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
• Compress Then Test accelerates kernel two-sample testing using high-fidelity compression

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=None, store_K=False, 
                  meanK=None, unique=False, verbose=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 (often a square-root kernel, krt,
        or a target kernel, k); 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
      meanK: None or array of length n with meanK[ii] = mean of swap_kernel(X[ii], X);
        used to speed up computation when not None
      unique: If True, constrains the output to never contain the same row index more than once
      verbose: If False, do not print intermediate time taken in thinning rounds, 
        if True print that info
    """

For example uses, please refer to 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 (2^g sqrt(n'), d) numpy array Y and returns
          sqrt(n') row indices into Y, identifying a thinned coreset
        g: Oversampling factor
    """

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

A more efficient convenience function is available when one wants to run Compress++ to speed up kernel thinning:

from goodpoints import compress
coreset = compress.compresspp_kt(X, kernel_type, g=g, mean0=mean0)
    """Returns KT-Compress++(g) coreset of size sqrt(n) as row indices into X

    Args: 
      X: Input sequence of sample points with shape (n, d)
      kernel_type: Byte string name of kernel to use
      g: Oversampling parameter, a nonnegative integer
      mean0: If False, final KT call minimizes MMD to empirical measure over 
        the input points. Otherwise minimizes MMD to the 0 measure; this
        is useful when the kernel has expectation zero under a target measure.
    """

The primary Compress Then Test function is ctt in the ctt module:

from goodpoints import ctt
test_results = ctt.ctt(X1, X2, g)
    """Compress Then Test two-sample test with sample sequences X1 and X2
    and auxiliary kernel k' = target kernel k.

    Args:
      X1: 2D array of size (n1,d)
      X2: 2D array of size (n2,d)
      g: compression level; integer >= 0
      B: number of permutations (int)
      s: total number of compression bins will be num_bins = min(2*s, n1+n2)
      lam: positive kernel bandwidth 
      kernel: kernel name; valid options include "gauss" for Gaussian kernel
        exp(-||x-y||^2/lam^2)
      null_seed: seed used to initialize random number generator for
        randomness in simulating null
      statistic_seed: seed used to initialize random number generator for
        randomness in computing test statistic
      alpha: test level
      delta: KT-Compress failure probability
      
    Returns: TestResults object.
    """

For example uses, please refer to examples/mmd_test/test.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 examples/kt/plot_results.ipynb can be used to reproduce the figures of Kernel Thinning.

Generalized Kernel Thinning

@inproceedings{dwivedi2022generalized,
  title={Generalized Kernel Thinning},
  author={Raaz Dwivedi and Lester Mackey},
  booktitle={International Conference on Learning Representations},
  year={2022}
}

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

@inproceedings{shetty2022distribution,
  title={Distribution Compression in Near-linear Time},
  author={Abhishek Shetty and Raaz Dwivedi and Lester Mackey},
  booktitle={International Conference on Learning Representations},
  year={2022}
}

1. The notebook examples/compress/script_to_deploy_jobs.ipynb reproduces the experiments of Distribution Compression in Near-linear Time in the following manner:
   1. 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.
   2. It computes the runtimes of different algorithms by executing examples/compress/run_time.py.
   3. 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.
   4. 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.

Compress Then Test: Powerful Kernel Testing in Near-linear Time

@inproceedings{domingoenrich2023compress,
  title={Compress Then Test: Powerful Kernel Testing in Near-linear Time},
  author={Carles Domingo-Enrich and Raaz Dwivedi and Lester Mackey},
  booktitle={Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
  year={2023},
  series={Proceedings of Machine Learning Research},
  month={25--27 Apr},
  publisher={PMLR}
}

See examples/mmd_test/README.md.

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