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.

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.

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.

The emerging big data in all walks of life has become the driving force of technological and economic development (Ghorbani and Zou, 2019; Huang et al., 2021). Various sectors such as finance and healthcare increasingly rely on individuals' data for predictions, decision-making, and generating business value, which promotes extensive data transactions (Barua et al., 2012). One of the most critical problems in data trading scenarios is data valuation. We consider data trading scenarios in data markets based on machine learning models, such as DATABRIGHT (Dao et al., 2018) and Sterling (Hynes et al., 2018). The data value in this scenario is largely determined by its contribution to a specific machine learning model. We focus on data valuation in supervised learning, which is one of the main pillars of machine learning. The core challenge is how to fairly evaluate the contribution of each data in the training set to the learning algorithm for a particular performance metric. A natural way to handle the aforementioned issue is to treat each data as a player in a cooperative game. Then, the value of each player can be assessed through utility functions from a game-theoretic perspective (Jia et al., 2019b).

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.

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.

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.

Singular value decomposition (SVD) is one of the most fundamental tools in machine learning and statistics.The modern machine learning community usually assumes that data come from and belong to small-scale device users. The low communication and computation power of such devices, and the possible privacy breaches of users' sensitive data make the computation of SVD challenging. Federated learning (FL) is a paradigm enabling a large number of devices to jointly learn a model in a communication-efficient way without data sharing. In the FL framework, we develop a class of algorithms called FedPower for the computation of partial SVD in the modern setting. Based on the well-known power method, the local devices alternate between multiple local power iterations and one global aggregation to improve communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with Orthogonal Procrustes Transformation (OPT). Considering the practical stragglers' effect, the aggregation can be fully participated or partially participated, where for the latter we propose two sampling and aggregation schemes. Further, to ensure strong privacy protection, we add Gaussian noise whenever the communication happens by adopting the notion of differential privacy (DP). We theoretically show the convergence bound for FedPower. The resulting bound is interpretable with each part corresponding to the effect of Gaussian noise, parallelization, and random sampling of devices, respectively. We also conduct experiments to demonstrate the merits of FedPower. In particular, the local iterations not only improve communication efficiency but also reduce the chance of privacy breaches.

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.

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 a hybrid (discrete and continuous) $K$-functional tied to 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.