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1answer
43 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 ...
8
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1answer
472 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?
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0answers
60 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 ...
3
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1answer
141 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: $$\epsilon^2 < \frac{\log{|H_\epsilon|} + \log{1/\delta}}{2m}$$ ...
4
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1answer
145 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 ...
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0answers
75 views

Reference request for the relationship between approximating degree of Boolean functions and learning algorithms

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 ...
6
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2answers
248 views

Proper PAC learning VC dimension bounds

It is well known that for a concept class $\mathcal{C}$ with VC dimension $d$, it suffices to obtain $O\left(\frac{d}{\varepsilon}\log\frac{1}{\varepsilon}\right)$ labelled examples to PAC learn $\...
3
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1answer
157 views

Rademacher complexity and lowerbounds in learning theory

Is there any function class known whose Rademacher complexity has a non-trivial lowerbound? Can the Rademacher complexity be used to lowerbound the generalization error in any learning situation?
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0answers
114 views

Boolean functions with high query complexity for PAC learning

The most general theorem for PAC learning of Boolean functions that I am aware of is the theorem in section 3.4 of Ryan O'Donnel's book where its basically shown that Boolean functions whose Fourier ...
1
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1answer
80 views

Learning from derivative data

In many machine learning algorithm, it is often assumed that outputs of unknown function and their corresponding inputs are given to estimate the unknown function. However, I wonder whether there ...
1
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1answer
125 views

Does MCMC belong to the statistical query model?

It is known that a wide range of algorithms fall into the statistical query (SQ) learning model by Michael Kearns. Examples include k-means, logistic regression, naive Bayes (NB), SVM, ICA, PCA, ...
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0answers
161 views

The Complexity of Properly Learning Decision Trees

Where does this paper prove the middle bullet point of its abstract? I have looked through that paper fairly thoroughly. There are three things I want to read how they're getting around. Reductions ...
6
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0answers
114 views

Learning read-once branching programs with membership queries

Let $B=\{0,1\}$. A read-once branching program of width $n$ and size $w$ is given by a graph with layers $0,\ldots, n$, where the first layer has just the starting node, the last layer has nodes ...
3
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1answer
169 views

Is this variant of PAC learning known?

Here is a problem I've never seen, in a model similar to the PAC model. It asks a similar question to PAC learning, but wishes to optimize, rather than learn. I wonder if this problem is known, has ...
7
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1answer
311 views

Statistical query model with Gaussian noise?

Kearns' statistical query model is a well-known learning model with noise tolerance. The statistical query oracle takes as input a statistical query of the form $\{\chi, \tau\}$. Here $\chi$ is any ...
6
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1answer
437 views

What does PAC-learnability say about the learner runtime?

I am new to PAC-learnability. Assume a class $\mathcal{H}$ of hypotheses is PAC-learnable. Then all we know that if we draw polynomial number of examples (in $\delta$ and $\epsilon$), we can return a ...