Daniel M. Kane

Optimal Algorithms and Lower Bounds for Testing Closeness of Structured Distributions

2015

We give a general unified method that can be used for L1closeness testing of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for testing …

Properly Learning Poisson Binomial Distributions in Almost Polynomial Time

2015 · arXiv (Cornell University)

We give an algorithm for properly learning Poisson binomial distributions. A Poisson binomial distribution (PBD) of order $n$ is the discrete probability distribution of the sum of $n$ mutually independent Bernoulli random variables. Given $\widetilde{O}(1/ε^2)$ …

Testing Conditional Independence of Discrete Distributions

2017 · arXiv (Cornell University)

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with probability at least …

Testing Conditional Independence of Discrete Distributions

2018

We study the problem of testing conditional independence for discrete distributions. Specifically, given samples from a discrete random variable (X,Y,Z) on domain [ℓ1] × [ℓ2] × [n], we want to distinguish, with probability at least …

Hardness of Learning Halfspaces with Massart Noise.

2020 · arXiv (Cornell University)

We study the complexity of PAC learning halfspaces in the presence of Massart (bounded) noise. Specifically, given labeled examples $(x, y)$ from a distribution $D$ on $\mathbb{R}^{n} \times \{ \pm 1\}$ such that the marginal …

Computational-Statistical Gaps in Reinforcement Learning

2022 · arXiv (Cornell University)

Reinforcement learning with function approximation has recently achieved tremendous results in applications with large state spaces. This empirical success has motivated a growing body of theoretical work proposing necessary and sufficient conditions under which efficient …