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6
votes
0answers
29 views

Boolean formula that agrees with most truth assignments

Let $X_1,\dots,X_n$ be $n$ boolean variables. I have an unknown predicate $P(X_1,\dots,X_n)$ on these boolean variables. Of course, I can view the predicate as a function $f_P : \{0,1\}^n \to ...
5
votes
2answers
87 views

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 ...
3
votes
2answers
62 views

How to determine the size of training data using VC dimension?

I want to determine the size of training data ($m$) when I know the parameters $VC(H)$, $δ$ and $e$. As I know the $VC$ bound satisfy this equation: $$ \mathrm{error}_{\mathrm{true}}(h) \le ...
2
votes
1answer
60 views

proving the error bound for a hypothesis

Given a hypothesis $h:X\rightarrow Y$ ($h$ is returned by an Empirical Risk Minimization (ERM) strategy with realizable case i.e. $h$ is consistent with the sample examples) over $X=[0,1]\subseteq R$ ...
5
votes
2answers
94 views

Learning juntas, with membership queries

The junta problem is the following: we have a boolean function $f:\{0,1\}^n \to \{0,1\}$ that actually happens to depend on only $k$ of its input variables. Given the value of $f(x)$ for many random ...
3
votes
1answer
88 views

VC dimension of linear separator in 3D

I am confused about the Vapnik-Chervonenkis dimension of a linear separator in 3 dimensions. In three dimensions, a linear separator would be a plane, and the classification model would be ...
6
votes
1answer
110 views

Adapting neural network

I have on a few occasions trained neural networks (back propagation networks) with some rather complicated data sets (backgammon positions and OCR). When doing this, it seems that a lot of the work ...
3
votes
1answer
462 views

What are the mathematical prerequisites for adaptive machine learning algorithms?

I am a PhD student in Computer Science who switched his PhD a little bit towards ML algorithms combined with something else... I am an expert in that something else, say image processing, but not an ...
21
votes
1answer
635 views

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 ...