GoodPoints

A Python package for generating concise, high-quality summaries of a probability distribution

GoodPoints is a collection of tools for compressing a distribution more effectively than independent sampling:

• Given an initial summary of n input points, kernel thinning returns s << n output points with comparable integration error across a reproducing kernel Hilbert space
• Compress++ reduces the runtime of generic thinning algorithms with minimal loss in accuracy

Installation

To install the goodpoints package, use the following pip command:

pip install goodpoints

Getting started

The primary kernel thinning function is thin in the kt module:

from goodpoints import kt
coreset = kt.thin(X, m, split_kernel, swap_kernel, delta=0.5, seed=123, store_K=False)
    """Returns kernel thinning coreset of size floor(n/2^m) as row indices into X
    
    Args:
      X: Input sequence of sample points with shape (n, d)
      m: Number of halving rounds
      split_kernel: Kernel function used by KT-SPLIT (typically a square-root kernel, krt);
        split_kernel(y,X) returns array of kernel evaluations between y and each row of X
      swap_kernel: Kernel function used by KT-SWAP (typically the target kernel, k);
        swap_kernel(y,X) returns array of kernel evaluations between y and each row of X
      delta: Run KT-SPLIT with constant failure probabilities delta_i = delta/n
      seed: Random seed to set prior to generation; if None, no seed will be set
      store_K: If False, runs O(nd) space version which does not store kernel
        matrix; if True, stores n x n kernel matrix
    """

For example uses, please refer to the notebook examples/kt/run_kt_experiment.ipynb.

The primary Compress++ function is compresspp in the compress module:

from goodpoints import compress
coreset = compress.compresspp(X, halve, thin, g)
    """Returns Compress++(g) coreset of size sqrt(n) as row indices into X

    Args: 
        X: Input sequence of sample points with shape (n, d)
        halve: Function that takes in an (n', d) numpy array Y and returns 
          floor(n'/2) distinct row indices into Y, identifying a halved coreset
        thin: Function that takes in an (n', d) numpy array Y and returns
          2^g sqrt(n') row indices into Y, identifying a thinned coreset
        g: Oversampling factor
    """

For example uses, please refer to the code examples/compress/construct_compresspp_coresets.py.

Examples

Code in the examples directory uses the goodpoints package to recreate the experiments of the following research papers.

Kernel Thinning

@article{dwivedi2021kernel,
  title={Kernel Thinning},
  author={Raaz Dwivedi and Lester Mackey},
  journal={arXiv preprint arXiv:2105.05842},
  year={2021}
}

1. The script examples/kt/submit_jobs_run_kt.py reproduces the vignette experiments of Kernel Thinning on a Slurm cluster by executing examples/kt/run_kt_experiment.ipynb with appropriate parameters. For the MCMC examples, it assumes that necessary data was downloaded and pre-processed following the steps listed in examples/kt/preprocess_mcmc_data.ipynb, where in the last code block we report the median heuristic based bandwidth parameteters (along with the code to compute it).
2. After all results have been generated, the notebook plot_results.ipynb can be used to reproduce the figures of Kernel Thinning.

Generalized Kernel Thinning

@article{dwivedi2021generalized,
  title={Generalized Kernel Thinning},
  author={Raaz Dwivedi and Lester Mackey},
  journal={arXiv preprint arXiv:2110.01593},
  year={2021}
}

1. The script examples/gkt/submit_gkt_jobs.py reproduces the vignette experiments of Generalized Kernel Thinning on a Slurm cluster by executing examples/gkt/run_generalized_kt_experiment.ipynb with appropriate parameters. For the MCMC examples, it assumes that necessary data was downloaded and pre-processed following the steps listed in examples/kt/preprocess_mcmc_data.ipynb.
2. Once the coresets are generated, examples/gkt/compute_test_function_errors.ipynb can be used to generate integration errors for different test functions.
3. After all results have been generated, the notebook examples/gkt/plot_gkt_results.ipynb can be used to reproduce the figures of Generalized Kernel Thinning.

Distribution Compression in Near-linear Time

@article{shetti2021distribution,
  title={Distribution Compression in Near-linear Time},
  author={Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
  journal={arXiv preprint arXiv:2111.07941},
  year={2021}
}

1. The notebook examples/compress/script_to_deploy_jobs.ipynb reproduces the experiments of Distribution Compression in Near-linear Time in the following manner: 1a. It generates various coresets and computes their mmds by executing examples/compress/construct_{THIN}_coresets.py for THIN in {compresspp, kt, st, herding} with appropriate parameters, where the flag kt stands for kernel thinning, st stands for standard thinning (choosing every t-th point), and herding refers to kernel herding. 1b. It compute the runtimes of different algorithms by executing examples/compress/run_time.py. 1c. For the MCMC examples, it assumes that necessary data was downloaded and pre-processed following the steps listed in examples/kt/preprocess_mcmc_data.ipynb. 1d. The notebook currently deploys these jobs on a slurm cluster, but setting deploy_slurm = False in examples/compress/script_to_deploy_jobs.ipynb will submit the jobs as independent python calls on terminal.
2. After all results have been generated, the notebook examples/compress/plot_compress_results.ipynb can be used to reproduce the figures of Distribution Compression in Near-linear Time.
3. The script examples/compress/construct_compresspp_coresets.py contains the function recursive_halving that converts a halving algorithm into a thinning algorithm by recursively halving.
4. The script examples/compress/construct_herding_coresets.py contains the herding function that runs kernel herding algorithm introduced by Yutian Chen, Max Welling, and Alex Smola.

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