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Unbiased Estimators

less than 1 minute read

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Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. Given iid samples $X_1, \ldots, X_n$, one knows that the sample mean $\bar{X} := \frac{1}{n}(X_1+\cdots+X_n)$ and sample variance $S^2 := \frac{1}{n-1}\sum (X_i - \bar{X})^2$ are unbiased estimators for $\mu$ and $\sigma^2$ respectively, meaning that $\mathbb{E}[\bar{X}] = \mu$ and $\mathbb{E}[S^2] = \sigma^2$.

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publications

Smart broadcasting: Do you want to be seen?

Published in KDD, 2016

This paper is about the problem of visibility in a social network. We give an optimal broadcasting scheme that maximizes user visibility in a network.

Mohammad Reza Karimi, Erfan Tavakoli, Mehrdad Farajtabar, Le Song, and Manuel Gomez Rodriguez (2016). "Smart broadcasting: Do you want to be seen?" ACM SIGKDD. (pp. 1635-1644). [pdf]

Stochastic Submodular Maximization: The Case of Coverage Functions

Published in NIPS, 2017

This paper is about maximizing a stochastic submodular function, where even evaluation of the function is noisy. We provide optimal guarantees for the class of Coverage functions.

Mohammad Reza Karimi, Mario Lucic, Hamed Hassani, and Andreas Krause. (2017). "Stochastic Submodular Maximization: The Case of Coverage Functions" NIPS. (pp. 6853-6863). [pdf]

Consistent Online Optimisation: Convex and Submodular

Published in AISTATS, 2019

This paper gives a trade-off between the number of updates and the regret in an online algorithm in a general setting.

Mohammad Reza Karimi Jaghargh, Andreas Krause, Silvio Lattanzi, Sergei Vassilvtiskii (2019). "Consistent Online Optimization: Convex and Submodular" AISTATS. (pp. 2241--2250). [pdf]

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teaching

The Math Circle

Extra Activity, ETH Zürich, Computer Science Department, 2018

Math Circle is a place where everyone with any background can experience the exhilaration of mathematical exploration!