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ICML experiments/Partition func & temperature


TT-MRF is a library for Markov random field inference with Tensor Train decomposition approach. The code is published in support to the following paper:

Putting MRFs on a Tensor Train
Alexander Novikov, Anton Rodomanov, Anton Osokin, Dmitry Vetrov; In Proceedings of The 31st International Conference on Machine Learning (ICML-2014) [paper] [suppl.] [poster].

Please cite it if you write scientific paper using this code.
In BiBTeX format:

  author    = {Novikov, Alexander and Rodomanov, Anton and Osokin, Anton and Vetrov, Dmitry},
  title     = {Putting {MRF}s on a {T}ensor {T}rain},
  journal   = {Proceedings of The 31st International Conference on Machine Learning},
  year      = {2014},


Install the TT-Toolbox (just download it and run setup.m to add everything important to MATLAB path).

Run setup.m to add required folders to MATLAB path.

Optional dependencies

If you want to compare with state-of-the-art techniques for computing partition function and marginal distributions, install LibDAI library with the MATLAB support.

If you need access to state-of-the-art MAP-inference routines OR want to be able to load models in OpenGM format, install OpenGM with MATLAB, HDF5, TRW-S and Maxflow support. Example bash input for compiling OpenGM:

cd opengm_folder

Model format

We use custom graphical model instance format. You can build problems like this:

% Build 5x4 grid spin glass model with temperature = 2.
Model = generate_spin_glass_model(5, 4, 2);

% Load model in OpenGM format.
Model = load_opengm_model('examples/geosurf.h5');

% Load model in uai format.
Model = load_uai_model('examples/spinglass.uai');

Format details:

Model.libdaiFactors     [Cell array] factors of the model in the LibDAI format
Model.numNodes          [Number] number of Model variables
Model.modeSizes         [Vector 1 x d] sizes of variables (e.g. x_1 is from {1, ..., modeSizes(1)})
Model.description       [String] text description
Model.type              [String] Type: 'Spin glass', 'OpenGM' or 'UAI'

% Problem specific, spin glass
Model.grid_n            [Number] vertical size of spin glass model grid
Model.grid_m            [Number] horizontal size of spin glass model grid
Model.temperature       [Number]
Model.unaryWeights      [Matrix n x m]
Model.unaryType         [String] 'number' if all unary weights equals to one number;
                            'matrix' matrix with unary weights was specified during model generation;
                            'rand' if weights were generated from uniform distribution
Model.unaryDistr        [Vector 1 x 2] unary wights uniform distribution support
                                          (e.g. [-1, 1] means that weights are from U(-1, 1))
Model.edgeWeights       [Vector numEdges x 1] all pairwise weights
Model.edgeType          [String] 'number' or 'rand', see details in unryType description
Model.edgesDistr        [Vector 1 x 2] pairwise weight uniform distribution support

Example code

% Build 5x4 grid spin glass model with temperature = 2
% and pairwise weights generated from uniform distribution on [0, 1].
Model = generate_spin_glass_model(5, 4, 2, 'J', 'rand', 'J_distr', [0, 1]);

% Compute logarithm of the partition function using Tensor Train approach
% with rounding precision equals 1e-6.
logZ = compute_log_z(Model, 1e-6);

% Compute logarithm of the partition function using junction tree method from the libDAI library.
[logZ_JT, ~, ~] = dai_jtree(Model.libdaiFactors, { 1 }, '[updates=HUGIN]');

relError = (logZ_JT - logZ) / logZ_JT;
disp(['Computed logarithm of the partition function with relative error ', num2str(relError)])