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How do you read VC dimensions?
The definition of VC dimension is: if there exists a set of n points that can be shattered by the classifier and there is no set of n+1 points that can be shattered by the classifier, then the VC dimension of the classifier is n. The definition does not say: if any set of n points can be shattered by the classifier…
What is VC H?
● Definition: The Vapnik-Chervonenkis dimension, VC(H), of. hypothesis space H defined over instance space X is the size. of the largest finite subset of X shattered by H . If arbitrarily. large finite sets of X can be shattered by H , then VC(H) ≡ ∞.
What is Hoeffding tree?
The Hoeffding tree is an incremental decision tree learner for large data streams, that assumes that the data distribution is not changing over time. It grows incrementally a decision tree based on the theoretical guarantees of the Hoeffding bound (or additive Chernoff bound).
What is the difference between decision tree and decision stump?
A decision stump is a Decision Tree, which uses only a single attribute for splitting. For discrete attributes, this typically means that the tree consists only of a single interior node (i.e., the root has only leaves as successor nodes). If the attribute is numerical, the tree may be more complex.
Which is the correct VC dimension for a k dimension?
In general, for a k-dimension space VC(H)=k+1 NB: It is useless selecting a set of linealy independent points Upper Bound on Sample Complexity Lower Bound on Sample Complexity Bound on the Classification error using VC-dimension
Why is the VC dimension of H 3?
And that’s why the VC dimension of H is 3. Because for any 4 points in 2D plane, a linear classifier can not shatter all the combinations of the points. For example, For this set of points, there is no separating hyper plane can be drawn to classify this set. So the VC dimension is 3.
Which is the correct definition of the VC-dim?
VC-Dimension definition (2) Def. 2: the VC-dimension of a function set F(VC- dim(F)) is the cardinality of the largest dataset that can be shattered by F. Observation: the type of the functions used for shattering data determines the VC-dim
How is the sample complexity related to the VC dimension?
Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. 0.