Andrew Mullhaupt
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Andrew Mullhaupt has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Cheng Peng
Department of Applied Mathematics and Statistics Stony Brook University
1 shared publication - Rui Ding
Applied Mathematics and Statistics, Stony Brook University, USA
1 shared publication
Latest Publications
- Open Access
Bounding Neyman-Pearson Region with $f$-Divergences
The Neyman-Pearson region of a simple binary hypothesis testing is the set of points whose coordinates represent the false positive rate and false negative rate of some test. The lower boundary of this region is given by the Neyman-Pearson lemma, and is up to a coordinate change, equivalent to the optimal ROC curve. We establish a novel lower bound for the boundary in terms of any $f$-divergence. Since the bound generated by hockey-stick $f$-divergences characterizes the Neyman-Pearson boundary, this bound is best possible. In the case of KL divergence, this bound improves Pinsker's inequality. Furthermore, we obtain a closed-form refined upper bound for the Neyman-Pearson boundary in terms of the Chernoff $α$-coefficient. Finally, we present methods for constructing pairs of distributions that can approximately or exactly realize any given Neyman-Pearson boundary.
Open AccessBounding Neyman-Pearson Region with $f$-Divergences
The Neyman-Pearson region of a simple binary hypothesis testing is the set of points whose coordinates represent the false positive rate and false negative rate of some test. The lower boundary of this region is given by the Neyman-Pearson lemma, and is up to a coordinate change, equivalent to the optimal ROC curve. We establish a novel lower bound for the boundary in terms of any $f$-divergence. Since the bound generated by hockey-stick $f$-divergences characterizes the Neyman-Pearson boundary, this bound is best possible. In the case of KL divergence, this bound improves Pinsker's inequality. Furthermore, we obtain a closed-form refined upper bound for the Neyman-Pearson boundary in terms of the Chernoff $α$-coefficient. Finally, we present methods for constructing pairs of distributions that can approximately or exactly realize any given Neyman-Pearson boundary.
- Open Access
Empirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities. We illustrate the proposed estimator on several one-dimensional probability distributions. Finally, we extend the estimator to a family of estimators for the family of -divergences, which almost surely converge as well, and discuss the uniqueness of this result. We demonstrate applications of the proposed Hellinger affinity estimators to approximately bounding the Neyman–Pearson regions.Open AccessEmpirical Squared Hellinger Distance Estimator and Generalizations to a Family of α-Divergence Estimators
We present an empirical estimator for the squared Hellinger distance between two continuous distributions, which almost surely converges. We show that the divergence estimation problem can be solved directly using the empirical CDF and does not need the intermediate step of estimating the densities. We illustrate the proposed estimator on several one-dimensional probability distributions. Finally, we extend the estimator to a family of estimators for the family of -divergences, which almost surely converge as well, and discuss the uniqueness of this result. We demonstrate applications of the proposed Hellinger affinity estimators to approximately bounding the Neyman–Pearson regions.