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Differential privacy is a mathematical framework for privacy-preserving data analysis. Changing the hyperparameters of a differentially private algorithm allows one to trade off privacy and utility in a principled way. Quantifying this…

We propose a novel and systematic differentially private (DP) inference framework for non-Euclidean data. First, we design two types of DP mechanisms for the Fr\'echet mean and variance with i.i.d. Riemannian manifold-valued data, tailored…

We develop differentially private hypothesis testing methods for the small sample regime. Given a sample $\cal D$ from a categorical distribution $p$ over some domain $\Sigma$, an explicitly described distribution $q$ over $\Sigma$, some…

Differential Privacy (DP) is a probabilistic framework that protects privacy while preserving data utility. To protect the privacy of the individuals in the dataset, DP requires adding a precise amount of noise to a statistic of interest;…

Differentially private learning on real-world data poses challenges for standard machine learning practice: privacy guarantees are difficult to interpret, hyperparameter tuning on private data reduces the privacy budget, and ad-hoc privacy…

A critical concern in data-driven decision making is to build models whose outcomes do not discriminate against some demographic groups, including gender, ethnicity, or age. To ensure non-discrimination in learning tasks, knowledge of the…

Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However,…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Confidence intervals are a fundamental tool for quantifying the uncertainty of parameters of interest. With the increase of data privacy awareness, developing a private version of confidence intervals has gained growing attention from both…

In modern settings of data analysis, we may be running our algorithms on datasets that are sensitive in nature. However, classical machine learning and statistical algorithms were not designed with these risks in mind, and it has been…

Differential Privacy (DP) provides a rigorous framework for releasing statistics while protecting individual information present in a dataset. Although substantial progress has been made on differentially private linear regression, existing…

Deep learning techniques based on neural networks have shown significant success in a wide range of AI tasks. Large-scale training datasets are one of the critical factors for their success. However, when the training datasets are…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator…

Differentially Private (DP) data release is a promising technique to disseminate data without compromising the privacy of data subjects. However the majority of prior work has focused on scenarios where a single party owns all the data. In…

Differential privacy is the state-of-the-art definition for privacy, guaranteeing that any analysis performed on a sensitive dataset leaks no information about the individuals whose data are contained therein. In this thesis, we develop…

Differential privacy is a privacy measure based on the difficulty of discriminating between similar input data. In differential privacy analysis, similar data usually implies that their distance does not exceed a predetermined threshold.…

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…

Learning a privacy-preserving model from sensitive data which are distributed across multiple devices is an increasingly important problem. The problem is often formulated in the federated learning context, with the aim of learning a single…

Recent years have witnessed growing concerns about the privacy of sensitive data. In response to these concerns, differential privacy has emerged as a rigorous framework for privacy protection, gaining widespread recognition in both…