Project details for Matlab toolbox for submodular function optimization

## Matlab toolbox for submodular function optimization 2.0

by krausea - April 7, 2010, 09:53:40 CET [ ]

Description:

Matlab Toolbox for Submodular Function Optimization

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).

A note on Octave compatibility:

This toolbox also works under Octave; however, since Octave handles function objects differently from Matlab. Use the function sfo_octavize to make a submodular function object Octave ready; type 'help sfo_octavize' for more information. The script sfo_tutorial_octave has been tested under Octave 3.2.3

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 minimum-norm-point algorithm for minimizing general submodular functions
• sfo_queyranne: Queyranne's algorithm for minimizing symmetric submodular functions
• sfo_sssp: Submodular-supermodular 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_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: Two-element 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
Changes to previous version:
• Modified specification of optional parameters (using sfo_opt)
• Added sfo_ls_lazy for maximizing nonnegative submodular functions
• Added sfo_fn_infogain, sfo_fn_lincomb, sfo_fn_invert, ...