Possible issue with PolynomialLeastSquares() Class

[Mazecreator]

I have been working with the following code snippet and getting erratic results. I suspect there may be something wrong with the PolynomialLeastSquares() class of I just don't fully understand what it does.

If I run this:

Period = 14;
inputs = new double[Period];
outputs = new double[Period];

ols = new PolynomialLeastSquares();
ols.Degree = 3;
		
for(i = 0; i < Period; i++)
{
    inputs[i] = Convert.ToDouble(i);
outputs[i] = inputs[i];
}

// Use OLS to learn the regression
reg = ols.Learn(inputs, outputs);
result = reg.Transform(-1.0);
Print(ols.Degree+"  "+reg.ToString()+"  Int "+ reg.Intercept);

This is what is returned:

3 y(x) = 2.37812678233955E-17x^2 + 1x^1 + 2.77718345656259x^0 Int -2.77718345656258

This appears to be a 2 Degree equation as there is no X^3 and it seems like the X^0 intercept is shown with a different sign from reg.Intercept. If I use a more complex input with higher values and more of a curve, the Intercept starts to get very larger in magnitude. I took a quick look at the source code:
https://github.com/accord-net/framework/blob/development/Sources/Accord.Statistics/Models/Regression/Linear/Fitting/PolynomialLeastSquares.cs

Some things look funny here to me in building the X matrix, I don't see the 1's for the X^0 parameter (maybe you handle that elsewhere), but also the Pow() function seems to never put in the X^Degree factor, but rather an X^(Degree-1), not sure if this helps but if you could help advice when you get time, I would appreciate it.

[cesarsouza]

Hi Mazecreator,

Many thanks for opening the issue. Indeed there are some issues with the PolynomiaLeastSquares class, that probably got introduced during the rush to port all learning algorithms to the new .Learn() interfaces.

There are at least two problems there, both happening for the roughly the same reason: The .ToString() method and the .Learn are still reflecting the old implementation, where the intercept was stored as the last element of the .Coefficients array (which now it is stored as separate value in the .Intercept property).

I will add more tests and fix it before the next pre-release.

Regards,
Cesar

[cesarsouza]

Fixed in 3.5.0.