274 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
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
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Correlating Theory and Practice in Finding Clubs and Plexes
For solving NP-hard problems there is often a huge gap between theoretical guarantees and observed running times on real-world instances. As a first step towards tackling this issue, we propose an approach to quantify the correlation between theoretical and observed running times.
We use two NP-hard problems related to finding large "cliquish" subgraphs in a given graph as demonstration of this measure. More precisely, we focus on finding maximum s-clubs and s-plexes, i. e., graphs of diameter s and graphs where each vertex is adjacent to all but s vertices. Preprocessing based on Turing kernelization is a standard tool to tackle these problems, especially on sparse graphs. We provide a parameterized analysis for the Turing kernelization and demonstrate their usefulness in practice. Moreover, we demonstrate that our measure indeed captures the correlation between these new theoretical and the observed running times
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 has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. 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 data-driven causal and equation discovery, point out connections, and showcase comprehensive 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 revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems
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