Related papers: On Differentially Private Subspace Estimation in a…
We study parametric change-point detection, where the goal is to identify distributional changes in time series, under local differential privacy. In the non-private setting, we derive improved finite-sample accuracy guarantees for a…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such…
A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same…
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
Data engineering often requires accuracy (utility) constraints on results, posing significant challenges in designing differentially private (DP) mechanisms, particularly under stringent privacy parameter $\epsilon$. In this paper, we…
This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…
We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
Despite the potential of differentially private data visualization to harmonize data analysis and privacy, research in this area remains underdeveloped. Boxplots are a widely popular visualization used for summarizing a dataset and for…
The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
We propose a multifidelity dimension reduction method to identify a low-dimensional structure present in many engineering models. The structure of interest arises when functions vary primarily on a low-dimensional subspace of the…
We propose an axiomatic approach to the concept of an intrinsic dimension of a dataset, based on a viewpoint of geometry of high-dimensional structures. Our first axiom postulates that high values of dimension be indicative of the presence…
Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s^*$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(s^{*}d / nm\varepsilon^2)$. This can be…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Concern about how to aggregate sensitive user data without compromising individual privacy is a major barrier to greater availability of data. The model of differential privacy has emerged as an accepted model to release sensitive…
The rapid development of affordable and compact high-fidelity sensors (e.g., cameras and LIDAR) allows robots to construct detailed estimates of their states and environments. However, the availability of such rich sensor information…