9 research outputs found
D'ya like DAGs? A Survey on Structure Learning and Causal Discovery
Causal reasoning is a crucial part of science and human intelligence. In
order to discover causal relationships from data, we need structure discovery
methods. We provide a review of background theory and a survey of methods for
structure discovery. We primarily focus on modern, continuous optimization
methods, and provide reference to further resources such as benchmark datasets
and software packages. Finally, we discuss the assumptive leap required to take
us from structure to causality.Comment: 35 page
Graphical models for de novo and pathway-based network prediction over multi-modal high-throughput biological data
It is now a standard practice in the study of complex disease to perform many high-throughput -omic experiments (genome wide SNP, copy number, mRNA and miRNA expression) on the same set of patient samples. These multi-modal data should allow researchers to form a more complete, systems-level picture of a sample, but this is only possible if they have a suitable model for integrating the data. Due to the variety of data modalities and possible combinations of data, general, flexible integration methods that will be widely applicable in many settings are desirable. In this dissertation I will present my work using graphical models for de novo structure learning of both undirected and directed sparse graphs over a mixture of Gaussian and categorical variables. Using synthetic and biological data I will show that these models are useful for both variable selection and inference. Selecting the regularization parameters is an important challenge for these models so I will also cover stability based methods for efficiently setting these parameters, and for controlling the false discovery rate of edge predictions. I will also show results from a biological application to data from metastatic melanoma patients where our methods identified a PARP1 slice site variant that is predictive of response to chemotherapy. Finally, I present work incorporating miRNA into a pathway based graphical model called PARADIGM. This extension of the model allows us to study patient-specific changes in miRNA induced silencing in cancer
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
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
Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations
The network structure (or topology) of a dynamical network is often
unavailable or uncertain. Hence, we consider the problem of network
reconstruction. Network reconstruction aims at inferring the topology of a
dynamical network using measurements obtained from the network. In this
technical note we define the notion of solvability of the network
reconstruction problem. Subsequently, we provide necessary and sufficient
conditions under which the network reconstruction problem is solvable. Finally,
using constrained Lyapunov equations, we establish novel network reconstruction
algorithms, applicable to general dynamical networks. We also provide
specialized algorithms for specific network dynamics, such as the well-known
consensus and adjacency dynamics.Comment: 8 page