/ GRADIENT DESCENT

/ We generate data based on a random weight matrix.
/ Then we train on that data and see what the correlation is.

/ generate data
numweights: 20;
numdatapoints: 5000;
eta: 0.001;

weights: 1 - 2*(numweights ? 1.0);

datamat: ();
target: (); / targets based on weight matrix 
do[numdatapoints;
  x: 10 * (numweights ? 1.0);
  datamat,: enlist x;
  y: sum weights * x;
  y+: first 1 - 2 * 1 ? 1.0; / randomize target
  target,: y];
  
/ So, now we have datamat and target value.
/ Later we can randomize target to throw in noise.

std:{sqrt var[x]}
corr:{ (cov[x;y])%((std[x]) * (std[y]))}

graddescent:{[datamat; target]
 candweights:  1 - 2*(numweights ? 1.0);
 origcorr: corr[candweights; weights]; / original correlation
 errorvec: ()
 i: 0;
 while[i < count datamat;
  predict: sum candweights * datamat[i];
  error: (target[i] - predict) % numweights;
  errorvec,: error;
  influence: error * eta * datamat[i];
  candweights+: influence;
  / candweights-: avg candweights;
  i+:1];
  newcorr: corr[candweights; weights];
 (origcorr; newcorr; candweights)}



trip: graddescent[datamat; target];

("Original correlation: " ), string trip[0]
("Correlation after training: "),string trip[1]