Concentration Bounds Lecturer : Sushant Sachdeva Scribe : Cyril
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چکیده
A way to think about what this proof is doing: X dominates the scaled indicator variable T = t · 1X≥t, so we have E[X] ≥ E[T ] = t · Pr[X ≥ t]. Markov’s inequality gives a rather weak bound when applied directly; the random variables we care about are usually much more highly concentrated. Let’s look at a toy example: flip 100 coins. What’s the probability that at least 70 of them come up heads? Markov’s inequality tells us that it’s no greater than 5/7. As we’ll see, we can do much better.
منابع مشابه
Lecturer : David P . Williamson Scribe : Faisal Alkaabneh
Today we will look at a matrix analog of the standard scalar Chernoff bounds. This matrix analog will be used in the next lecture when we talk about graph sparsification. While we’re more interested in the application of the theorem than its proof, it’s still useful to see the similarities and the differences of moving from the proof of the result for scalars to the same result for matrices. Sc...
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تاریخ انتشار 2015