# Tag Info

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 ...
• 3,402
Accepted

### 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 ...
• 24.9k
Accepted

### 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 ...
• 18.2k

### 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 ...
• 2,803

### 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 ...
• 10.6k
Accepted

### 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 ...
• 146

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

We have largely resolved the question for product measures. I'm going to change the notation from the OP to be in line with our paper, https://arxiv.org/abs/2209.04054 I'll be writing $\mu$ rather ...
• 10.6k
Accepted

### 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 ...
• 10.6k
Accepted

### 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 ...
• 630
1 vote
Accepted

From the DKW inequality, it follows one can learn an arbitrary distribution over $\mathbb{R}$ (and in particular over $\{1,2,\dots,n\}$ to Kolmogorov distance* $\varepsilon$ with probability at least $... • 4,481 1 vote ### Sample Complexity for Order Statistics One way to approach this problem is via the CDF transformation. Consider$Z=F(X)$. We know$Z$is uniformly distributed in$[0,1]$. Let$Z_{(1)},...,Z_{(m)}$be the order statistics of these$m\$ ...

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