thesis published Filip Korc author 476A2FD6-F248-11E8-B48F-1D18A9856A87 Vladimir Kolmogorov author 3D50B0BA-F248-11E8-B48F-1D18A9856A87 Christoph Lampert author 40C20FD2-F248-11E8-B48F-1D18A9856A870000-0001-8622-7887 VlKo department ChLa department We consider the problem of inference in agraphical model with binary variables. While in theory it is arguably preferable to compute marginal probabilities, in practice researchers often use MAP inference due to the availability of efficient discrete optimization algorithms. We bridge the gap between the two approaches by introducing the Discrete Marginals technique in which approximate marginals are obtained by minimizing an objective function with unary and pair-wise terms over a discretized domain. This allows the use of techniques originally devel-oped for MAP-MRF inference and learning. We explore two ways to set up the objective function - by discretizing the Bethe free energy and by learning it from training data. Experimental results show that for certain types of graphs a learned function can out-perform the Bethe approximation. We also establish a link between the Bethe free energy and submodular functions. https://research-explorer.ista.ac.at/download/5396/5490/IST-2012-0003_IST-2012-0003.pdf application/pdfno IST Austria2012 eng 2664-169010.15479/AT:IST-2012-0003 13 https://research-explorer.ista.ac.at/record/3124 F. Korc, V. Kolmogorov, C. Lampert, Approximating Marginals Using Discrete Energy Minimization, IST Austria, 2012. Korc, Filip, et al. <i>Approximating Marginals Using Discrete Energy Minimization</i>. IST Austria, 2012, doi:<a href="https://doi.org/10.15479/AT:IST-2012-0003">10.15479/AT:IST-2012-0003</a>. Korc, F., Kolmogorov, V., &#38; Lampert, C. (2012). <i>Approximating marginals using discrete energy minimization</i>. IST Austria. <a href="https://doi.org/10.15479/AT:IST-2012-0003">https://doi.org/10.15479/AT:IST-2012-0003</a> F. Korc, V. Kolmogorov, and C. Lampert, <i>Approximating marginals using discrete energy minimization</i>. IST Austria, 2012. Korc, Filip, Vladimir Kolmogorov, and Christoph Lampert. <i>Approximating Marginals Using Discrete Energy Minimization</i>. IST Austria, 2012. <a href="https://doi.org/10.15479/AT:IST-2012-0003">https://doi.org/10.15479/AT:IST-2012-0003</a>. Korc F, Kolmogorov V, Lampert C. <i>Approximating Marginals Using Discrete Energy Minimization</i>. IST Austria; 2012. doi:<a href="https://doi.org/10.15479/AT:IST-2012-0003">10.15479/AT:IST-2012-0003</a> Korc F, Kolmogorov V, Lampert C. 2012. Approximating marginals using discrete energy minimization, IST Austria, 13p. 53962018-12-12T11:39:06Z2024-10-09T20:54:48Z