744 research outputs found
Better predictions when models are wrong or underspecified
Many statistical methods rely on models of reality in order to learn from data and to make predictions about future data. By necessity, these models usually do not match reality exactly, but are either wrong (none of the hypotheses in the model provides an accurate description of reality) or underspecified (the hypotheses in the model describe only part of the data). In this thesis, we discuss three scenarios involving models that are wrong or underspecified. In each case, we find that standard statistical methods may fail, sometimes dramatically, and present different methods that continue to perform well even if the models are wrong or underspecified. The first two of these scenarios involve regression problems and investigate AIC (Akaike's Information Criterion) and Bayesian statistics. The third scenario has the famous Monty Hall problem as a special case, and considers the question how we can update our belief about an unknown outcome given new evidence when the precise relation between outcome and evidence is unknown.UBL - phd migration 201
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
Bounds on the Game Transversal Number in Hypergraphs
Let be a hypergraph with vertex set and edge set of order
\nH = |V| and size \mH = |E|. A transversal in is a subset of vertices
in that has a nonempty intersection with every edge of . A vertex hits
an edge if it belongs to that edge. The transversal game played on involves
of two players, \emph{Edge-hitter} and \emph{Staller}, who take turns choosing
a vertex from . Each vertex chosen must hit at least one edge not hit by the
vertices previously chosen. The game ends when the set of vertices chosen
becomes a transversal in . Edge-hitter wishes to minimize the number of
vertices chosen in the game, while Staller wishes to maximize it. The
\emph{game transversal number}, , of is the number of vertices
chosen when Edge-hitter starts the game and both players play optimally. We
compare the game transversal number of a hypergraph with its transversal
number, and also present an important fact concerning the monotonicity of
, that we call the Transversal Continuation Principle. It is known that
if is a hypergraph with all edges of size at least~, and is not a
-cycle, then \tau_g(H) \le \frac{4}{11}(\nH+\mH); and if is a
(loopless) graph, then \tau_g(H) \le \frac{1}{3}(\nH + \mH + 1). We prove
that if is a -uniform hypergraph, then \tau_g(H) \le \frac{5}{16}(\nH +
\mH), and if is -uniform, then \tau_g(H) \le \frac{71}{252}(\nH +
\mH).Comment: 23 pages
Combinatorics, Probability and Computing
The main theme of this workshop was the use of probabilistic
methods in combinatorics and theoretical computer science. Although
these methods have been around for decades, they are being refined all
the time: they are getting more and more sophisticated and powerful.
Another theme was the study of random combinatorial structures,
either for their own sake, or to tackle extremal questions. The workshop
also emphasized connections between probabilistic combinatorics and
discrete probability
Chromatic numbers of exact distance graphs
For any graph G = (V;E) and positive integer p, the exact distance-p graph G[\p] is the graph with vertex set V , which has an edge between vertices x and y if and only if x and y have distance p in G. For odd p, Nešetřil and Ossona de Mendez proved that for any fixed graph class with bounded expansion, the chromatic number of G[\p] is bounded by an absolute constant. Using the notion of generalised colouring numbers, we give a much simpler proof for the result of Nešetřil and Ossona de Mendez, which at the same time gives significantly better bounds. In particular, we show that for any graph G and odd positive integer p, the chromatic number of G[\p] is bounded by the weak (2
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