Learning to Add

KnowledgeMiner has an advantage over other statistical programs because it can actually learn from a given set of data and reveal any relationships that might not be obvious, even to a trained eye.

A simple example that illustrates this ability can be observed using the Input-Output model method and the data below. If you haven't done so already, download the KnowledgeMiner Demo and follow along.

Given some source (X) and target data (Y), there is (almost) no knowledge about how these data relate. This lack of knowledge is called a "black box."

The Input-Output model tries to illuminate the "black box" by creating a mathematical equation that most reliably imitates the relationship between the source data and the desired target data. While it does not mimic the exact processes that created the results, it can derive some general principals that might prove insightful.

Part One: The Data
Before KnowledgeMiner can be of use to you, it has to learn. However, there is no need for you to teach KnowledgeMiner anything or suggest what relationships might exist within the data. To begin, enter the data below into KnowledgeMiner's spreadsheet.

Choose the target data by selecting the label for y and then hold down the Command or Shift key while selecting the three source columns a, b, c. Here's what the Data Window should look like in KnowledgeMiner.

At first glance at the data, it appears y = b + c. We want to find out if KnowledgeMiner can correctly deduce the correct relationship. To begin, under the Modeling Menu select Create Input-Output-Model...

KnowledgeMiner will present you with a list of model settings. In this case, just keep them set to the default settings and click the Modeling button.

The KnowledgeMiner will then start deducing relationships in the data and you should see this progress bar:

Part Two: Looking at the Equation

When the modeling is complete, select Modeling Equation under the Window menu. KnowledgeMiner creates three "true" models but defaults to showing the best solution. The model equation correctly identifies the relevant variables as being b and c. Although column a is nearly identical to column c except for the last entry, KnowledgeMiner correctly sees it as unnecessary information.

The simplified equation that KnowledgeMiner comes up with is found below:

X1 = -0.005530 + 1.000538X3 + 1.000700X4

which is very close to y = b + c.

To test the model, enter data into the columns b and c.

Then, select What-If-Prediction under the Modeling menu. Enter "1" for the "Forcast Horizon" and make sure you click "Add prediction data to table automatically" and click the "Prediction" button.

KnowledgeMiner returns 20.0063667 into column y. Due to the limitations of numerical precision, it is not possible to model exact relationships. But KnowledgeMiner does get very close and more important, discovers some knowledge not necessarily known, in this case y= b + c.

If your interested in trying more complex examples, check out the "Logistic Function" example found in the "Examples Folder" found with the KnowledgeMiner Demo.