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Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Federated learning (FL for simplification) is a distributed machine learning technique that utilizes global servers and collaborative clients to achieve privacy-preserving global model training without direct data sharing. However,…
We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…
In personalized Federated Learning, each member of a potentially large set of agents aims to train a model minimizing its loss function averaged over its local data distribution. We study this problem under the lens of stochastic…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…
This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…
Models trained in federated settings often suffer from degraded performances and fail at generalizing, especially when facing heterogeneous scenarios. In this work, we investigate such behavior through the lens of geometry of the loss and…
Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off…
We investigate the generalization error of statistical learning models in a Federated Learning (FL) setting. Specifically, we study the evolution of the generalization error with the number of communication rounds $R$ between $K$ clients…
Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…
Heterogeneity in federated learning (FL) is a critical and challenging aspect that significantly impacts model performance and convergence. In this paper, we propose a novel framework by formulating heterogeneous FL as a hierarchical…
Fair prediction across protected groups is an important constraint for many federated learning applications. However, prior work studying group fair federated learning lacks formal convergence or fairness guarantees. In this work we propose…
When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a learning method designed to…
Machine learning algorithms operating on mobile networks can be characterized into three different categories. First is the classical situation in which the end-user devices send their data to a central server where this data is used to…
We consider the problem of personalized federated learning when there are known cluster structures within users. An intuitive approach would be to regularize the parameters so that users in the same cluster share similar model weights. The…
We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…
We use distributionally-robust optimization for machine learning to mitigate the effect of data poisoning attacks. We provide performance guarantees for the trained model on the original data (not including the poison records) by training…
Data normalization is a crucial preprocessing step for enhancing model performance and training stability. In federated learning (FL), where data remains distributed across multiple parties during collaborative model training, normalization…