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Processes in ocean physics, air-sea interaction and ocean biogeochemistry span enormous ranges in spatial and temporal scales, that is, from molecular to planetary and from seconds to millennia. Identifying and implementing sustainable…
In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…
These are lecture notes based on the first part of a course on 'Mathematical Data Science', which I taught to final year BSc students in the UK in 2019-2020. Topics include: concentration of measure in high dimensions; Gaussian random…
In the last decade a new generation of telescopes and sensors has allowed the production of a very large amount of data and astronomy has become, a data-rich science; this transition is often labeled as: "data revolution" and "data…
Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were…
Data science is the business of learning from data, which is traditionally the business of statistics. Data science, however, is often understood as a broader, task-driven and computationally-oriented version of statistics. Both the term…
Modern data and applications pose very different challenges from those of the 1950s or even the 1980s. Students contemplating a career in statistics or data science need to have the tools to tackle problems involving massive, heavy-tailed…
The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to…
Data science requires time-consuming iterative manual activities. In particular, activities such as data selection, preprocessing, transformation, and mining, highly depend on iterative trial-and-error processes that could be sped-up…
Introduction: Even in effectively conducted randomised trials, the probability of a successful study remains relatively low. With recent advances in the next-generation sequencing technologies, there is a rapidly growing number of…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Advances in science are being sought in newly available opportunities to collect massive quantities of data about complex systems. While key advances are being made in detailed mapping of systems, how to relate this data to solving many of…
The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…
Astrophysics and cosmology are rich with data. The advent of wide-area digital cameras on large aperture telescopes has led to ever more ambitious surveys of the sky. Data volumes of entire surveys a decade ago can now be acquired in a…
Emerging Big Data analytics and machine learning applications require a significant amount of computational power. While there exists a plethora of large-scale data processing frameworks which thrive in handling the various complexities of…
Most domains of science are experiencing a paradigm shift due to the advent of a new generation of instruments and detectors which produce data and data streams at an unprecedented rate. The scientific exploitation of these data, namely…
Datasets have played a foundational role in the advancement of machine learning research. They form the basis for the models we design and deploy, as well as our primary medium for benchmarking and evaluation. Furthermore, the ways in which…
Machine learning (ML) is revolutionizing the world, affecting almost every field of science and industry. Recent algorithms (in particular, deep networks) are increasingly data-hungry, requiring large datasets for training. Thus, the…
Differentially private data generation techniques have become a promising solution to the data privacy challenge -- it enables sharing of data while complying with rigorous privacy guarantees, which is essential for scientific progress in…
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…