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Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

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…

We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…

The concept of differential privacy (DP) has gained substantial attention in recent years, most notably since the U.S. Census Bureau announced the adoption of the concept for its 2020 Decennial Census. However, despite its attractive…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…

We investigate how to optimally design local differential privacy (LDP) mechanisms that reduce data unfairness and thereby improve fairness in downstream classification. We first derive a closed-form optimal mechanism for binary sensitive…

Differential privacy (DP), provides a framework for provable privacy protection against arbitrary adversaries, while allowing the release of summary statistics and synthetic data. We address the problem of releasing a noisy real-valued…

We propose two synthetic microdata approaches to generate private tabular survey data products for public release. We adapt a pseudo posterior mechanism that downweights by-record likelihood contributions with weights $\in [0,1]$ based on…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Differential privacy (DP) considers a scenario, where an adversary has almost complete information about the entries of a database This worst-case assumption is likely to overestimate the privacy thread for an individual in real life.…

Domain adaptation (DA) is transfer learning which aims to leverage labeled data in a related source domain to achieve informed knowledge transfer and help the classification of unlabeled data in a target domain. In this paper, we propose a…

LDP (Local Differential Privacy) has been widely studied to estimate statistics of personal data (e.g., distribution underlying the data) while protecting users' privacy. Although LDP does not require a trusted third party, it regards all…

Personalized privacy becomes critical in deep learning for Trustworthy AI. While Differentially Private Stochastic Gradient Descent (DP-SGD) is widely used in deep learning methods supporting privacy, it provides the same level of privacy…

Differential privacy (DP) is a widely used notion for reasoning about privacy when publishing aggregate data. In this paper, we observe that certain DP mechanisms are amenable to a posteriori privacy analysis that exploits the fact that…

Decentralized optimization is gaining increased traction due to its widespread applications in large-scale machine learning and multi-agent systems. The same mechanism that enables its success, i.e., information sharing among participating…

Decentralized stochastic optimization is the basic building block of modern collaborative machine learning, distributed estimation and control, and large-scale sensing. Since involved data usually contain sensitive information like user…

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically…

Differential Privacy (DP) provides a formal privacy guarantee preventing adversaries with access to a machine learning model from extracting information about individual training points. Differentially Private Stochastic Gradient Descent…

The purpose of statistical disclosure control (SDC) of microdata, a.k.a. data anonymization or privacy-preserving data mining, is to publish data sets containing the answers of individual respondents in such a way that the respondents…