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This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…

Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off…

The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…

Identifying meaningful relationships between the price movements of financial assets is a challenging but important problem in a variety of financial applications. However with recent research, particularly those using machine learning and…

High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…

In this paper, we propose an information-theoretic approach to design the functional representations to extract the hidden common structure shared by a set of random variables. The main idea is to measure the common information between the…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations…

There is a growing need for the ability to analyse interval-valued data. However, existing descriptive frameworks to achieve this ignore the process by which interval-valued data are typically constructed; namely by the aggregation of…

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…

High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems…

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…

Many real-world networks are known to exhibit facts that counter our knowledge prescribed by the theories on network creation and communication patterns. A common prerequisite in network analysis is that information on nodes and links will…

Despite substantial progress in promoting fairness in high-stake applications using machine learning models, existing methods often modify the training process, such as through regularizers or other interventions, but lack formal guarantees…

Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite…

This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods…

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…

Economists are blessed with a wealth of data for analysis, but more often than not, values in some entries of the data matrix are missing. Various methods have been proposed to handle missing observations in a few variables. We exploit the…