# Tag Info

## Hot answers tagged sample-complexity

Accepted

### Sampling monotone Boolean functions

In [1], the paper where Propp & Wilson introduce the "coupling from the past" technique for MCMC sampling, they also outline a "heat bath algorithm" applicable to a certain kind of spin system ...
• 3,381
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### Almost uniform sampling implies approximate counting

Given a set $A \subseteq B$, if you can sample uniformly from $B$, then you can estimate by repeated sampling the probability of the event that the sample is in $A$. That is, you can approximate the ...
• 9,566
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### Qubit gates in google supremacy

Based on a fairly cursory inspection of their paper, IBM is clearly aware of the spatial locality. They seem to in fact have taken spatial locality into account when designing their simulation. They ...
• 23.7k

### Coreset and VC dimension

Samples provides you only with statistical guarantees. For a fixed $\epsilon$ whatever you compute would hold for everything "except" $(1-\epsilon)$ fraction (I am being very informal here). Thus, ...
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### Sample complexity of distinguishing two Gaussian distributions?

I don't have a solution to this problem, but the analogous case where the two distributions are discrete has been analyzed in the cryptographic literature. Suppose we want to distinguish between two ...
• 10.5k
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### Determining the number of clusters using property testing algorithm

First. One can do better as far as the sampling - at least if $d$ is large - $O(\frac{kd \log k}{\epsilon} \log \frac{1}{\epsilon})$ should follow easily from relative approximations http://sarielhp....
• 9,566
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### How many samples are needed to reconstruct a path?

Here’s a simple idea: try a certain number $s$ of samples, and for each vertex, record how many times its colour agreed with the provided bit. For vertices outside the path, they agree with ...
• 14.8k

### Is uniform convergence faster for low-entropy distributions?

This is very much a partial answer to my question. I'm hoping for a much better bound (or a counterexample). I managed to show a very weak bound. It is not very useful, but it does at least show that ...
• 2,743

### Is uniform convergence faster for low-entropy distributions?

First, let's use McDiarmid's inequality to conclude that $$\mathbb{P}\left[|| \bar X - \mu ||_\infty \ge \mathbb{E}|| \bar X - \mu ||_\infty + \varepsilon \right] \le e^{-2n\varepsilon^2},$$ so it ...
• 10.1k
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### Coreset and VC dimension

The answer of Har-Peled is mainly regarding problems where you wish to cover points by shapes (e.g. balls). A strong relation to eps-nets and hitting sets can be found e.g. in his paper here For the ...
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### Approximating the value of k in $k$-mean clustering problem

This problem is known as Geometric Set Cover (which deals with covering with different shapes, so unit balls are a special case). I'm unaware of any relation to $k$-means which is a clustering ...
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### What is the proper role of verification in quantum sampling, simulation, and extended-Church-Turing (E-C-T) testing?

The gist of the question is, given that quantum probability is a source of true randomness, how does that effect the extended (or efficient, or polynomial-time) Church-Turing thesis? The answer is ...
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### Sample complexity for learning Boltzmann Distribution parameters

Under appropriate smoothness conditions (satisfied by the Boltzmann distribution), the maximum likelihood is asymptotically normal. Meaning: the vector $\sqrt n(\theta-\hat\theta)$ will have ...
• 10.1k
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### Lower bound for the OR problem

After some more searching, I managed to find a proof in these lecture notes [1]. The proof goes via Yao's principle and the lower bound is n/3. If someone knows of a published paper or a book that I ...
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1 vote
Accepted

1 vote

### Evaluating the expected value of negatively correlated random variables

I think that in principle it would take exponential time to compute this probability exactly. Hence sampling would be the only option here, although you would have to settle for additive and ...

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