Related papers: Inference of a Dyadic Measure and its Simplicial G…

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that…

The need to analyze sensitive data, such as medical records or financial data, has created a critical research challenge in recent years. In this paper, we adopt the framework of differential privacy, and explore mechanisms for generating…

Structural and functional neuroimaging modalities provide complementary windows into brain organization: structural imaging characterizes neural tissue anatomy and microstructure, while functional imaging captures dynamic patterns of neural…

Private synthetic data sharing is preferred as it keeps the distribution and nuances of original data compared to summary statistics. The state-of-the-art methods adopt a select-measure-generate paradigm, but measuring large domain…

We present a novel discrete optimization-based approach to generate downsampled versions of binary images that are guaranteed to have the same topology as the original, measured by the zeroth and first Betti numbers of the black regions,…

Differential privacy (DP) has arisen as the gold standard in protecting an individual's privacy in datasets by adding calibrated noise to each data sample. While the application to categorical data is straightforward, its usability in the…

Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply…

We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…

Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. In…

We provide a differentially private algorithm for producing synthetic data simultaneously useful for multiple tasks: marginal queries and multitask machine learning (ML). A key innovation in our algorithm is the ability to directly handle…

This paper presents a generic probabilistic framework for estimating the statistical dependency and finding the anatomical correspondences among an arbitrary number of medical images. The method builds on a novel formulation of the…

We extend the log-mean linear parameterization introduced by Roverato et al. (2013) for binary data to discrete variables with arbitrary number of levels, and show that also in this case it can be used to parameterize bi-directed graph…

Differential Privacy (DP) is being increasingly adopted for non-Euclidean data that lie on complex, high-dimensional manifolds. Existing DP mechanisms for manifold data consider geometric properties when calibrating privacy perturbations,…

Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a…

We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require…

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…

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.…

We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…

Parameter estimation in statistics and system identification relies on data that may contain sensitive information. To protect this sensitive information, the notion of \emph{differential privacy} (DP) has been proposed, which enforces…

Measures of dependence among variables, and measures of information content and shared information have become valuable tools of multi-variable data analysis. Information measures, like marginal entropies, mutual and multi-information, have…