40 research outputs found
Sparse Learning for Variable Selection with Structures and Nonlinearities
In this thesis we discuss machine learning methods performing automated
variable selection for learning sparse predictive models. There are multiple
reasons for promoting sparsity in the predictive models. By relying on a
limited set of input variables the models naturally counteract the overfitting
problem ubiquitous in learning from finite sets of training points. Sparse
models are cheaper to use for predictions, they usually require lower
computational resources and by relying on smaller sets of inputs can possibly
reduce costs for data collection and storage. Sparse models can also contribute
to better understanding of the investigated phenomenons as they are easier to
interpret than full models.Comment: PhD thesi
Discovering Causal Relations and Equations from Data
Physics is a field of science that has traditionally used the scientific
method to answer questions about why natural phenomena occur and to make
testable models that explain the phenomena. Discovering equations, laws and
principles that are invariant, robust and causal explanations of the world has
been fundamental in physical sciences throughout the centuries. Discoveries
emerge from observing the world and, when possible, performing interventional
studies in the system under study. With the advent of big data and the use of
data-driven methods, causal and equation discovery fields have grown and made
progress in computer science, physics, statistics, philosophy, and many applied
fields. All these domains are intertwined and can be used to discover causal
relations, physical laws, and equations from observational data. This paper
reviews the concepts, methods, and relevant works on causal and equation
discovery in the broad field of Physics and outlines the most important
challenges and promising future lines of research. We also provide a taxonomy
for observational causal and equation discovery, point out connections, and
showcase a complete set of case studies in Earth and climate sciences, fluid
dynamics and mechanics, and the neurosciences. This review demonstrates that
discovering fundamental laws and causal relations by observing natural
phenomena is being revolutionised with the efficient exploitation of
observational data, modern machine learning algorithms and the interaction with
domain knowledge. Exciting times are ahead with many challenges and
opportunities to improve our understanding of complex systems.Comment: 137 page