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JorisMooij11302022
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%HEAD{ NAME="Joris M. Mooij, !PhD" AFFILIATION="Professor in Mathematical Statistics</br> Korteweg-De Vries Institute for Mathematics </br> University of Amsterdam" TITLE="Towards Markov Properties for Differential-Algebraic Equations" IMAGELINK="https://staff.fnwi.uva.nl/j.m.mooij/prof_mooij_small.jpg" }% Real-world systems---both static and dynamic---are often modelled by differential-algebraic equations (DAEs), systems of equations in which first and higher-order derivatives may appear. Well-known examples are chemical reactions, electric circuits and constrained mechanical systems. DAEs generalize systems of (ordinary, algebraic) equations as well as ordinary differential equations. Stochasticity can be introduced via exogenous variables and initial states. However, DAEs have no intrinsic notion of causality, unlike for example structural (dynamical) causal models. We show how the structure of the equations nonetheless gives rise to Markov properties by means of Simon's causal ordering algorithm and the Dulmage-Mendelsohn decomposition, thereby extending well-known Markov properties for directed graphical models to DAEs represented by bipartite graphs. As an immediate consequence, we obtain possible causal interpretations of the DAE as well as formal causal reasoning methods for domain adaptation that extend Pearl's do-calculus. Our approach also provides the building blocks towards generalizing identification methods (such as Tian's ID algorithm) and constraint-based causal discovery (such as the FCI algorithm) towards a very general class of (possibly) cyclic and (possibly) dynamical systems. %TAIL{DATE="30 November 2022"}% <!-- * Set HEAD = <div class="w3-card-2" id="task" style="max-width:750px; margin-left: 0px;"> <header class="w3-container w3-blue" style="padding:40px"><h1>Biostatistics Weekly Seminar</h1><br><h2 style="color:white;">%TITLE%<br><br>%NAME%<br>%AFFILIATION%</h2></header><div class="w3-container" style="padding:40px"><IMG SRC=%IMAGELINK% align="left" id="mug"/> * Set TAIL = <br><h3>Zoom (Link to Follow)<br>%DATE%<br>1:30pm</h3></div></div><br>[[%TOPIC%Itinerary][Speaker Itinerary]] --> <style> .w3-card-2,.w3-example{box-shadow:0 2px 4px 0 rgba(0,0,0,0.16),0 2px 10px 0 rgba(0,0,0,0.12)!important} .w3-blue,.w3-hover-blue:hover{color:#fff!important;background-color:#2196F3!important} .w3-container{padding:0.01em 16px} .foswikiTopic {font-family: 'Open Sans', sans-serif;} /* Removes location hierarchy (usually written in grey text) */ .patternHomePath {display:none;} /* Removes bar with edit and attach buttons and location hierarchy */ .patternTop{display:none;} h1, h2, h3, h4, h5, h6{font-family: 'Montserrat','Open Sans', sans-serif;font-weight:700;} h1, h2, h3, h4, h5, h6{color:#bf1735;} h1:first-of-type{color:#2a3e6e;margin-bottom:25px;margin-top:5px;} .foswikiImage{margin-left:-9px;} img#mug{padding-right: 40px; padding-bottom:25px; height:250px;} </style>
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Topic revision: r1 - 18 Nov 2022,
CierraStreeter
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