MullOverThing

Useful tips for everyday

# Which is the best definition of the VC dimension?

## Which is the best definition of the VC dimension?

The VC dimension (for Vapnik–Chervonenkis dimension) is a measure of the capacity (complexity, expressive power, richness, or flexibility) of a statistical classification algorithm, defined as the cardinality of the largest set of points that the algorithm can shatter.

## How is the VC dimension related to the size of ε nets?

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. The VC dimension of the dual set-family of

When to use VC dimension for binary functions?

The VC dimension is defined for spaces of binary functions (functions to {0,1}). Several generalizations have been suggested for spaces of non-binary functions. For multi-valued functions (functions to {0,…,n}), the Natarajan dimension can be used.

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.

### What is the VC dimension of a rotatable rectangle?

Rotatable rectangles are VC dimension 7. Suppose we have a regular heptagon. It’s easy to get any subset of 0, 1, 2, 6, or 7 points. For 3 points, all conﬁgurations are symmetric to ABC, ABD, ABE, or ACE. The ﬁgure below shows how can we can rotate rectangles to capture these 3 point conﬁgurations.

### How does the Gradient Boosting Machine work in GBM?

Boosting is the process of iteratively adding basis functions in a greedy fashion so that each additional basis function further reduces the selected loss function. This implementation closely follows Friedman’s Gradient Boosting Machine (Friedman, 2001).

How to calculate the VC dimension in machine learning?

VC-Dimension 2: It can classify all four situations correctly. class (0) = True, class (42) = True => a = − 1, b = 1337 classifies this correctly. VC-Dimension 3: No, that doesn’t work.

How to use generalized boosted regression modeling ( GBM )?

A symbolic description of the model to be fit. The formula may include an offset term (e.g. y~offset (n)+x). If keep.data = FALSE in the initial call to gbm then it is the user’s responsibility to resupply the offset to gbm.more.