arXiv
Open Access
2024
Distribution Estimation under the Infinity Norm
Aryeh Kontorovich
Amichai Painsky
Abstrak
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees for the maximum likelihood estimator significantly improve upon the currently known results. A variety of techniques are utilized and innovated upon, including Chernoff-type inequalities and empirical Bernstein bounds. We illustrate our results in synthetic and real-world experiments. Finally, we apply our proposed framework to a basic selective inference problem, where we estimate the most frequent probabilities in a sample.
Penulis (2)
A
Aryeh Kontorovich
A
Amichai Painsky
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2024
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓