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# Zoekresultaten

Zoekopdracht: faculteit: "FNWI" en publicatiejaar: "2007"

 Auteur Wouter Koolen Titel Discovering the truth by conducting experiments Jaar 2007 Faculteit Faculteit der Natuurwetenschappen, Wiskunde en Informatica Instituut/afd. FNWI/FGw: Institute for Logic, Language and Computation (ILLC) Serie ILLC Master of Logic Theses / ILLC ; MoL-2007-02 Samenvatting Discovering the truth by conducting experimentsWouter KoolenAbstract:Paul Vitanyi's 2003 Kolmogorov complexity lecture included a computerexercise in which a polynomial relation had to be learnt fromsamples.1 The following data were provided: a sequence of pairs ofnumbers (h1, d1), (h2, d2), . . . , (hn, dn), supposedly noisymeasurements of a classical urn, hi being the height from the floorand di being the diameter of the urn at the height hi. The goal was toinfer a polynomial that represented the relation between height anddiameter. For a given degree, this can easily be done using linearalgebra. The crux of the exercise was finding the best degree.To me, learning from given data is only part of a more general conceptof learning, and I started to wonder whether the techniques that Ilearnt during my studies could be adapted to an interactive setting,allowing the learner to perform experiments. For example, whenlearning polynomials, the learner could be allowed to choose a point,and she would then receive the value of the polynomial at that point.For this thesis, I started working on the interactive polynomiallearning problem, but it turned out to be much too hard. I thendevised the balance scale problem, a toy problem that conserves theimportant features of the polynomial learning problem: it isinteractive, probabilistic, model-based, but finite. I had by thendeveloped a slight aversion to subjective Bayesian methods, for myinitial work on the polynomial learning problem suggested that theyare not robust. It seemed that a subjective Bayesian learner can betricked into assigning high posterior probability to a certainproposition while this proposition is false, and additionally, greatconfidence in this proposition leads to great confidence in theusefulness of experiments that in fact do not help to determine thatthis proposition is false.With this in mind, I decided to perform a worst-case analysis of thebalance scale problem, and of similar problems in general. Thisproblem naturally decomposed into the truth-finding problem, where wewant to find the true model from given data, and the experiment-designproblem, where experiments have to be selected, whose outcomessubsequently serve as the data for truth finding.I have yet to solve the balance scale problem completely. But I havealready learned and discovered much more than I could initiallyimagine. I hope that this thesis will provide inspiration to others. Soort document Preprint Download document/443388 Document finder