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- Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Zheng Li, Ankur Moitra, Alistair Stewart
- 2016 IEEE 57th Annual Symposium on Foundations ofâ€¦
- 2016

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an epsilon fraction of the samples. Such questions have a rich historyâ€¦ (More)

- Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
- 2017 IEEE 58th Annual Symposium on Foundations ofâ€¦
- 2016

We describe a general technique that yields the first Statistical Query lower bounds} fora range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main resultsâ€¦ (More)

- Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
- COLT
- 2016

We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order n âˆˆ Z+ is the discrete probability distribution of the sum of nmutuallyâ€¦ (More)

- Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
- ArXiv
- 2016

We study the robust proper learning of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want toâ€¦ (More)

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system ofâ€¦ (More)

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise â€” where an Îµ-fraction of our samples were chosen by an adversary. We give robustâ€¦ (More)

- Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
- ArXiv
- 2016

We investigate the problem of learning Bayesian networks in an agnostic model where an Ç«-fraction of the samples are adversarially corrupted. Our agnostic learning model is similar to â€“ in fact,â€¦ (More)

This work initiates a systematic investigation of testing hi h-dimensional structured distributions by focusing on testingBayesian networksâ€“ the prototypical family of directed graphical models. Aâ€¦ (More)

- Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
- COLT
- 2017

We study the problem of estimating multivariate log-concave probability density functions. We prove the first sample complexity upper bound for learning log-concave densities on Rd, for all d â‰¥ 1.â€¦ (More)

- Kousha Etessami, Alistair Stewart, Mihalis Yannakakis
- Inf. Comput.
- 2015

We give polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs). Speci cally, given a BMDP, and given an initialâ€¦ (More)