Exact Fractional Inference via Re-Parametrization & Interpolation between Tree-Re-Weighted- and Belief Propagation- Algorithms
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Computing the partition (Z) of an Ising models over a graph of N spins are most likely exponential in N. Efficient variational methods, such as Belief Propagation (BP) and Tree Re-Weighted (TRW) algorithms, compute Z approximately minimizing respective (BP- or TRW-) free energy. In this presentation, we generalize fractional free energy and interpolate between TRW and BP to find the exact value of partition function. Our new model has some interesting properties such as monotonicity and convexity with respect to the fractional parameters. Finally, we provide numerical experiments to validate the theory and discuss interesting venues and applications.
Place: Math, 402 and Zoom: Link https://arizona.zoom.us/j/83541348598 Password: BB2022