
Submodular Function Optimization 1.0 File ID: 80097 


 Submodular Function Optimization 1.0 License: Freeware File Size: 266.2 KB Downloads: 12
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Submodular Function Optimization 1.0 Description 

Description: Matlab Toolbox for Submodular Function Optimization (v 2.0)
By Andreas Krause (krausea@gmail.com). Slides, videos and detailed references available at http://www.submodularity.org
Tested in MATLAB 7.0.1 (R14), 7.2.0 (R2006a), 7.4.0 (R2007a, MAC), 7.9.0 (MAC)
This toolbox provides functions for optimizing submodular set functions, i.e., functions that take a subset A of a finite ground set V to the real numbers, satisfying
$$F(A)+F(B)geq F(Acup B)+F(Acap B)$$
It also presents several examples of applying submodular function optimization to important machine learning problems, such as clustering, inference in probabilistic models and experimental design. There is a demo script: sfo_tutorial.m
Some information on conventions:
All algorithms will use function objects (see sfo_tutorial.m for examples). For example, to measure variance reduction in a Gaussian model, call F = sfo_fn_varred(sigma,V) where sigma is the covariance matrix and V is the ground set, e.g., 1:size(sigma,1) They will also take an index set V, and A must be a subset of V.
Implemented algorithms:
1) Minimization:
* sfo_min_norm_point: Fujishige's minimumnormpoint algorithm for minimizing general submodular functions * sfo_queyranne: Queyranne's algorithm for minimizing symmetric submodular functions * sfo_ssp: Submodularsupermodular procedure of Narasimhan & Bilmes for minimizing the difference of two submodular functions * sfo_s_t_min_cut: For solving min F(A) s.t. s in A, t not in A * sfo_minbound: Return an online bound on the minimum solution * sfo_greedy_splitting: Greedy splitting algorithm for clustering of Zhao et al
2) Maximization:
* sfo_polyhedrongreedy: For solving an LP over the submodular polytope * sfo_greedy_lazy: The greedy algorithm for constrained maximization / coverage using lazy evaluations * sfo_greedy_welfare: The greedy algorithm for solving allocation problems * sfo_cover: Greedy coverage algorithm using lazy evaluations * sfo_celf: The CELF algorithm of Leskovec et al. for budgeted maximization * sfo_ls_lazy: Local search algorithm for maximizing nonnegative submodular functions * sfo_saturate: The _SATURATE_ algorithm of Krause et al. for robust optimization of submodular functions * sfo_max_dca_lazy: The Data Correcting algorithm of Goldengorin et al. for maximizing general (not necessarily nondecreasing) submodular functions * sfo_maxbound: Return an online bound on the maximum solution * sfo_pspiel: pSPIEL algorithm for trading off information and communication cost * sfo_pspiel_orienteering: pSPIEL algorithm for submodular orienteering * sfo_balance: eSPASS algorithm for simultaneous placement and balanced scheduling
3) Miscellaneous
* sfo_lovaszext: Computes the Lovasz extension for a submodular function * sfo_mi_cluster: Example clustering algorithm using both maximization and minimization * sfo_pspiel_get_path: Convert a tree into a path using the MST heuristic algorithm * sfo_pspiel_get_cost: Compute the Steiner cost of a tree / path
4) Submodular functions:
* sfo_fn_cutfun: Cut function * sfo_fn_detect: Outbreak detection / facility location * sfo_fn_infogain: Information gain about gaussian random variables * sfo_fn_entropy: Entropy of Gaussian random variables * sfo_fn_mi: Gaussian mutual information * sfo_fn_varred: Variance reduction (truncatable, for use in SATURATE) * sfo_fn_example: Twoelement submodular function example from tutorial slides * sfo_fn_iwata: Iwata's test function for testing minimization code * sfo_fn_ising: Energy function for Ising model for image denoising * sfo_fn_residual: For defining residual submodular functions * sfo_fn_invert: For defining F(A) = F'(VA)F(V) * sfo_fn_lincomb: For defining linear combinations of submodular functions
If you use the toolbox for your research, please cite A. Krause. "SFO: A Toolbox for Submodular Function Optimization". Journal of Machine Learning Research (2010).
License: Freeware Related: they will also, important machine, Toolbox, submodular polytope, saturate algorithm, steiner cost, measure variance, Real, trading information, tree path submodular, toolbox functions, toolbox submodular, real numbers, mst heuristic, testing minimization O/S:BSD, Linux, Solaris, Mac OS X File Size: 266.2 KB Downloads: 12


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