RBF - distance and weights

[rainbow]

Hi,

I have some questions about lecture 16 slides 3 and 6.

1. In slide 3, the distance is squared when included in the basis function of the hypothesis. This would bring down the significance of far away points even more, but what is the rationale behind the square?

2. In slide 6, you get the impression that each is distributed. Is this correctly understood given each weight is solved for exactly? Or should it be that each is distributed?

[yaser]

Originally Posted by rainbow

Hi,

I have some questions about lecture 16 slides 3 and 6.

1. In slide 3, the distance is squared when included in the basis function of the hypothesis. This would bring down the significance of far away points even more, but what is the rationale behind the square?

2. In slide 6, you get the impression that each is distributed. Is this correctly understood given each weight is solved for exactly? Or should it be that each is distributed?

1. The rationale behind the square is often the favorable analytic behavior and the relation to Gaussian.

2. If by distributed you mean is affected and affects different points, then yes. In slide 6, there is one , but it can be different 's a s well.

[rainbow]

Originally Posted by yaser

2. If by distributed you mean is affected and affects different points, then yes. In slide 6, there is one , but it can be different 's a s well.

Each point on the thick curve is a combination of N gaussians, weighted by . In the general case, most of the individual contributions are 0 due to the distance metrics as specified by the basis function. If increases the method becomes even more "local", and therefore a parameter to be tuned.

I probably got confused by my own notation, where I have written that each of the 3 minor (grey) gaussians are .

I hope I got it right... thanks!

[yaser]

Originally Posted by rainbow

I hope I got it right.

You did.