tmanole / Randomized-Markov

Statistical applications of the exchangeable and uniformly-randomized analogues of the Markov inequality.

Randomized-Markov

Code repository for reproducing the simulation studies in the paper

Ramdas, A. and Manole, T. (2023). Randomized and Exchangeable Improvements of Markov’s, Chebyshev’s and Chernoff’s Inequalities. arXiv preprint arXiv:2304.02611.

Dependencies

This code has only been tested using Python 3.10 on a standard Linux machine. Beyond the Python Standard Library, the only required packages for the main code are NumPy, sklearn, and confseq.

Usage

To reproduce the simulation studies in Sections 7.1--7.4 of the paper, run the respective files intervals.py, Ke-vals.py, mixture_ui.py, and betting.py. To reproduce the respective plots, run plot_intervals.py, plot_Ke-vals.py, plot_ui.py, and plot_betting.py. To reproduce the additional simulations in Appendix C, run the file e-vals.py, and to obtain the corresponding plots, run plot_e-vals.py.