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We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
In recent years, geotagged social media has become popular as a novel source for geographic knowledge discovery. Ground-level images and videos provide a different perspective than overhead imagery and can be applied to a range of…
Multifractal formalisms provide an apt framework to study random cascades in which multifractal spectrum width $\Delta\alpha$ fluctuates depending on the number of estimable power-law relationships. Then again, multifractality without…
Investigation of the underlying physics or biology from empirical data requires a quantifiable notion of similarity - when do two observed data sets indicate nearly identical generating processes, and when they do not. The discriminating…
This topic review communicates working experiences regarding interaction of a multiplicity of processes. Our experiences come from climate change modelling, materials science, cell physiology and public health, and macroeconomic modelling.…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
We study the fluctuations in the measured atmospheric CO2 records from several stations and show that it displays 1/f noise and multifractality. Using detrended fluctuation analysis and wavelet based methods, we estimate thescaling…
Climate science has become more ambitious in recent years as global awareness about the environment has grown. To better understand climate, historical climate (e.g. archived meteorological variables such as temperature, wind, water, etc.)…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods…
In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…
This paper reviews recent advances in missing data research using graphical models to represent multivariate dependencies. We first examine the limitations of traditional frameworks from three different perspectives: \textit{transparency,…
Since the behavior of a neural network model is adversely affected by a lack of diversity in training data, we present a method that identifies and explains such deficiencies. When a dataset is labeled, we note that annotations alone are…
Network-based analyses of dynamical systems have become increasingly popular in climate science. Here we address network construction from a statistical perspective and highlight the often ignored fact that the calculated correlation values…
This work considers the problem of fitting functional models with sparsely and irregularly sampled functional data. It overcomes the limitations of the state-of-the-art methods, which face major challenges in the fitting of more complex…
International comparisons of hierarchical time series data sets based on survey data, such as annual country-level estimates of school enrollment rates, can suffer from large amounts of missing data due to differing coverage of surveys…
Missing data is a ubiquitous problem. It is especially challenging in medical settings because many streams of measurements are collected at different - and often irregular - times. Accurate estimation of those missing measurements is…
Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…
Wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data with poorly characterized errors. Most work on functional data views the data as smooth, latent curves obtained at discrete…
We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…