Simple postprocess multiple regression/classification

[Shoeboxam]

There are multiple potential implementations. Here is how a covariance implementation could look. We need the additional components Inverse and Matmul.

Component: Inverse

Arguments

• data

Component: Matmul

Arguments

• left
• right

  Options

• pseudoinverse

Then the top-level component that expands:

Component: DPLinearRegression

Arguments

• predictors (matrix or dataframe)
• target (column vector

  Options

• implementation
• mechanism
• ddof

The expansion for the 'covariance' implementation could be:

parameters = Matmul(Inverse(DPCovariance(predictors)), DPCovariance(predictors, target))
intercept = DPMean(target) - Matmul(DPMean(predictors), parameters)
ColumnBind(intercept, parameters)

DPCovariance already covers cross-covariance as a special case. We can propagate nulls up from the inverse. To make this quick to implement, we could only allow public data and aggressively drop properties.