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Abstract
Privacy-preserving data analysis has become a central challenge in modern statistics, and federated learning has increasingly attracted attention in both statistics and machine learning. In this talk, we study minimax and adaptive federated learning under differential privacy (FDP) in the context of density estimation, considering both global and pointwise estimation over Besov spaces.
We first establish minimax rates of convergence under FDP and propose optimal distributed, privacy-preserving estimators. Our results uncover phase-transition phenomena that highlight the trade-offs between statistical accuracy and privacy, showing how privacy budgets, the number of servers, and sample size jointly determine achievable performance.
We then turn to adaptive estimation when the smoothness parameters are unknown. We derive sharp characterizations of the cost of adaptation under FDP for both global and pointwise estimation and introduce an adaptive estimator based on a new noise mechanism that enables one-shot adaptation via post-processing. This method provides strict improvements over existing adaptive DP approaches.
Our findings reveal a striking contrast between private and non-private settings. For global estimation, where adaptation can be achieved for free in the classical non-private setting, we prove that under FDP an intrinsic adaptation cost is unavoidable. For pointwise estimation, where a logarithmic penalty is already known to arise in the non-private setting, we show that FDP introduces an additional logarithmic factor, thereby compounding the cost of adaptation. Taken together, these results provide the first rigorous characterization of the adaptive privacy-accuracy trade-off.
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Abstract
The world is undergoing a profound technological transformation, driven by the explosive growth of Big Data and advances in data-driven AI. At the heart of this revolution lie Statistics, Machine Learning, and AI—powerful tools that are reshaping how we work, live, and communicate. Data science is driving innovation across virtually every sector. This unprecedented shift brings immense opportunities for the field of Statistics, both in research and education. As the demand for data-driven insights grows, the role of statisticians and data scientists has become increasingly vital. In this talk, I will discuss the pressing challenges and exciting opportunities facing the field of Statistics in the Age of AI.
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Abstract
In this talk, we consider minimax and adaptive transfer learning for nonparametric classification under the posterior drift model with distributed differential privacy constraints. We first establish the minimax misclassification rate, precisely characterizing the effects of privacy constraints, source samples, and target samples on classification accuracy. The results reveal interesting phase transition phenomena and highlight the intricate trade-offs between preserving privacy and achieving classification accuracy. We then develop a data-driven adaptive classifier that achieves the optimal rate within a logarithmic factor across a large collection of parameter spaces while satisfying the same set of differential privacy constraints. Simulation studies and real-world data applications further elucidate the theoretical analysis with numerical results.
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Abstract
Federated learning is a machine learning paradigm designed to tackle the challenges of data governance and privacy. It enables organizations (e.g., hospitals) to collaboratively train and enhance a shared global statistical model without sharing raw data externally. Instead, the learning process occurs locally at each participating entity, and only model characteristics, such as parameters and gradients, are exchanged, while preserving privacy.
In this talk, we consider statistical optimality for federated learning in the context of nonparametric regression. The setting we study is heterogeneous, encompassing varying sample sizes and differential privacy constraints across different servers. Within this framework, both global and pointwise estimation are considered, and optimal rates of convergence over the Besov spaces are established.
We propose distributed privacy-preserving estimation procedures and analyze their theoretical properties. The findings shed light on the delicate balance between accuracy and privacy preservation. In particular, we characterize the compromise not only in terms of the privacy budget but also concerning the loss incurred by distributing data within the privacy framework as a whole. This insight captures the folklore wisdom that it is easier to retain privacy in larger samples, and explores the differences between pointwise and global estimation under distributed privacy constraints.
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Abstract
In the conventional statistical framework, a major goal is to develop optimal statistical procedures based on the sample size and statistical model. However, in many contemporary applications, non-statistical concerns such as privacy, communication, and computational constraints associated with the statistical procedures become crucial. This raises a fundamental question in data science: how can we make optimal statistical inference under these non-statistical constraints?
In this talk, we explore recent advances in differentially private learning and distributed learning under communication constraints in a few specific settings. Our results demonstrate novel and interesting phenomena and suggest directions for further investigation.
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Abstract
Distributed estimation is increasingly important when data remain in separate locations because of scale, privacy, or security requirements. Such settings are common in medicine, finance, and business.
The lecture studies optimal nonparametric regression under communication and privacy constraints. It establishes minimax convergence rates, quantifies the tradeoff between statistical accuracy and those constraints, and develops procedures that attain the optimal rates.
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Abstract
In the conventional statistical framework, a major goal is to develop optimal statistical procedures based on the sample size and statistical model. However, in many contemporary applications, non-statistical concerns such as privacy and communication constraints associated with the statistical procedures become crucial. This raises a fundamental question in data science: how can we make optimal statistical inference under these non-statistical constraints?
In this talk, we explore recent advances in differentially private learning and distributed learning under communication constraints in a few specific settings. Our results demonstrate novel and interesting phenomena and suggest directions for further investigation.
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Abstract
Transfer learning uses knowledge from one task to improve learning in a related setting. The lecture considers several statistical transfer-learning problems, with an emphasis on nonparametric classification under the posterior-drift model.
It establishes the minimax rate, constructs a rate-optimal weighted nearest-neighbor classifier, and measures how source observations improve the target task. A data-driven classifier adapts over a broad collection of parameter spaces within a logarithmic factor of the optimal rate.
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Abstract
In high-dimensional problems, computational demands become part of statistical method design. The lecture asks whether restricting attention to polynomial-time procedures imposes a cost in statistical performance.
Submatrix localization and sparse matrix detection illustrate the relationship between statistical accuracy and computational efficiency, including regimes in which optimal inference is easy, difficult, or impossible.
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Abstract
These lectures examine compressed sensing and linear regression when the dimension can greatly exceed the sample size. They develop a unified analysis of constrained and penalized l1 methods for sparse recovery with noiseless, bounded-noise, and Gaussian-noise observations.
Additional topics include the Johnson–Lindenstrauss lemma, construction of compressed-sensing matrices, and optimal and adaptive estimation of high-dimensional covariance and precision matrices.
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Abstract
Covariance structure is central to inference and to applications including genomics, fMRI, risk management, and web search. Conventional fixed-dimension methods are inadequate when the number of variables exceeds the sample size.
The lectures present optimal and adaptive methods for estimating large covariance matrices, highlighting theoretical features that differ from classical nonparametric function estimation and discussing related applications.
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Abstract
The lecture develops optimal methods for estimating large covariance matrices and explains why their behavior differs from conventional nonparametric estimation. It also treats sparse precision-matrix estimation through constrained l1 minimization.
Related questions include the optimality of precision-matrix procedures and high-dimensional tests of covariance structure based on random-matrix theory.
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Abstract
These lectures study linear regression when the number of variables is much larger than the number of observations. They begin with the high-dimensional Gaussian sequence model and then turn to sparse linear models.
A unified analysis covers the Lasso and Dantzig selector under noiseless, bounded-error, and Gaussian-noise settings, with an extension to l1 methods for sparse precision-matrix estimation.
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Abstract
The lectures connect foundations in nonparametric function estimation—including minimaxity, adaptation, oracle inequalities, and wavelet thresholding—to contemporary problems in high-dimensional inference.
Topics include compressed sensing, sparse-signal detection, and covariance estimation. Constrained l1 methods are analyzed across several noise settings, and optimal matrix-estimation results reveal behavior unlike classical function and sequence estimation.
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Abstract
The lecture considers two central high-dimensional problems: recovering a sparse signal from relatively few noisy measurements and estimating a large covariance matrix. For sparse recovery, it studies constrained l1 minimization under restricted-isometry and mutual-incoherence conditions.
A unified analysis covers noiseless, bounded-error, and Gaussian-noise settings. The shifting inequality provides a simple route to identifiability, stable recovery, and oracle guarantees.
For covariance matrices, the lecture establishes optimal convergence rates under operator, Frobenius, and matrix l1 losses. The results show that optimal row-by-row estimation need not produce an optimal matrix estimator and require new minimax lower-bound constructions.
Special Invited lectures