Regression

Generate Data

> npts := 50:

> with(stats);

> noise := map(x->.1*x,[stats[random,normald](npts)]):

> inputs := [stats[random,uniform](npts)]:

> targs := map(x->2*x + .5,inputs) + noise:

> with(plots):

> with(linalg):

Warning, new definition for norm

Warning, new definition for trace

> datapts := transpose([inputs,targs]):

> dataplot := pointplot(datapts, color = red):

> display(dataplot);

Network Function

> w := [stats[random,normald](2)] ;

> nout := proc(w,pt) w[1] + pt*w[2];

> end;

> plotNet := proc(w,range,col)

> plot(nout(w,x),x=range[1]..range[2],color=col);

> end;

> display(dataplot,plotNet(w,[min(op(inputs)),max(op(inputs))],green));

> calcSqErr := proc(inputs,targs,w) local totalerrSq, i;

> totalerrSq := 0;

> for i from 1 to nops(inputs) do

> totalerrSq := totalerrSq +
.5*(targs[i] - nout(w,inputs[i]))^2;

> od;

> end:

> sqErrs := [calcSqErr(inputs,targs,w)];

> train := proc(inputs,targs,mu)
local pick, i, p, index, err, wold; global w;

> wold := w;

> pick := rand(1..npts);

> for i from 1 to 100 do

> index := pick();

> p := inputs[index]; # pick an input

> index := pick();

> err := targs[index] - nout(w,inputs[index]);

> w[1] := w[1] + mu*err; # bias term

> w[2] := w[2] + mu*err*inputs[index];

> od;

> display(dataplot,plotNet(w,[min(op(inputs)),max(op(inputs))],green),
dataplot,plotNet(wold,[min(op(inputs)),max(op(inputs))],blue));

> end:

> wold := w:

> train(inputs,targs,.02);

> sqErrs := [op(sqErrs),calcSqErr(inputs,targs,w)];

> print("The old weight:",wold); print(" The new weight:",w);

Plot the error as a function of time.

> s1 := [seq(i,i=1..nops(sqErrs))];
pointplot(transpose([s1,sqErrs ] ),color=red);

> sqLogErrs :=evalf(map(x->log10(x),sqErrs));

> pointplot(transpose([s1,sqLogErrs ] ),color=red);

>