goodpoints 0.4.1
Tools to generate concise high-quality summaries of a probability distribution

# 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
- **Stein Kernel Thinning**, **Stein Recombination**, and **Stein Cholesky** deliver unweighted, simplex-weighted, and constant-preserving coresets that reduce biases due to off-target sampling, tempering, or burn-in

## Installation
To install the `goodpoints` package, use the following pip command:
```
pip install goodpoints
```
For **Debiased Distribution Compression**, JAX and additional dependencies are required. See [goodpoints/jax](goodpoints/jax) for more details.

## Getting started
The primary kernel thinning function is `thin` in the `kt` module:
```python
from goodpoints import kt
coreset = kt.thin(X, m, split_kernel, swap_kernel, delta=0.5, seed=None, store_K=True, 
                  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
    """
```
> [!TIP]
> Choosing `store_K=True` is equivalent to running the faster but more memory-intensive `kt.thin_K` Cython implementation,
while `store_K=False` uses the slower Python implementation `kt.thin_X`.
See [examples/kt/run_kt_experiment.ipynb](examples/kt/run_kt_experiment.ipynb) for example uses.
> 
> A more efficient JAX implementation with GPU and CPU support is also available in [`goodpoints.jax.kt.kt`](goodpoints/jax/kt.py).


---
The primary function for speeding up kernel thinning with Compress++ is the `compresspp_kt` function in the `compress` module: 
```python
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.
    """
```
> [!TIP]
> A more efficient JAX implementation with GPU and CPU support is also available in [`goodpoints.jax.compress.kt_compresspp`](goodpoints/jax/compress.py).
> 
> See also [Thinformer](https://github.com/microsoft/thinformer) for a PyTorch implementation of Compress++ applied to kernel halving with GPU and CPU support.

---
To speed up a generic halving algorithm with Compress++, we also provide the `compresspp` function in the `compress` module:
```python
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
    """
```
> [!TIP]
> See [examples/compress/construct_compresspp_coresets.py](examples/compress/construct_compresspp_coresets.py) for example uses.
> 
> A more efficient JAX implementation with GPU and CPU support is also available in [`goodpoints.jax.compress.compresspp`](goodpoints/jax/compress.py).

---
The primary Compress Then Test function is `ctt` in the `ctt` module:
```python
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.
    """
```
> [!TIP]
> See [examples/mmd_test/test.py](examples/mmd_test/test.py) for example uses.

***
The primary Debiased Distribution Compression functions are in the `jax.dtc` module, including:
- Stein Kernel Thinning (`skt`) and Low-rank Stein Kernel Thinning (`lskt`) for equal-weighted coresets
- Stein Recombination (`sr`) and Low-rank Stein Recombination (`lsr`) for simplex-weighted coresets
- Stein Cholesky (`sc`) and Low-rank Stein Cholesky (`lsc`) for constant-preserving coresets

Moreover, Debiased Distribution Compression provides JAX implementation of Kernel Thinning, Compress++, and [Stein Thinning](https://arxiv.org/pdf/2005.03952) that can be of independent interest.
Please refer to [goodpoints/jax/README.md](goodpoints/jax/README.md) for all available functions.

## Examples

Code in the `examples` directory uses the `goodpoints` package to recreate the experiments of the following research papers.
***
#### [Kernel Thinning](https://arxiv.org/pdf/2105.05842.pdf)
```
@article{dwivedi2024kernel,
  title={Kernel Thinning},
  author={Dwivedi, Raaz and Mackey, Lester},
  journal={Journal of Machine Learning Research},
  volume={25},
  number={152},
  pages={1--77},
  year={2024}
}
```
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](https://arxiv.org/pdf/2110.01593.pdf) 
```
@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](https://arxiv.org/pdf/2111.07941.pdf)
```
@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](https://arxiv.org/pdf/2301.05974.pdf)
```
@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](examples/mmd_test/README.md).

#### [Debiased Distribution Compression](https://arxiv.org/pdf/2404.12290)
```
@InProceedings{li2024debiased,
    title = {Debiased Distribution Compression},
    author = {Li, Lingxiao and Dwivedi, Raaz and Mackey, Lester},
    booktitle = {Proceedings of the 41st International Conference on Machine Learning},
    year = {2024},
    volume = {203},
    series = {Proceedings of Machine Learning Research},
    month = {21--27 Jul},
    publisher = {PMLR},
}
```
See [examples/debias/README.md](examples/debias/README.md).

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