Python Code for Augmented Permanental Process

This library provides augmented permanental process (APP) implemented in Tensorflow. APP provides a scalable Bayesian framework for estimating point process intensity as a function of covariates, with the assumption that covariates are given at every point in the observation domain. For details, see our NeurIPS2022 paper [1].

The code was tested on Python 3.7.2, Tensorflow 2.2.0, and qmcpy 1.3.

Installation

To install latest version:

pip install git+https://github.com/HidKim/APP

Basic Usage

Import APP class:

from HidKim_APP import augmented_permanental_process as APP

Initialize APP:

model = APP(kernel='Gaussian', eq_kernel='RFM',  
            eq_kernel_options={'cov_sampler':'Sobol','n_cov':2**11,'n_dp':500,'n_rfm':500})

• kernel: string, default='Gaussian'
  

  The kernel function for Gaussian process. Only 'Gaussian' is available now.

• eq_kernel: string, default='RFM'
  

  The approach to constructing equivalent kernel. 'RFM' and 'Nystrom' are the degenerate approaches with random feature map and Nystrom method, respectively. 'Naive' is the naive approach.

• eq_kernel_options: dict, default={'cov_sampler': 'Sobol', 'n_cov': 2**11, 'n_dp': 500, 'n_rfm': 100}
  

  The options for constructing equivalent kernel.

  • 'cov_sampler': The method for numerical integration. 'Sobol', 'Halton', and 'Lattice' are the quasi-Monte Carlo methods (see qmcpy). 'Random' is the Monte-Carlo method.
  • 'n_cov': Number of samples for (quasi-)Monte Carlo integration.
  • 'n_dp': Number of data points used for the Nystrom approach to constructing equivalent kernel.
  • 'n_rfm': Number of feature samples for the random feature map approach to constructing equivalent kernel.

Fit APP with data:

time = model.fit(d_spk, obs_region, cov_fun, set_par, display=True)

• d_spk: ndarray of shape (n_samples, dim_observation)
  

  The point event data.

• obs_region: ndarray of shape (dim_observation, 2)
  

  The hyper-rectangular region of observation. For example, [[x0,x1],[y0,y1]] for two-dimensional region.

• cov_fun: callable
  

  The covariate map "cov_fun(t) -> y", where t is a point in the obervation domain, and y is the covariate value at the point.

• set_par: ndarray of shape (n_candidates, dim_hyperparameter)
  

  The set of hyper-parameters for hyper-parameter optimization. The optimization is performed by maximizing the marginal likelihood.

• display: bool, default=True
  

  Display the summary of the data and the fitting.

• Return: float
  

  The execution time.

Predict point process intensity as function of covariates:

r_est = model.predict(y, conf_int=[0.025,0.5,0.975])

• y: ndarray of shape (n_points, dim_covariate)
  

  The points on covariate domain for evaluating intensity values.

• conf_int: ndarray of shape (n_quantiles,), default=[.025, .5, .975]
  

  The quantiles for predicted intenity.

• Return: ndarray of shape (n_quantiles, n_points)
  

  The predicted values of intensity at the specified points.

Reference

1. Hideaki Kim, Taichi Asami, and Hiroyuki Toda. "Fast Bayesian Estimation of Point Process Intensity as Function of Covariates", Advances in Neural Information Processing Systems 35, 2022.

@inproceedings{kim2022fastbayesian,
  title={Fast {B}ayesian Estimation of Point Process Intensity as Function of Covariates},
  author={Kim, Hideaki and Asami, Taichi and Toda, Hiroyuki},
  booktitle={Advances in Neural Information Processing Systems 35},
  year={2022}
}

License

Released under "SOFTWARE LICENSE AGREEMENT FOR EVALUATION". Be sure to read it.

Contact

Feel free to contact the first author Hideaki Kim (hideaki.kin.cn@hco.ntt.co.jp).