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Results tagged with computational-learning-theory
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user 4446
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).
3
votes
Why does estimation error increase with $|H|$ and decrease with $m$ in PAC learning?
Definitely, you can find the proof in different resources (for example, in these notes or in the paper that originally proposed PAC learnability, A Theory of the Learnable). However, the intuition beh …
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2
votes
Accepted
Is the VC Dimension meaningful in the context of Reinforcement Learning?
Yes, it is. This article (Approximate Planning in Large POMDPs via Reusable Trajectories) explain about it by means of the trajectory tree:
A trajectory tree is a binary tree in which each node is la …
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3
votes
Accepted
How does size of the dataset depend on VC dimension of the hypothesis class?
From [1] we know that we have the following bound between the test and train error for i.i.d samples:
$$
\mathbb{P}\left(R \leqslant R_{emp} + \sqrt{\frac{d\left(\log{\left(\frac{2m}{d}\right)}+1\righ …
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1
vote
How do you distinguish between a complex and a simple model in machine learning?
If you want to find a proper architecture for your model, you can use the NAS (neural architecture search) methods instead of running some naive models to find a model and involving to decide which mo …
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2
votes
Accepted
How do I prove that $\mathcal{H}$, with $\mathcal{VC}$ dimension $d$, shatters all subsets w...
We can show that it is not true by a counterexample. For example, $X = \{1,2,3\}$ and $\mathcal H = \{\{\},\{1\},\{2\},\{1,2\}\}$ is the finite set hypothesis class. By definition, in this case, the $ …
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1
vote
Accepted
What is meant by "stable training" of a deep learning model?
I can say "Stable Learning" of a supervised machine learner is as follows:
A stable learning algorithm is one for which the prediction does not change much when the training data is modified slightly …
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1
vote
1
answer
328
views
Is the VC Dimension meaningful in the context of Reinforcement Learning?
Is the VC dimension meaningful for reinforcement learning (RL), as a machine learning (ML) method? How?
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3
votes
Accepted
Understanding relation between VC Symmetrization Lemma and Generalization Bounds
Let $\varepsilon$ in (17) is equal to $\sqrt{\frac{4}{n}\left(\log{(2\mathsf{N}(\mathcal{F},n))}-\log{\delta}\right)}$. We have:
$$
P\left(\sup_{f\in\mathcal{F}}|R(f)-R_{emp}(f)| > \sqrt{\frac{4}{n}\ …
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