Prospective Learning: Principled Extrapolation to the Future

Overview

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10.

Dependencies

To setup a mamba (conda) environment, run

micromamba env create -f environment.yml

Figures

Run the following to generate the results and figures for the binary examples.

bash binary/binary_examples.sh

To run the neural net experiments, run

cd deep_nets
bash scripts/generate_data.sh
bash scripts/train_scenario2.sh
bash scripts/train_scenario3.sh
bash scripts/create_plots.sh

Cite us

If you find this code useful consider citing

@article{desilva2024prospective,
  title={Prospective Learning: Principled Extrapolation to the Future
  author={De Silva*, Ashwin and Ramesh*, Rahul and Yang*, Rubing and Yu, Siyu and Vogelstein*, Joshua T and Chaudhari*, Pratik},
  journal={Advances in neural information processing systems},
  year={2024}
}