http://bactra.org/notebooks Cosma's Notebooks en http://bactra.org/notebooks/2009/04/10#structured-data <P>A lot of <a href="statistics.html">statistical theory and methods</a> are developed for fairly unstructred data --- each data-point is just that, a single unarticulated point in some space. What to do when observations have complicated internal structure? <P>One option: Break the structures into a collection of <em>dependent</em> unstructured observations, i.e., each observation is a realization of a non-trivial stochastic process. Examples: multivariate analysis (including its grown-up version, <a href="graphical-models.html">graphical models</a>), <a href="time-series.html">time series</a>, <a href="spatial-statistics.html">spatial statistics</a>, <a href="network-data-analysis.html">network data analysis</a>. Time series and spatial statistics are much better developed than network statistics not least because the dependency structures there are <em>much simpler</em>. Directed networks give us essentially arbitrary binary relations; hypergraphs arbitrary relational structures. This threatens (or promises) to bring up all sorts of issues from <a href="mathematical-logic.html">logic</a>. <P>Can one do inference on the relational structure of complex observations? How? (<a href="grammatical-inference.html">Grammatical inference</a>, for instance? <a href="community-discovery.html">Community discovery<a>?) <P>See also: <a href="data-mining.html">Data Mining</a>; <a href="learning-inference-induction.html">Machine Learning, Statistical Inference and Induction</a> <ul>Recommended, big-picture: <li><a href="http://www.cs.umd.edu/~getoor/">Lise Getoor</a> and Ben Taskar (eds.), <cite>Introduction to Statistical Relational Learning</cite> [<a href="http://mitpress.mit.edu/978-0-262-07288-5">Official blurb</a>, Lise's <a href="http://www.cs.umd.edu/srl-book/">book site</a> with more links] <li>Ulf Grenander, <cite>Elements of Pattern Theory</cite> </ul> <ul>Recommended, miscellaneous close-ups: <li>Tommi S. Jaakkola and David Haussler, "Exploiting generative models in discriminative classifiers", <cite>NIPS 11</cite> (1998) [<a href="http://books.nips.cc/papers/files/nips11/0487.pdf">PDF</a>] <li>Leonid Peshkin, "Structure induction by lossless graph compression", <a href="http://arxiv.org/abs/cs.DS/0703132">cs.DS/0703132</a> [Adapting data-compression ideas to discover hierarchical structures in graphs, e.g., the 4 bases from a tinker-toy model of DNA.] </ul> <ul>To read: <li>Yonatan Amit, Shai Shalev-Shwartz, Yoram Singer, "Online Learning of Complex Prediction Problems Using Simultaneous Projections", <a href="http://jmlr.csail.mit.edu/papers/v9/amit08a.html"><cite>Journal of Machine Learning Research</cite> <strong>9</strong> (2008): 1399--1435</a> <li>G&ouml;khan Bakir, Thomas Hofmann, Bernhard Sch&ouml;lkopf, Alexander J. Smola, Ben Taskar and S. V. N. Vishwanathan (eds.), <cite>Predicting Structred Data</cite> [<a href="http://mitpress.mit.edu/978-0-262-02617-8">blurb</a>] <li>Peter J. Green, Peter, Nils Lid Hjort and Sylvia Richardson (eds.), <cite>Highly Structured Stochastic Systems</cite> <li>Ulf Grenander and Michael Miller, <cite>Pattern Theory: From Representation to Inference</cite> <li>Fionn Murtagh, "Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy", <a href="http://arxiv.org/abs/0805.2744">arxiv:0805.2744</a> <li>Marlos A. G. Viana, <cite>Symmetry Studies: An Introduction to the Analysis of Structured Data in Applications</cite> [<a href="http://cambridge.org/9780521841030">blurb</a>] <li>Haonan Wang, J. S. Marron, "Object oriented data analysis: Sets of trees", <a href="http://arxiv.org/abs/0711.3147">arxiv:0711.3147</a> ["Object oriented data analysis is the statistical analysis of populations of complex objects"] </ul>