Training , Validation , Test set , A more general case

A regular practice is dividing training data into tree parts to evaluate the performance of the algorithm. Training set is used to train  parameters of the model. Validation set is used to "train" hyper parameters of the model and test set is used to evaluate the model.
     For more general sense what if I divide my training set into n part and use first set to bottom level parameters  for the tree (One can use topological sort in graphical model) of the parameters. Than iterate next upper level training upper level parameters in next set. At the end we would have no parameters above the top which corresponds to a test set. Basically , make the distinction between parameters and hyper parameters fuzzy.

Polynomial multiplication , base x

For representing polynomials we can use base notation , it will make some operation easier.
for example 1+x+x^2 = (111)_x

For multiplication (x+1) * (x+1) = x^2 + 2x + 1
We can represent as (11)_x + (11)_x = (121)_x
It becomes like a regular multiplication if it does not excess 10 for one digit , but if it does than we need to seperate number e.g. (1,13,1)_x = x^2 + 13x + 1
We can assume at this point x > R (all real numbers) in base notation.

Robot Particles Display:

Current display devices can show any image for a very cheap price. But it will be very intresting if someone tries to implement display using multiple robots. For example each robot will have fixed color and will stay in rectengular area. After input comes the positions of the robots will change to approximate the given image input. If this could be done in 2D in Earth. It could be extentable 3D in space since gravity no longer becomes a problem. That will result real 3D display using robotic particles. A good science finction scenario :).

It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.

Albert Einstein

Power Law

What is the relation between power law behavior and TF.Idf frequencies. They are supporting each other.

Arbitrary Complexity PageRank-Prestige

Prestige :

A

Page Rank:

 

A + A_f 

Hub - Authority :

HITS algorithm - Incoming -> Authority , Outgoing -> Hub 

Arbitrary  :

Hub Authority + Unknown L class if pointed by Hubs the more the L it is and if A pointed by L the more the Authority it is (Or maybe having too many Hubs makes L strong). You can define anything.

The question is for a real world scoring could we find a optimum score graph given a large data ? Since no true score value exist for arbitrary model there is no criteria for evaluation yet.