# Tag Info

Accepted

### Proper PAC learning VC dimension bounds

My thanks to Aryeh for bringing this question to my attention. As others have mentioned, the answer to (1) is Yes, and the simple method of Empirical Risk Minimization in $\mathcal{C}$ achieves the ...
• 126
Accepted

### VC dimension of polynomials over tropical semirings?

I've realized that the answer to my question is - yes: the VC dimension of degree $\leq d$ polynomials on $n$ variables over any tropical semiring is at most a constant times $n^2\log(n+d)$. This can ...
• 6,635
Accepted

### How can we compute the VC dimension of a finite class of sets?

In 1996 Papadimitriou and Yannakakis noted that there exists an $n^{O(\log n)}$ brute-force algorithm (where $n$ is the size of the input) for computing VC-dimension of a 0-1 matrix by checking all ...
• 11.8k

### What is the VC Dimension of the $k-$Junta class

For the very limited situation in which $k=1$ and we're only interested in functions whose domain is $\{0,1\}^n$, the VC dimension is $\lfloor \log_2(n+1) + 1 \rfloor$. The upper bound follows ...
• 1,419
Accepted

### Tight VC bound for agnostic learning

This was proven in M. Talagrand. Sharper bounds for Gaussian and empirical processes. The Annals of Probability, pages 28–76, 1994. This is mentioned in e.g. this paper (Section 1.1.2), which does ...
• 4,341

• 10.1k
1 vote

### VC generalization bound extended to other types of target functions

Daniely et al had some works on the subject back in 2012--2015. In particular, it is referred to (there) as "multiclass learning". Here are two works on this: Multiclass learnability and the ...
• 5,261
1 vote

### VC-dimension of infinite set of triangle wave

First of all, presumably you want the VC-dimension of your class of composed with the sign function, which yields a class of Boolean functions (otherwise, VC-dim is not defined). With that out of the ...
• 10.1k

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