I am a Ph.D. candidate at the department of Computer Science and Applied Mathematics at the Weizmann Institute of Science, working with Prof. Boaz Nadler. My research interests are in the theory of Statistics and Machine Learning, specifically in the development of new statistical tools and computational methods.
contact: moscovich (at gmail.com), office: 301, Ziskind building, Weizmann Institute of Science.
Consider a one-dimensional homogeneous Poisson process. How can we compute the boundary crossing probability of this process, given arbitrary boundaries from above and below? Previously known methods can compute this probability in O(n^3) time, where n is an upper bound on the boundary functions. In this work, we present a faster O(n^2 log n) algorithm.
Preprint on arXiv.org: http://arxiv.org/abs/1503.04363
Co-author: Boaz Nadler
Poster presented at the wonderful MLSS 2015 Kyoto: PDF, LaTeX
This method has several potential applications, mainly in statistics, including the computation of exact p-values for continuous goodness-of-fit tests.
A fast C++ implementation of the algorithms discussed in the paper is available on github: crossing-probability
Co-authors: Boaz Nadler, Clifford Spiegelman
A continuous goodness-of-fit test that is uniformly sensitive throughout the entire range of the distribution.
Particularly suited for the detection of alternatives that differ from the null hypothesis mainly at the tails of the distribution.
Please email me if you are wondering whether or not CKS is applicable to your data (come on, don't be shy!)
Preprint on arXiv.org: http://arxiv.org/abs/1311.3190
This paper presents the one-sided and two-sided CKS tests and proves asymptotic optimality under various alternatives. In addition to that, a practical method for the computation of one-sided p-values is given.
Slides I gave at the Weizmann department of Computer Science and Applied Math: PDF, LaTeX
Poster I presented at the 2014 "Structural Inference in Statistics: Adaptation and Efficiency" spring school: PDF
Code for reproducing all of the figures in the paper: cks_paper_produce_figures.zip
Python CKS library