Questions tagged [chernoff-bound]

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20 questions
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How to use a 𝑝-coin so a TM can decide an undecidable language in polynomial time? [closed]

In "Computational complexity- A modern approach" book (page 117) for the lemma 7.12 (following) the author mentioned that if the ρ is efficiently computable ρ-coin cannot give probabilistic algorithm ...
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Concentration Bounds for functions of matrices

This is a question about properties of large directed graphs which are preserved when we randomly sample edges. Imagine I have an infinite sequence of positively weighted directed graphs. The ...
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Differential Privacy and Randomized Responses for Counting Queries

I'm trying to understand a basic randomized response mechanism for differential privacy (concrete definition not relevant for the question), but I have some trouble understanding the last step in the ...
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Tools to bound the singular values of a finite sum of random matrices from below?

Matrix Chernoff bounds (see also this arXiv paper) are usually used to give upper bounds on the largest eigenvalue of a finite sum of random matrices. Sometimes it can also be used to give a lower ...
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How to derandomize the Chernoff bound?

Avi Wigderson have a paper on how to derandomize the matrix-valued Chernoff bound. I would like to know whether there exists a simple version of paper on how to derandomize the real-valued Chernoff ...
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Sums of products of bernoulli random variables

Let $x_1 \ldots x_a,y_1 \ldots y_b$ be independent random variables taking values +1 or -1. Consider the sum $$S = \sum_{i,j} x_iy_j.$$ I wish to upper bound the probability $P(|S| > t)$. The ...
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Estimator for sum of independent and identically distributed (iid) variables

This is a repost of a question at math.stackexchange, but I was told by a reliable source that people around here might be able to help me, so I thought I'd give it a shot. Consider the Chernoff ...
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An extension of Chernoff bound

I am looking for a reference (not a proof, that I can do) to the following extension of Chernoff. Let $X_1,..,X_n$ be Boolean random variables, not necessarily independent. Instead, it is guaranteed ...
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Chernoff-type inequality for random variable with 3 outcomes

Suppose we have a random variable which takes non-numeric values a,b,c and want to quantify how empirical distribution of $n$ samples of this variable deviates from true distribution. The following ...
Consider $X = \sum_i \lambda_i Y_i^2$, where lambda_i > 0 and Y_i is distributed as a standard normal. What kind of concentration bounds can one prove on X, as a function of the (fixed) coefficients ...