Let's assume we have a motion sensor that provides us X and Y data for a target where the measurement error is normally distributed with parameters:

First we will need to train our prediction model with some training data. We add a square term to give the target a parabolic path.

Now build the five different supported predictor functions:

With minimal parameter input here is Information about the predictors as built with default parameters:

$\begin{array}{cc}''Method''& ''Linear\; regression''\\ ''Number\; of\; features''& 1\\ ''Number\; of\; training\; examples''& 200\\ ''L1\; regularization\; coefficient''& 0\\ ''L2\; regularization\; coefficient''& 1.\end{array}$

$\begin{array}{cc}''Method''& ''Gaussian\; Process''\\ ''Number\; of\; features''& 1\\ ''Number\; of\; training\; examples''& 200\\ \mathrm{AssumeDeterministic}& \mathrm{False}\\ ''Numerical\; Covariance\; Type''& ''SquaredExponential''\\ ''Nominal\; Covariance\; Type''& ''HammingDistance''\\ ''EstimationMethod''& ''MaximumPosterior''\\ ''OptimizationMethod''& ''FindMinimum''\end{array}$

$\begin{array}{cc}''Method''& ''K-nearest\; neighbors''\\ ''Number\; of\; features''& 1\\ ''Number\; of\; training\; examples''& 200\\ ''Number\; of\; neighbors''& 10\\ ''Distance\; function''& \mathrm{EuclideanDistance}\end{array}$

$\begin{array}{cc}''Method''& ''Neural\; network''\\ ''Number\; of\; features''& 1\\ ''Number\; of\; training\; examples''& 200\\ ''L1\; regularization\; coefficient''& 0\\ ''L2\; regularization\; coefficient''& 0.1\\ ''Number\; of\; hidden\; layers''& 2\\ ''Hidden\; nodes''& \\ ''Hidden\; layer\; activation\; functions''& \\ ''CostFunction''& ''Cost\; Function''\end{array}$

$\begin{array}{cc}''Method''& ''Random\; forest''\\ ''Number\; of\; features''& 1\\ ''Number\; of\; training\; examples''& 200\\ ''Number\; of\; trees''& 50\end{array}$

Now we build a new random sensor track and test it against our trained prediction functions.

Here is our "training track" plotted against the trackData1 we created.

We create a plot function that allows us to pass track data and show the first plot's prediction, confidence interval and raw data using a linear regression predictor:

We decide we'd rather parameterize the prediction method so we steel a cool method found on the Wolfram site.

Finally let's plot them all in one combined chart.

Viola' we get this chart:

The Gaussian Process provides the best fit and tightest confidence interval for our track predictor.

You can download the CDF and/or the Notebook for this work. Enjoy and let me know if you find something wrong or improve it.

Thanks,

Phil Neumiller