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, ...
• Added additional documentation and more examples
• Now Octave ready

BibTeX Entry: Download

Corresponding Paper BibTeX Entry: Download

Supported Operating Systems: Linux, Macosx, Windows

Data Formats: Matlab, Octave

Tags: Matlab, Active Learning, Optimization, Markov Random Fields, Experimental Design, Submodularity

Archive: download here

Other available revisons

Version	Changelog	Date
2.0	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, ... Added additional documentation and more examples Now Octave ready	March 24, 2010, 05:58:23
1.0	Initial Announcement on mloss.org.	July 3, 2009, 20:02:01

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