Vector-valued Control Variates

Code release for our paper Vector-valued Control Variates.

Requirements

To create identical conda environmentn in MacOS, please run,

conda create --name vvCV --file spec-file.txt

Use VVCVs for your own data

# An example
# Step 1. Initialize vvCV model class
my_vvCV_model = VV_CV_vectorvaluedfuncs_model_MDMP(vv_cv_objective, \
                                                   prior_kernel, base_kernel, \
                                                   Xs_tensor, Ys_tensor, scores_Tensor)
       # """
       # :param vv_cv_objective:  an objective class. Here should be 'penalized_ls_objective_vectorvaluedfunc_MDMP'
       # :param prior_kernel:   a class. Here should be 'stein_matrix_valued_kernel'
       # :param base_kernel:    a class; since we use K = B k, so here this class is scalar-valued kernel class, e.g, base_kernel_2
       # :param Xs_tensor:     3d tensor, T * m * d when assuming all datasets have m points, i.e. m = m_1 =... =m_T
       # :param Ys_tensor:     3d tensor, T * m * 1 when assuming all datasets have m points, i.e. m = m_1 =... =m_T
       # :param scores_Tensor: 4d Tensor, T * m * T * d ; That is, we have T tasks, each has a dataset with sample size m. For each instance x_i, we need a 2d Tensor of size T*d, i.e., dlog\pi_t(x_i)dx_i for t=1, ...T.
       # """

# Step 2. Tune kernel hyper-parameters
my_vvCV_model.do_tune_kernelparams_negmllk(batch_size_tune, flag_if_use_medianheuristic, beta_cstkernel, lr, epochs, verbose=False)

# Step 3. Optimize model parameters
my_vvCV_model.do_optimize_vv_CV(self, regularizer_const, regularizer_const_FB, batch_size, lr, epochs, verbose=False)

Reproducing Experiments

• The code of Vector-valued Control Variates (vvCVs) is in the folder Vector-valued-Control-Variates-Code/src/src_vvCV_MDMP/. This includes the most generalised version of vvCVs used in our paper, i.e., when all distributions and integrands are different.

  • A simpler case is when we only have one target distribution and mulitple integrands, of which code is in the folder Vector-valued-Control-Variates-Code/src/src_vvCV_MD1P/.

• To reproduce the results of South function example, run Vector-valued-Control-Variates-Code/South_Function/Plot_South_function_experiments.py (this will use the data stored in Vector-valued-Control-Variates-Code/data/South_function_pdframe_saved.pkl).

  • If you want to rerun the whole experiments, save your own data and get the corresponding plot, read (uncomment the code of storing data) and run Vector-valued-Control-Variates-Code/South_Function/South_function_experiments.py and then run Vector-valued-Control-Variates-Code/South_Function/Plot_South_function_experiments.py

• To reproduce the results of Computation of the Model Evidence for Dynamical Systems, run Vector-valued-Control-Variates-Code/TI_Example/Plot_TI_example.py (this will use the data stored in Vector-valued-Control-Variates-Code/data/TI_example_all_data.pkl).

  • If you want to rerun the whole experiments, save your own data and get the corresponding plot, read (uncomment the code of storing data) and run Vector-valued-Control-Variates-Code/TI_Example/Thermodynamic_Integration_experiments.py and then run Vector-valued-Control-Variates-Code/TI_Example/Plot_TI_example.py

• For the experiments of step function example and Borehole function example, the steps are similar.

Citation

If you find our paper interesting and relevant, please consider to cite our paper.

@inproceedings{sun2023vector,
  title={Vector-Valued Control Variates},
  author={Sun, Zhuo and Barp, Alessandro and Briol, Fran{\c{c}}ois-Xavier},
  booktitle={International Conference on Machine Learning},
  year={2023},
  organization={PMLR}
}

Acknowledgement

• The authors would like to thank Chris J. Oates for helpful discussions.
• The samples data.mat and samples.mat of Computation of the Model Evidence for Dynamical Systems are provided by Chris J. Oates, which are the ones used in Control functionals for Monte Carlo integration.