Questions tagged [learning-theory]

Questions about the design and analysis of machine learning algorithms.

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34 votes
2 answers

Are there improvements on Dana Angluin's algorithm for learning regular sets

In her 1987 seminal paper Dana Angluin presents a polynomial time algorithm for learning a DFA from membership queries and theory queries (counterexamples to a proposed DFA). She shows that if you are ...
Artem Kaznatcheev's user avatar
6 votes
2 answers

What is usually the next step after showing the VC dimension?

I am new to statistical learning. I have a structure $X$ where I showed its hypothesis class $H$ has VC dimension $d$. All I know now is that I can bound the number of examples by $m\geq \frac{1}{\...
seteropere's user avatar
2 votes
1 answer

Learning a small disjunction

I have a boolean function $f: \{0,1\}^n \to \{0,1\}$ that I know takes the form $$f(x_1,\dots,x_n) = x_{i_1} \lor x_{i_2} \lor \dots \lor x_{i_k},$$ but I don't know the values of $i_1,\dots,i_k$. ...
D.W.'s user avatar
  • 154k
1 vote
0 answers

Why is it NP-hard to learn a disjunction of k variables as a disjunction of fewer than k log n variables?

I'm looking at the claim in An algorithmic theory of learning: Robust concepts and random projection by R. I. Arriaga and S. Vempala (2006): Further, it is NP-hard to learn a disjunction of k ...
djechlin's user avatar
  • 487
0 votes
1 answer

VC dimension of monotone disjunctions of length k over n variables?

There are of course $n \choose k$ monotone disjunctions which bounds the VC dimension at $\log_2 {n \choose k}$. I'm wondering if this is bound at $k \log_2 n$? (Possibly follows from combinatorial ...
djechlin's user avatar
  • 487