OWL: Robustifying likelihoods by optimistically re-weighting data

This package implements OWL, a robust approach for fitting probabilistic models with likelihood functions.

Installing OWL

If you have conda installed, then you can install by running the following from the base directory.

conda env create -f env.yaml
conda activate owl
pip install -e .

Otherwise, you should install the packages listed in env.yaml before running pip install -e ..

Running OWL

To fit a probabilistic model using OWL, create a class that extends the OWLModel class. You must implement two functions: maximize_weighted_likelihood and log_likelihood. Below is a simple exponential distribution.

from owl.models import OWLModel

'''
    Simple univariate exponential distribution.
'''
class Exponential(OWLModel):
    def __init__(self, 
        X: np.ndarray, ## Input samples (1-dimensional)
        w:np.ndarray = None, ## Weights over the samples (set to None for uniform)
        **kwargs
        ):
        self.X = X.copy()
        n  = len(X)
        super().__init__(n=n, w=w, **kwargs)

        self.lam = 1.0 ## Parameter of the exponential distribution
    
    def maximize_weighted_likelihood(self, **kwargs):
        self.lam = np.sum(self.w)/np.dot(self.w, self.X)

    def log_likelihood(self):
        return( np.log(self.lam) - (self.lam*self.X) )

Once the class is created, then we need to choose the Ball class that we will fit it with. In all the experiments in the paper, the L1Ball class is used.

from owl.ball import L1Ball

## Generate data from an exponential distribution
n = 1000
lam = 5.0
x = np.random.exponential(scale=(1./lam), size=n)

## Randomly corrupt 5 percent of the data
epsilon = 0.05
corrupt_inds = np.random.choice(n, size=int(n*epsilon), replace=False)
for i in corrupt_inds:
    x[i] = 5.0 + np.random.standard_normal()
   
## Fit an owl estimate to the data
owl = Exponential(X=x)
l1ball = L1Ball(n=n, r=epsilon)
owl.fit_owl(ball=l1ball, n_iters=10, verbose=True)

More examples are in the examples/Simple OWL models.ipynb notebook.

Running the data analysis and simulations from the paper

To download most of the external datasets used in the paper (i.e., MNIST, QSAR, ENRON, and scRNA-Seq data), run python simulations/download.py from the command line. This will create the relevant files in the data subdirectory of the main directory. To obtain the preliminary data for the micro-credit study (in data/microcredit.csv) you will need to run the following Quarto document.

Reproducing the micro-credit example from Broderick et al. (2023)

1. Download and extract the Meager (2019) replication data into the ./simulations/116357-V1 folder.
2. Download Quarto and run the command

quarto render simulations/Reproduce-Broderick-et-al-2023-outlier.qmd

Running the simulations and analysis from the paper

The subdirectory simulations contains the python scripts for running the various simulations in the paper. To see the arguments for the script, call the script with the --help flag. For example, simulations/gmm_simulation.py --help. The bash script simulations/reproduce_paper_plots.sh contains all the calls necessary to reproduce the plots in the paper (be warned that calling this script will take a very long time).

Citation

If you use this code, please cite the preprint:

Robustifying likelihoods by optimistically re-weighting data
M. Dewaskar, C.Tosh, J. Knoblauch, and D. Dunson

@misc{dewaskar2023robustifying,
      title={Robustifying likelihoods by optimistically re-weighting data}, 
      author={Miheer Dewaskar and Christopher Tosh and Jeremias Knoblauch and David B. Dunson},
      year={2023},
      eprint={2303.10525},
      archivePrefix={arXiv},
      primaryClass={stat.ME}
}