LRA -> PLA Effect of Alpha

[tcristo]

I noticed that when running the Linear Regression on a training data set followed by running the PLA using the same data and LRA weights, that the Learning Rate (Alpha) of the PLA seems to significantly effect the rate of convergence. I am assuming that the optimal size of alpha is directly related to the size of the convergence errors from the Linear Regression.

Is there a way to model this mathematically such that the Alpha parameter can automatically be calculated for each training set?

[htlin]

Originally Posted by tcristo

I noticed that when running the Linear Regression on a training data set followed by running the PLA using the same data and LRA weights, that the Learning Rate (Alpha) of the PLA seems to significantly effect the rate of convergence. I am assuming that the optimal size of alpha is directly related to the size of the convergence errors from the Linear Regression.

Is there a way to model this mathematically such that the Alpha parameter can automatically be calculated for each training set?

For PLA, I cannot recall any. For some more general models like Neural Networks, there are efforts (in terms of optimization) for adaptively changing the value. BTW, I think the homework problem asks you to take no (or a naive choice of ) Hope this helps.

[tcristo]

Originally Posted by htlin

For PLA, I cannot recall any. For some more general models like Neural Networks, there are efforts (in terms of optimization) for adaptively changing the value. BTW, I think the homework problem asks you to take no (or a naive choice of ) Hope this helps.

I originally had my set at one. I was surprised that running the LRA first to preset the weights and then running the PLA didn't significantly decrease the number of iterations required. I am getting a 50% reduction or thereabouts and expected an order of magnitude reduction. When you view it graphically, the LRA does what seems like 98+% of the work most of the time.

The size of alpha doesn't always seem to matter but there are specific cases of where the appropriately assigned is able to drop the number of iterations down by an additional 50%-75%.

I am going to chew on this for a little while and see if I can figure out the relationship.

[jsarrett]

No one ever said the PLA was a *good* algorithm. It's only guaranteed to converge eventually. I'm sure later in the lecture we'll get to better optimization algorithms.

[gah44]

Originally Posted by tcristo

I originally had my set at one. I was surprised that running the LRA first to preset the weights and then running the PLA didn't significantly decrease the number of iterations required. I am getting a 50% reduction or thereabouts and expected an order of magnitude reduction. When you view it graphically, the LRA does what seems like 98+% of the work most of the time.

(snip)

I wondered about this in the class discussion, but I only noticed this one now.

As the problem is done with then, as you note, the effect is small. What it seems is that if the LRA solution correctly classifies the points, then no cycles of PLA are used, otherwise just about as many as before. The 50% is the cases where no cycles of PLA are used.