communities among different layers. To remove the bias incurred by RR and the squared network matrices, we develop a two-step bias-adjustment procedure. Then we perform eigen-decomposition on the debiased matrices, aggregation of the local eigenvectors using an orthogonal Procrustes transformation, and k-means clustering. We provide theoretical analysis on the statistical errors of ppDSC in terms of eigen-vector estimation. In addition, the blessings and curses of network heterogeneity are well-explained by our bounds.

Xiaotong Liu, Yunwen Lei, Xiangyu Chang et al.

This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify iteration increments in KGD, deriving an adaptive parameter selection strategy that is implementable. Theoretical verifications are provided within the framework of learning theory. Utilizing the recently developed integral operator approach, we rigorously demonstrate that KGD, equipped with the proposed adaptive parameter selection strategy, achieves the optimal generalization error bound and adapts effectively to different kernels, target functions, and error metrics. Consequently, this strategy showcases significant advantages over existing parameter selection methods for KGD.

Jinye Du, Quan Yuan, Zuyao Zhang et al.

Modern AI models demand high-performance computation kernels. The growing complexity of LLMs, multimodal architectures, and recommendation systems, combined with techniques like sparsity and quantization, creates significant computational challenges. Moreover, frequent hardware updates and diverse chip architectures further complicate this landscape, requiring tailored kernel implementations for each platform. However, manual optimization cannot keep pace with these demands, creating a critical bottleneck in AI system development. Recent advances in LLM code generation capabilities have opened new possibilities for automating kernel development. In this work, we propose AKG kernel agent (AI-driven Kernel Generator), a multi-agent system that automates kernel generation, migration, and performance tuning. AKG kernel agent is designed to support multiple domain-specific languages (DSLs), including Triton, TileLang, CPP, and CUDA-C, enabling it to target different hardware backends while maintaining correctness and portability. The system's modular design allows rapid integration of new DSLs and hardware targets. When evaluated on KernelBench using Triton DSL across GPU and NPU backends, AKG kernel agent achieves an average speedup of 1.46$\times$ over PyTorch Eager baselines implementations, demonstrating its effectiveness in accelerating kernel development for modern AI workloads.

Xi Zheng, Xiangyu Chang, Ruoxi Jia et al.

As data emerges as a vital driver of technological and economic advancements, a key challenge is accurately quantifying its value in algorithmic decision-making. The Shapley value, a well-established concept from cooperative game theory, has been widely adopted to assess the contribution of individual data sources in supervised machine learning. However, its symmetry axiom assumes all players in the cooperative game are homogeneous, which overlooks the complex structures and dependencies present in real-world datasets. To address this limitation, we extend the traditional data Shapley framework to asymmetric data Shapley, making it flexible enough to incorporate inherent structures within the datasets for structure-aware data valuation. We also introduce an efficient $k$-nearest neighbor-based algorithm for its exact computation. We demonstrate the practical applicability of our framework across various machine learning tasks and data market contexts. The code is available at: https://github.com/xzheng01/Asymmetric-Data-Shapley.

Mengmeng Wu, Zhihong Liu, Xiang Li et al.

As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method for data valuation. However, a limitation of Data Shapley is its assumption of a fixed dataset, contrasting with the dynamic nature of real-world applications where data constantly evolves and expands. This paper establishes the relationship between Data Shapley and infinite-order U-statistics and addresses this limitation by quantifying the uncertainty of Data Shapley with changes in data distribution from the perspective of U-statistics. We make statistical inferences on data valuation to obtain confidence intervals for the estimations. We construct two different algorithms to estimate this uncertainty and provide recommendations for their applicable situations. We also conduct a series of experiments on various datasets to verify asymptotic normality and propose a practical trading scenario enabled by this method.

Hao Di, Yi Yang, Haishan Ye et al.

Personalization aims to characterize individual preferences and is widely applied across many fields. However, conventional personalized methods operate in a centralized manner, potentially exposing raw data when pooling individual information. In this paper, with privacy considerations, we develop a flexible and interpretable personalized framework within the paradigm of federated learning, called \texttt{PPFL} (Population Personalized Federated Learning). By leveraging ``canonical models" to capture fundamental characteristics of a heterogeneous population and employing ``membership vectors" to reveal clients' preferences, \texttt{PPFL} models heterogeneity as clients' varying preferences for these characteristics. This approach provides substantial insights into client characteristics, which are lacking in existing Personalized Federated Learning (PFL) methods. Furthermore, we explore the relationship between \texttt{PPFL} and three main branches of PFL methods: clustered FL, multi-task PFL, and decoupling PFL, and demonstrate the advantages of \texttt{PPFL}. To solve \texttt{PPFL} (a non-convex optimization problem with linear constraints), we propose a novel random block coordinate descent algorithm and establish its convergence properties. We conduct experiments on both pathological and practical data sets, and the results validate the effectiveness of \texttt{PPFL}.

Ying Wu, Hanzhong Liu, Kai Ren et al.

Interpretability plays a crucial role in the application of statistical learning to estimate heterogeneous treatment effects (HTE) in complex diseases. In this study, we leverage a rule-based workflow, namely causal rule learning (CRL), to estimate and improve our understanding of HTE for atrial septal defect, addressing an overlooked question in the previous literature: what if an individual simultaneously belongs to multiple groups with different average treatment effects? The CRL process consists of three steps: rule discovery, which generates a set of causal rules with corresponding subgroup average treatment effects; rule selection, which identifies a subset of these rules to deconstruct individual-level treatment effects as a linear combination of subgroup-level effects; and rule analysis, which presents a detailed procedure for further analyzing each selected rule from multiple perspectives to identify the most promising rules for validation. Extensive simulation studies and real-world data analysis demonstrate that CRL outperforms other methods in providing interpretable estimates of HTE, especially when dealing with complex ground truth and sufficient sample sizes.

Yinghui Huang, Zihao Tang, Xiangyu Chang

The biases and discrimination of machine learning algorithms have attracted significant attention, leading to the development of various algorithms tailored to specific contexts. However, these solutions often fall short of addressing fairness issues inherent in machine learning operations. In this paper, we present an adaptive debiasing framework designed to find an optimal fair transformation of input data that maximally preserves data predictability under dynamic conditions. A distinctive feature of our approach is its flexibility and efficiency. It can be integrated with pretrained black-box classifiers, providing fairness guarantees with minimal retraining efforts, even in the face of frequent data drifts, evolving fairness requirements, and batches of similar tasks. To achieve this, we leverage the normalizing flows to enable efficient, information-preserving data transformation, ensuring that no critical information is lost during the debiasing process. Additionally, we incorporate the Wasserstein distance as the fairness measure to guide the optimization of data transformations. Finally, we introduce an efficient optimization algorithm with closed-formed gradient computations, making our framework scalable and suitable for dynamic, real-world environments.

Lisong He, Yi Yang, Xiangyu Chang

As the right to be forgotten becomes legislated worldwide, machine unlearning mechanisms have emerged to efficiently update models for data deletion and enhance user privacy protection. However, existing machine unlearning algorithms frequently neglect the fact that different data points may contribute unequally to model performance (i.e., heterogeneous data values). Treat them equally in machine unlearning procedure can potentially degrading the performance of updated models. To address this limitation, we propose Data Value-Weighted Unlearning (DVWU), a general unlearning framework that accounts for data value heterogeneity into the unlearning process. Specifically, we design a weighting strategy based on data values, which are then integrated into the unlearning procedure to enable differentiated unlearning for data points with varying utility to the model. The DVWU framework can be broadly adapted to various existing machine unlearning methods. We use the one-step Newton update as an example for implementation, developing both output and objective perturbation algorithms to achieve certified unlearning. Experiments on both synthetic and real-world datasets demonstrate that our methods achieve superior predictive performance and robustness compared to conventional unlearning approaches. We further show the extensibility of our framework on gradient ascent method by incorporating the proposed weighting strategy into the gradient terms, highlighting the adaptability of DVWU for broader gradient-based deep unlearning methods.

Xuechen Zhang, Xiangyu Chang, Mingchen Li et al.

The attention mechanism within the transformer architecture enables the model to weigh and combine tokens based on their relevance to the query. While self-attention has enjoyed major success, it notably treats all queries $q$ in the same way by applying the mapping $V^\top\text{softmax}(Kq)$, where $V,K$ are the value and key embeddings respectively. In this work, we argue that this uniform treatment hinders the ability to control contextual sparsity and relevance. As a solution, we introduce the $\textit{Selective Self-Attention}$ (SSA) layer that augments the softmax nonlinearity with a principled temperature scaling strategy. By controlling temperature, SSA adapts the contextual sparsity of the attention map to the query embedding and its position in the context window. Through theory and experiments, we demonstrate that this alleviates attention dilution, aids the optimization process, and enhances the model's ability to control softmax spikiness of individual queries. We also incorporate temperature scaling for value embeddings and show that it boosts the model's ability to suppress irrelevant/noisy tokens. Notably, SSA is a lightweight method which introduces less than 0.5% new parameters through a weight-sharing strategy and can be fine-tuned on existing LLMs. Extensive empirical evaluations demonstrate that SSA-equipped models achieve a noticeable and consistent accuracy improvement on language modeling benchmarks.

Xiangyu Chang, Sk Miraj Ahmed, Srikanth V. Krishnamurthy et al.

The key premise of federated learning (FL) is to train ML models across a diverse set of data-owners (clients), without exchanging local data. An overarching challenge to this date is client heterogeneity, which may arise not only from variations in data distribution, but also in data quality, as well as compute/communication latency. An integrated view of these diverse and concurrent sources of heterogeneity is critical; for instance, low-latency clients may have poor data quality, and vice versa. In this work, we propose FLASH(Federated Learning Across Simultaneous Heterogeneities), a lightweight and flexible client selection algorithm that outperforms state-of-the-art FL frameworks under extensive sources of heterogeneity, by trading-off the statistical information associated with the client's data quality, data distribution, and latency. FLASH is the first method, to our knowledge, for handling all these heterogeneities in a unified manner. To do so, FLASH models the learning dynamics through contextual multi-armed bandits (CMAB) and dynamically selects the most promising clients. Through extensive experiments, we demonstrate that FLASH achieves substantial and consistent improvements over state-of-the-art baselines -- as much as 10% in absolute accuracy -- thanks to its unified approach. Importantly, FLASH also outperforms federated aggregation methods that are designed to handle highly heterogeneous settings and even enjoys a performance boost when integrated with them.

Sk Miraj Ahmed, Fahim Faisal Niloy, Xiangyu Chang et al.

Adapting to dynamic data distributions is a practical yet challenging task. One effective strategy is to use a model ensemble, which leverages the diverse expertise of different models to transfer knowledge to evolving data distributions. However, this approach faces difficulties when the dynamic test distribution is available only in small batches and without access to the original source data. To address the challenge of adapting to dynamic distributions in such practical settings, we propose Continual Multi-source Adaptation to Dynamic Distributions (CONTRAST), a novel method that optimally combines multiple source models to adapt to the dynamic test data. CONTRAST has two distinguishing features. First, it efficiently computes the optimal combination weights to combine the source models to adapt to the test data distribution continuously as a function of time. Second, it identifies which of the source model parameters to update so that only the model which is most correlated to the target data is adapted, leaving the less correlated ones untouched; this mitigates the issue of ``forgetting" the source model parameters by focusing only on the source model that exhibits the strongest correlation with the test batch distribution. Through theoretical analysis we show that the proposed method is able to optimally combine the source models and prioritize updates to the model least prone to forgetting. Experimental analysis on diverse datasets demonstrates that the combination of multiple source models does at least as well as the best source (with hindsight knowledge), and performance does not degrade as the test data distribution changes over time (robust to forgetting).

Yingcong Li, Xiangyu Chang, Muti Kara et al.

Recent research shows that in-context learning (ICL) can be effective even when demonstrations have missing or incorrect labels. To shed light on this capability, we examine a canonical setting where the demonstrations are drawn according to a binary Gaussian mixture model (GMM) and a certain fraction of the demonstrations have missing labels. We provide a comprehensive theoretical study to show that: (1) The loss landscape of one-layer linear attention models recover the optimal fully-supervised estimator but completely fail to exploit unlabeled data; (2) In contrast, multilayer or looped transformers can effectively leverage unlabeled data by implicitly constructing estimators of the form $\sum_{i\ge 0} a_i (X^\top X)^iX^\top y$ with $X$ and $y$ denoting features and partially-observed labels (with missing entries set to zero). We characterize the class of polynomials that can be expressed as a function of depth and draw connections to Expectation Maximization, an iterative pseudo-labeling algorithm commonly used in semi-supervised learning. Importantly, the leading polynomial power is exponential in depth, so mild amount of depth/looping suffices. As an application of theory, we propose looping off-the-shelf tabular foundation models to enhance their semi-supervision capabilities. Extensive evaluations on real-world datasets show that our method significantly improves the semisupervised tabular learning performance over the standard single pass inference.

Haishan Ye, Yinghui Huang, Hao Di et al.

We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance reduction framework that effectively reduces the gradient approximation variance induced by zeroth-order oracles and the stochastic sampling variance from finite-sum objectives. By leveraging this framework, our algorithm achieves significant improvements in query efficiency, making it particularly well-suited for high-dimensional optimization tasks. Specifically, for convex objectives, the algorithm achieves a query complexity of O(d \sqrt{n}/ε) to find an epsilon-suboptimal solution, where d is the dimensionality and n is the number of functions in the finite-sum objective. For non-convex objectives, it achieves a query complexity of O(d^{3/2}\sqrt{n}/ε^2 ) without requiring the computation ofd partial derivatives at each iteration. These complexities are the best known among zeroth-order stochastic Frank-Wolfe algorithms that avoid explicit gradient calculations. Empirical experiments on convex and non-convex machine learning tasks, including sparse logistic regression, robust classification, and adversarial attacks on deep networks, validate the computational efficiency and scalability of our approach. Our algorithm demonstrates superior performance in both convergence rate and query complexity compared to existing methods.

Xiangyu Chang, Manyi Yao, Srikanth V. Krishnamurthy et al.

In Asynchronous Federated Learning (AFL), the central server immediately updates the global model with each arriving client's contribution. As a result, clients perform their local training on different model versions, causing information staleness (delay). In federated environments with non-IID local data distributions, this asynchronous pattern amplifies the adverse effect of client heterogeneity (due to different data distribution, local objectives, etc.), as faster clients contribute more frequent updates, biasing the global model. We term this phenomenon heterogeneity amplification. Our work provides a theoretical analysis that maps AFL design choices to their resulting error sources when heterogeneity amplification occurs. Guided by our analysis, we propose ACE (All-Client Engagement AFL), which mitigates participation imbalance through immediate, non-buffered updates that use the latest information available from all clients. We also introduce a delay-aware variant, ACED, to balance client diversity against update staleness. Experiments on different models for different tasks across diverse heterogeneity and delay settings validate our analysis and demonstrate the robust performance of our approaches.

Yunxuan Jiang, Silan Hu, Xiaoning Wang et al.

Large language models (LLMs) become increasingly integrated into data science workflows for automated system design. However, these LLM-driven data science systems rely solely on the internal reasoning of LLMs, lacking guidance from scientific and theoretical principles. This limits their trustworthiness and robustness, especially when dealing with noisy and complex real-world datasets. This paper provides VDSAgents, a multi-agent system grounded in the Predictability-Computability-Stability (PCS) principles proposed in the Veridical Data Science (VDS) framework. Guided by PCS principles, the system implements a modular workflow for data cleaning, feature engineering, modeling, and evaluation. Each phase is handled by an elegant agent, incorporating perturbation analysis, unit testing, and model validation to ensure both functionality and scientific auditability. We evaluate VDSAgents on nine datasets with diverse characteristics, comparing it with state-of-the-art end-to-end data science systems, such as AutoKaggle and DataInterpreter, using DeepSeek-V3 and GPT-4o as backends. VDSAgents consistently outperforms the results of AutoKaggle and DataInterpreter, which validates the feasibility of embedding PCS principles into LLM-driven data science automation.

Xiangyu Chang, Xi Chen, Yining Wang et al.

This paper studies a bandit optimization problem where the goal is to maximize a function $f(x)$ over $T$ periods for some unknown strongly concave function $f$. We consider a new pairwise comparison oracle, where the decision-maker chooses a pair of actions $(x, x')$ for a consecutive number of periods and then obtains an estimate of $f(x)-f(x')$. We show that such a pairwise comparison oracle finds important applications to joint pricing and inventory replenishment problems and network revenue management. The challenge in this bandit optimization is twofold. First, the decision-maker not only needs to determine a pair of actions $(x, x')$ but also a stopping time $n$ (i.e., the number of queries based on $(x, x')$). Second, motivated by our inventory application, the estimate of the difference $f(x)-f(x')$ is biased, which is different from existing oracles in stochastic optimization literature. To address these challenges, we first introduce a discretization technique and local polynomial approximation to relate this problem to linear bandits. Then we developed a tournament successive elimination technique to localize the discretized cell and run an interactive batched version of LinUCB algorithm on cells. We establish regret bounds that are optimal up to poly-logarithmic factors. Furthermore, we apply our proposed algorithm and analytical framework to the two operations management problems and obtain results that improve state-of-the-art results in the existing literature.

Yi Yang, Yinghui Huang, Xiangyu Chang

Existing theoretical work on Bayes-optimal fair classifiers usually considers a single (binary) sensitive feature. In practice, individuals are often defined by multiple sensitive features. In this paper, we characterize the Bayes-optimal fair classifier for multiple sensitive features under general approximate fairness measures, including mean difference and mean ratio. We show that these approximate measures for existing group fairness notions, including Demographic Parity, Equal Opportunity, Predictive Equality, and Accuracy Parity, are linear transformations of selection rates for specific groups defined by both labels and sensitive features. We then characterize that Bayes-optimal fair classifiers for multiple sensitive features become instance-dependent thresholding rules that rely on a weighted sum of these group membership probabilities. Our framework applies to both attribute-aware and attribute-blind settings and can accommodate composite fairness notions like Equalized Odds. Building on this, we propose two practical algorithms for Bayes-optimal fair classification via in-processing and post-processing. We show empirically that our methods compare favorably to existing methods.

Xiao Guo, Xuming He, Xiangyu Chang et al.

This paper develops a new spectral clustering-based method called TransNet for transfer learning in community detection of network data. Our goal is to improve the clustering performance of the target network using auxiliary source networks, which are heterogeneous, privacy-preserved, and locally stored across various sources. The edges of each locally stored network are perturbed using the randomized response mechanism to achieve differential privacy. Notably, we allow the source networks to have distinct privacy-preserving and heterogeneity levels as often desired in practice. To better utilize the information from the source networks, we propose a novel adaptive weighting method to aggregate the eigenspaces of the source networks multiplied by adaptive weights chosen to incorporate the effects of privacy and heterogeneity. We propose a regularization method that combines the weighted average eigenspace of the source networks with the eigenspace of the target network to achieve an optimal balance between them. Theoretically, we show that the adaptive weighting method enjoys the error-bound-oracle property in the sense that the error bound of the estimated eigenspace only depends on informative source networks. We also demonstrate that TransNet performs better than the estimator using only the target network and the estimator using only the weighted source networks.

Xiangyu Chang, Yingcong Li, Muti Kara et al.

The in-context learning capabilities of modern language models have motivated a deeper mathematical understanding of sequence models. A line of recent work has shown that linear attention models can emulate projected gradient descent iterations to implicitly learn the task vector from the data provided in the context window. In this work, we consider a novel setting where the global task distribution can be partitioned into a union of conditional task distributions. We then examine the use of task-specific prompts and prediction heads for learning the prior information associated with the conditional task distribution using a one-layer attention model. Our results on loss landscape show that task-specific prompts facilitate a covariance-mean decoupling where prompt-tuning explains the conditional mean of the distribution whereas the variance is learned/explained through in-context learning. Incorporating task-specific head further aids this process by entirely decoupling estimation of mean and variance components. This covariance-mean perspective similarly explains how jointly training prompt and attention weights can provably help over fine-tuning after pretraining.

Xiangyu Chang, Sk Miraj Ahmed, Srikanth V. Krishnamurthy et al.

Parameter-efficient tuning (PET) methods such as LoRA, Adapter, and Visual Prompt Tuning (VPT) have found success in enabling adaptation to new domains by tuning small modules within a transformer model. However, the number of domains encountered during test time can be very large, and the data is usually unlabeled. Thus, adaptation to new domains is challenging; it is also impractical to generate customized tuned modules for each such domain. Toward addressing these challenges, this work introduces PLUTO: a Plug-and-pLay modUlar Test-time domain adaptatiOn strategy. We pre-train a large set of modules, each specialized for different source domains, effectively creating a ``module store''. Given a target domain with few-shot unlabeled data, we introduce an unsupervised test-time adaptation (TTA) method to (1) select a sparse subset of relevant modules from this store and (2) create a weighted combination of selected modules without tuning their weights. This plug-and-play nature enables us to harness multiple most-relevant source domains in a single inference call. Comprehensive evaluations demonstrate that PLUTO uniformly outperforms alternative TTA methods and that selecting $\leq$5 modules suffice to extract most of the benefit. At a high level, our method equips pre-trained transformers with the capability to dynamically adapt to new domains, motivating a new paradigm for efficient and scalable domain adaptation.

Yi Yang, Ying Wu, Mei Li et al.

Scoring systems, as a type of predictive model, have significant advantages in interpretability and transparency and facilitate quick decision-making. As such, scoring systems have been extensively used in a wide variety of industries such as healthcare and criminal justice. However, the fairness issues in these models have long been criticized, and the use of big data and machine learning algorithms in the construction of scoring systems heightens this concern. In this paper, we propose a general framework to create fairness-aware, data-driven scoring systems. First, we develop a social welfare function that incorporates both efficiency and group fairness. Then, we transform the social welfare maximization problem into the risk minimization task in machine learning, and derive a fairness-aware scoring system with the help of mixed integer programming. Lastly, several theoretical bounds are derived for providing parameter selection suggestions. Our proposed framework provides a suitable solution to address group fairness concerns in the development of scoring systems. It enables policymakers to set and customize their desired fairness requirements as well as other application-specific constraints. We test the proposed algorithm with several empirical data sets. Experimental evidence supports the effectiveness of the proposed scoring system in achieving the optimal welfare of stakeholders and in balancing the needs for interpretability, fairness, and efficiency.

Xiang Li, Jiadong Liang, Xiangyu Chang et al.

Federated Learning (FL) makes a large amount of edge computing devices (e.g., mobile phones) jointly learn a global model without data sharing. In FL, data are generated in a decentralized manner with high heterogeneity. This paper studies how to perform statistical estimation and inference in the federated setting. We analyze the so-called Local SGD, a multi-round estimation procedure that uses intermittent communication to improve communication efficiency. We first establish a {\it functional central limit theorem} that shows the averaged iterates of Local SGD weakly converge to a rescaled Brownian motion. We next provide two iterative inference methods: the {\it plug-in} and the {\it random scaling}. Random scaling constructs an asymptotically pivotal statistic for inference by using the information along the whole Local SGD path. Both the methods are communication efficient and applicable to online data. Our theoretical and empirical results show that Local SGD simultaneously achieves both statistical efficiency and communication efficiency.

Xiao Guo, Xiang Li, Xiangyu Chang et al.

Eigenspace estimation is fundamental in machine learning and statistics, which has found applications in PCA, dimension reduction, and clustering, among others. The modern machine learning community usually assumes that data come from and belong to different organizations. The low communication power and the possible privacy breaches of data make the computation of eigenspace challenging. To address these challenges, we propose a class of algorithms called \textsf{FedPower} within the federated learning (FL) framework. \textsf{FedPower} leverages the well-known power method by alternating multiple local power iterations and a global aggregation step, thus improving communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with {\it Orthogonal Procrustes Transformation} (OPT) for better alignment. To ensure strong privacy protection, we add Gaussian noise in each iteration by adopting the notion of \emph{differential privacy} (DP). We provide convergence bounds for \textsf{FedPower} that are composed of different interpretable terms corresponding to the effects of Gaussian noise, parallelization, and random sampling of local machines. Additionally, we conduct experiments to demonstrate the effectiveness of our proposed algorithms.

Xiangyu Chang, Yingcong Li, Samet Oymak et al.

Deep networks are typically trained with many more parameters than the size of the training dataset. Recent empirical evidence indicates that the practice of overparameterization not only benefits training large models, but also assists - perhaps counterintuitively - building lightweight models. Specifically, it suggests that overparameterization benefits model pruning / sparsification. This paper sheds light on these empirical findings by theoretically characterizing the high-dimensional asymptotics of model pruning in the overparameterized regime. The theory presented addresses the following core question: "should one train a small model from the beginning, or first train a large model and then prune?". We analytically identify regimes in which, even if the location of the most informative features is known, we are better off fitting a large model and then pruning rather than simply training with the known informative features. This leads to a new double descent in the training of sparse models: growing the original model, while preserving the target sparsity, improves the test accuracy as one moves beyond the overparameterization threshold. Our analysis further reveals the benefit of retraining by relating it to feature correlations. We find that the above phenomena are already present in linear and random-features models. Our technical approach advances the toolset of high-dimensional analysis and precisely characterizes the asymptotic distribution of over-parameterized least-squares. The intuition gained by analytically studying simpler models is numerically verified on neural networks.

Shao-Bo Lin, Xiangyu Chang, Xingping Sun

Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These features defy any theoretical treatment that requires local or global quasi-uniformity of distribution of data sites. Incorporating a recently-developed application of integral operator theory in machine learning, we propose and study in the current article a new framework to analyze kernel interpolation of high dimensional data, which features bounding stochastic approximation error by the spectrum of the underlying kernel matrix. Both theoretical analysis and numerical simulations show that spectra of kernel matrices are reliable and stable barometers for gauging the performance of kernel-interpolation methods for high dimensional data.

Xiao Guo, Yixuan Qiu, Hai Zhang et al.

Directed networks are broadly used to represent asymmetric relationships among units. Co-clustering aims to cluster the senders and receivers of directed networks simultaneously. In particular, the well-known spectral clustering algorithm could be modified as the spectral co-clustering to co-cluster directed networks. However, large-scale networks pose great computational challenges to it. In this paper, we leverage sketching techniques and derive two randomized spectral co-clustering algorithms, one \emph{random-projection-based} and the other \emph{random-sampling-based}, to accelerate the co-clustering of large-scale directed networks. We theoretically analyze the resulting algorithms under two generative models -- the stochastic co-block model and the degree-corrected stochastic co-block model, and establish their approximation error rates and misclustering error rates, indicating better bounds than the state-of-the-art results of co-clustering literature. Numerically, we design and conduct simulations to support our theoretical results and test the efficiency of the algorithms on real networks with up to millions of nodes. A publicly available R package \textsf{RandClust} is developed for better usability and reproducibility of the proposed methods.

Yining Wang, Xi Chen, Xiangyu Chang et al.

Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision focuses on designing an online policy to maximize the revenue. However, the research on uncertainty quantification on the underlying true model function (e.g., demand function), a critical problem for practitioners, has not been well explored. In this paper, using the problem of demand function prediction in dynamic pricing as the motivating example, we study the problem of constructing accurate confidence intervals for the demand function. The main challenge is that sequentially collected data leads to significant distributional bias in the maximum likelihood estimator or the empirical risk minimization estimate, making classical statistics approaches such as the Wald's test no longer valid. We address this challenge by developing a debiased approach and provide the asymptotic normality guarantee of the debiased estimator. Based this the debiased estimator, we provide both point-wise and uniform confidence intervals of the demand function.

Yi Yang, Yuxuan Guo, Xiangyu Chang

Many real-world classification problems come with costs which can vary for different types of misclassification. It is thus important to develop cost-sensitive classifiers which minimize the total misclassification cost. Although binary cost-sensitive classifiers have been well-studied, solving multicategory classification problems is still challenging. A popular approach to address this issue is to construct K classification functions for a K-class problem and remove the redundancy by imposing a sum-to-zero constraint. However, such method usually results in higher computational complexity and inefficient algorithms. In this paper, we propose a novel angle-based cost-sensitive classification framework for multicategory classification without the sum-to-zero constraint. Loss functions that included in the angle-based cost-sensitive classification framework are further justified to be Fisher consistent. To show the usefulness of the framework, two cost-sensitive multicategory boosting algorithms are derived as concrete instances. Numerical experiments demonstrate that proposed boosting algorithms yield competitive classification performances against other existing boosting approaches.

Hai Zhang, Xiao Guo, Xiangyu Chang

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public.

Xiangyu Chang, Shao-Bo Lin

In this paper, we propose an adaptive stopping rule for kernel-based gradient descent (KGD) algorithms. We introduce the empirical effective dimension to quantify the increments of iterations in KGD and derive an implementable early stopping strategy. We analyze the performance of the adaptive stopping rule in the framework of learning theory. Using the recently developed integral operator approach, we rigorously prove the optimality of the adaptive stopping rule in terms of showing the optimal learning rates for KGD equipped with this rule. Furthermore, a sharp bound on the number of iterations in KGD equipped with the proposed early stopping rule is also given to demonstrate its computational advantage.

Aven Samareh, Yan Jin, Zhangyang Wang et al.

We present our preliminary work to determine if patient's vocal acoustic, linguistic, and facial patterns could predict clinical ratings of depression severity, namely Patient Health Questionnaire depression scale (PHQ-8). We proposed a multi modal fusion model that combines three different modalities: audio, video , and text features. By training over AVEC 2017 data set, our proposed model outperforms each single modality prediction model, and surpasses the data set baseline with ice margin.

Shao-Bo Lin, Jinshan Zeng, Xiangyu Chang

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, provided the regression function is smooth. Our second result shows that, for a large number of loss functions, under some Tsybakov noise assumption, if the regression function is infinitely smooth, then SVM with Gaussian kernel can achieve the learning rate of order $m^{-1}$, where $m$ is the number of samples.

Xiangyu Chang, Shaobo Lin, Yao Wang

The divide and conquer strategy, which breaks a massive data set into a se- ries of manageable data blocks, and then combines the independent results of data blocks to obtain a final decision, has been recognized as a state-of-the-art method to overcome challenges of massive data analysis. In this paper, we merge the divide and conquer strategy with local average regression methods to infer the regressive relationship of input-output pairs from a massive data set. After theoretically analyzing the pros and cons, we find that although the divide and conquer local average regression can reach the optimal learning rate, the restric- tion to the number of data blocks is a bit strong, which makes it only feasible for small number of data blocks. We then propose two variants to lessen (or remove) this restriction. Our results show that these variants can achieve the optimal learning rate with much milder restriction (or without such restriction). Extensive experimental studies are carried out to verify our theoretical assertions.

Xiangyu Chang, Yu Wang, Rongjian Li et al.

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in a framework of maximizing the weighted feature contributions subject to a $\ell_2/\ell_1$ penalty. Nevertheless, this framework has two serious drawbacks: One is that the solution of the framework unavoidably involves a considerable portion of redundant noise features in many situations, and the other is that the framework neither offers intuitive explanations on why this framework can select relevant features nor leads to any theoretical guarantee for feature selection consistency. In this article, we attempt to overcome those drawbacks through developing a new sparse clustering framework which uses a $\ell_{\infty}/\ell_0$ penalty. First, we introduce new concepts on optimal partitions and noise features for the high-dimensional data clustering problems, based on which the previously known framework can be intuitively explained in principle. Then, we apply the suggested $\ell_{\infty}/\ell_0$ framework to formulate a new sparse k-means model with the $\ell_{\infty}/\ell_0$ penalty ($\ell_0$-k-means for short). We propose an efficient iterative algorithm for solving the $\ell_0$-k-means. To deeply understand the behavior of $\ell_0$-k-means, we prove that the solution yielded by the $\ell_0$-k-means algorithm has feature selection consistency whenever the data matrix is generated from a high-dimensional Gaussian mixture model. Finally, we provide experiments with both synthetic data and the Allen Developing Mouse Brain Atlas data to support that the proposed $\ell_0$-k-means exhibits better noise feature detection capacity over the previously known sparse k-means with the $\ell_2/\ell_1$ penalty ($\ell_1$-k-means for short).