# Questions tagged [pac-learning]

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55 views

### An (unusual?) risk bound

I am told that that a bound on the generalization error of the following form exists in terms of something called the shattering coefficient" - but I am not able to reference this quantity in ...
80 views

### Generalization bound for parameters rather than loss functions

I was wondering if it is possible to obtain high probability bounds (provided finite sample size of the training data) for the distance (say in the l-1 or l-2 norm) between the best parameter set and ...
64 views

### No free lunch theorem and finite hypothesis classes

I have read the no free lunch theorem(NFLT) section 5.1 of Understanding machine learning by Shai Shalev-Shwartz. There is also this Corollary 4.6 which states any finite hypothesis class is PAC ...
104 views

### Generalisations of the Fundamental Theorem of Statistical Learning to different tasks and losses

The fundamental theorem of statistical learning gives an equivalence between uniform convergence of the empirical risk to learning in the PAC framework. I have only seen this stated in the case of ...
38 views

### Is statistical query learning equivalent to correlational statistical query learning given a fixed distribution?

As title, I saw some paper mentioned they are equivalent, but I'd wonder how to prove they are? is it something to do with PAC as SQ is a restricted version of PAC?
98 views

### Logic of learning

Does Robust logic (Leslie Valiant), Default logic (Raymond Reiter) and Circumscription logic (John McCarthy) have any relation? I was Mathematician and Computer Science (dual degree undergraduate) ...
47 views

### Is there a notion of Probably Approximately Correctness in Unsupervised Learning? [closed]

I've been learning a little bit about computational learning theory, but most of what I've seen so far is related to supervised learning. Perhaps dimensionality reduction will be touched on, but not ...
127 views

74 views

### representation of concept classes and pac learning

I was reading the book of Kearns and Vazirani and I didn't completely understand the following: Let C be a concept class and suppose we want to PAC learn C, they say first consider a larger ...
85 views

### Agnostic query learning of decision trees

Gopalan, Kalai, Klivans gave an algorithm https://dl.acm.org/citation.cfm?id=1374376.1374451 for agnostically learning decision trees $h:\{0,1\}^n\to\{0,1\}$ under the uniform distribution given ...
125 views

### Lower bound of real valued bounded function

Is well known that the lower bound on number of example necessary to reach a given error for concept classes $\Omega(d/\varepsilon)$ (cf. also Agnostic PAC sampling lower bound ) I am looking for the ...
163 views

112 views

### Sample complexity for learning Boltzmann Distribution parameters

I am trying to think through the number of samples that I would need to estimate the parameters of a Boltzmann partition function to a desirable precision. Suppose that there are $N$ possible states ...
498 views

### Difficulty of “learning” rare instances

Is there any result showing that models (say SVM, Neural-Net, kNN, etc) will have difficulty in learning "rare" instances/tail phenomena?
61 views

### Learnability of under some characteristics of the distribution

TLDR; is there any results showing that more concentrated (or easier) distributions are easier to learn? In PAC-learning, the guarantee is given for any underlying distributions. But in reality, we ...
564 views

### PAC-learning bound with epsilon-cover of hypothesis class

In this video at 43:00, a version of the PAC bound for generalization error $\epsilon$, which I hadn't seen before, is quoted: $$\epsilon^2 < \frac{\log{|H_\epsilon|} + \log{1/\delta}}{2m}$$ ...
359 views

### Rademacher complexity beyond the agnostic setting

The way I know of to bound generalization error by Rademacher complexity is Theorem 2.4 in this lecture notes, http://ttic.uchicago.edu/~tewari/lectures/lecture9.pdf. Here the quantity on the LHS that ...
This paper (http://www.cs.columbia.edu/~rocco/Public/stoc01.pdf) from STOC 2001 is possibly the first paper to show how to convert upperbounds on the $\frac{1}{3}-$approximation degree of a Boolean ...