Carlos Y. Soto

Carlos Soto, Karthik Bharath, Matthew Reimherr et al.

It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold. The utility of a mechanism to produce sanitized differentially private estimates from such data is intimately linked to how compatible it is with the underlying structure and geometry of the space. In particular, as recently shown, utility of the Laplace mechanism on a positively curved manifold, such as Kendall's 2D shape space, is significantly influences by the curvature. Focusing on the problem of sanitizing the Fréchet mean of a sample of points on a manifold, we exploit the characterisation of the mean as the minimizer of an objective function comprised of the sum of squared distances and develop a K-norm gradient mechanism on Riemannian manifolds that favors values that produce gradients close to the the zero of the objective function. For the case of positively curved manifolds, we describe how using the gradient of the squared distance function offers better control over sensitivity than the Laplace mechanism, and demonstrate this numerically on a dataset of shapes of corpus callosa. Further illustrations of the mechanism's utility on a sphere and the manifold of symmetric positive definite matrices are also presented.

Daniel Potemkin, Carlos Soto, Ruipeng Li et al.

The extraordinarily high X-ray flux and specialized instrumentation at synchrotron beamlines have enabled versatile in-situ and high throughput studies that are impossible elsewhere. Dexterous and efficient control of experiments are thus crucial for efficient beamline operation. Artificial intelligence and machine learning methods are constantly being developed to enhance facility performance, but the full potential of these developments can only be reached with efficient human-computer-interaction. Natural language is the most intuitive and efficient way for humans to communicate. However, the low credibility and reproducibility of existing large language models and tools demand extensive development to be made for robust and reliable performance for scientific purposes. In this work, we introduce the prototype of virtual scientific companion (VISION) and demonstrate that it is possible to control basic beamline operations through natural language with open-source language model and the limited computational resources at beamline. The human-AI nature of VISION leverages existing automation systems and data framework at synchrotron beamlines.

Aditya Kulkarni, Carlos Soto

In statistical applications it has become increasingly common to encounter data structures that live on non-linear spaces such as manifolds. Classical linear regression, one of the most fundamental methodologies of statistical learning, captures the relationship between an independent variable and a response variable which both are assumed to live in Euclidean space. Thus, geodesic regression emerged as an extension where the response variable lives on a Riemannian manifold. The parameters of geodesic regression, as with linear regression, capture the relationship of sensitive data and hence one should consider the privacy protection practices of said parameters. We consider releasing Differentially Private (DP) parameters of geodesic regression via the K-Norm Gradient (KNG) mechanism for Riemannian manifolds. We derive theoretical bounds for the sensitivity of the parameters showing they are tied to their respective Jacobi fields and hence the curvature of the space. This corroborates recent findings of differential privacy for the Fréchet mean. We demonstrate the efficacy of our methodology on the sphere, $\mbS^2\subset\mbR^3$ and, since it is general to Riemannian manifolds, the manifold of Euclidean space which simplifies geodesic regression to a case of linear regression. Our methodology is general to any Riemannian manifold and thus it is suitable for data in domains such as medical imaging and computer vision.