Questions tagged [computational-learning-theory]

For questions related to computational learning theory (or, in short, learning theory), which is a research subfield of artificial intelligence devoted to studying the design and mathematical analysis of machine learning algorithms. Computational learning theory (COLT) is largely concerned with computational and data efficiency. A seminal paper in COLT is Valiant's "A theory of the learnable" (1984).

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How to estimate the capacity of a neural network?

Is it possible to estimate the capacity of a neural network model? If so, what are the techniques involved?
jaeger6's user avatar
  • 308
9 votes
1 answer
3k views

What are some resources on computational learning theory?

Pretty soon I will be finishing up Understanding Machine Learning: From Theory to Algorithms by Shai Ben-David and Shai Shalev-Shwartz. I absolutely love the subject and want to learn more, the only ...
PMaynard's user avatar
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13 votes
2 answers
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What are other examples of theoretical machine learning books?

I am looking for a book about machine learning that would suit my physics background. I am more or less familiar with classical and complex analysis, theory of probability, сcalculus of variations, ...
Ilya's user avatar
  • 133
1 vote
1 answer
270 views

How can a machine learning problem be reduced as a communication problem?

I once heard that the problem of approximating an unknown function can be modeled as a communication problem. How is this possible?
Raphael Augusto's user avatar
14 votes
1 answer
572 views

What are the state-of-the-art results on the generalization ability of deep learning methods?

I've read a few classic papers on different architectures of deep CNNs used to solve varied image-related problems. I'm aware there's some paradox in how deep networks generalize well despite ...
Shirish Kulhari's user avatar
11 votes
3 answers
500 views

Are there any rules of thumb for having some idea of what capacity a neural network needs to have for a given problem?

To give an example. Let's just consider the MNIST dataset of handwritten digits. Here are some things which might have an impact on the optimum model capacity: There are 10 output classes The inputs ...
Alexander Soare's user avatar
8 votes
3 answers
4k views

What is the difference between hypothesis space and representational capacity?

I am reading Goodfellow et al Deeplearning Book. I found it difficult to understand the difference between the definition of the hypothesis space and representation capacity of a model. In Chapter 5,...
Qwarzix's user avatar
  • 83
10 votes
2 answers
779 views

What are the learning limitations of neural networks trained with backpropagation?

In 1969, Seymour Papert and Marvin Minsky showed that Perceptrons could not learn the XOR function. This was solved by the backpropagation network with at least one hidden layer. This type of network ...
S.L. Barth is on codidact.com's user avatar
4 votes
2 answers
410 views

Mathematical foundations of the ability to learn

I am an undergraduate student in applied mathematics with an interest in artificial intelligence. I am currently exploring topics where I could do research. Coming from a mathematical background I am ...
Matheo's user avatar
  • 143
19 votes
1 answer
1k views

What is the number of neurons required to approximate a polynomial of degree n?

I learned about the universal approximation theorem from this guide. It states that a network even with a single hidden layer can approximate any function within some bound, given a sufficient number ...
mark mark's user avatar
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7 votes
1 answer
796 views

Are PAC learning and VC dimension relevant to machine learning in practice?

Are PAC learning and VC dimension relevant to machine learning in practice? If yes, what is their practical value? To my understanding, there are two hits against these theories. The first is that ...
FourierFlux's user avatar
5 votes
4 answers
2k views

How does size of the dataset depend on VC dimension of the hypothesis class?

This might be a little broad question, but I have been watching Caltech youtube videos on Machine Learning, and in this video prof. is trying to explain how we should interpret the VC dimension in ...
Stefan Radonjic's user avatar
3 votes
1 answer
543 views

What is meant by "stable training" of a deep learning model?

I have read it said that the "stable training" of a deep learning model is important. What is meant by "stable training" of a deep learning model?
The Pointer's user avatar
3 votes
2 answers
4k views

What's the difference between estimation and approximation error?

I'm unable to find online, or understand from context - the difference between estimation error and approximation error in the context of machine learning (and, specifically, reinforcement learning). ...
stoic-santiago's user avatar
2 votes
2 answers
1k views

What is the difference between a learning algorithm and a hypothesis?

What's the distinction between a learning algorithm $A$ and a hypothesis $f$? I'm looking for a few concrete examples, if possible. For example, would the decision tree and random forest be considered ...
Shirish Kulhari's user avatar
2 votes
1 answer
619 views

How do I prove that $\mathcal{H}$, with $\mathcal{VC}$ dimension $d$, shatters all subsets with size less than $d-1$?

If a certain hypothesis class $\mathcal{H}$ has a $\mathcal{VC}$ dimension $d$ over a domain $X$, how can I prove that $H$ will shatter all subsets of $X$ with size less than $d$, i.e. $\mathcal{H}$ ...
user avatar
1 vote
1 answer
110 views

If Least-Squares TD is computationally more expensive, then why is it more data efficient than semi-gradient TD(0)?

In Sutton-Barto (Section: 9.8 Least-Squares TD, page 228): Authors say that Least-Squares TD is the most "data efficient" form of linear TD(0). Later, in this section, they say the ...
user3489173's user avatar