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Synthetic data are becoming a critical tool for building artificially intelligent systems. Simulators provide a way of generating data systematically and at scale. These data can then be used either exclusively, or in conjunction with real…
Data discovery is crucial for data management and analysis and can benefit from better utilization of metadata. For example, users may want to search data using queries like ``find the tables created by Alex and endorsed by Mike that…
Big data is no more "all just hype" but widely applied in nearly all aspects of our business, governments, and organizations with the technology stack of AI. Its influences are far beyond a simple technique innovation but involves all rears…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
We provide a MATLAB toolbox, BFDA, that implements a Bayesian hierarchical model to smooth multiple functional data with the assumptions of the same underlying Gaussian process distribution, a Gaussian process prior for the mean function,…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
Big data is data that exceeds the processing capacity of traditional databases. The data is too big to be processed by a single machine. New and innovative methods are required to process and store such large volumes of data. This paper…
The history of data analysis that is addressed here is underpinned by two themes, -- those of tabular data analysis, and the analysis of collected heterogeneous data. "Exploratory data analysis" is taken as the heuristic approach that…
Data augmentation, by the introduction of auxiliary variables, has become an ubiquitous technique to improve convergence properties, simplify the implementation or reduce the computational time of inference methods such as Markov chain…
Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…
Loss Data Analytics is an interactive, online, freely available text. The idea behind the name Loss Data Analytics is to integrate classical loss data models from applied probability with modern analytic tools. In particular, we seek to…
Data are rapidly growing in size and importance for society, a trend motivated by their enabling power. The accumulation of new data, sustained by progress in technology, leads to a boundless expansion of stored data, in some cases with an…
As the adoption of Artificial Intelligence (AI) models expands into critical real-world applications, ensuring the explainability of these models becomes paramount, particularly in sensitive fields such as medicine and finance. Linear…
Extracting information from functional magnetic resonance (fMRI) images has been a major area of research for more than two decades. The goal of this work is to present a new method for the analysis of fMRI data sets, that is capable to…
"Data" is becoming an indispensable production factor, just like land, infrastructure, labor or capital. As part of this, a myriad of applications in different sectors require huge amounts of information to feed models and algorithms…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
We argue that while this discourse on data ethics is of critical importance, it is missing one fundamental point: If more and more efforts in business, government, science, and our daily lives are data-driven, we should pay more attention…
This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been…
A method for representing the digest information of each dataset is proposed, oriented to the aid of innovative thoughts and the communication of data users who attempt to create valuable products, services, and business models using or…