Prediction intervals for linear regression models

[gkronber]

r15743: created a branch

[gkronber]

r15744: implemented a new class LinearRegressionModel that produces variances for predictions (IConfidenceRegressionModel). Changed LR to produce a ConfidenceRegressionSolution (old static method is kept but marked obsolete)

[gkronber]

r16388: Merging r15750:16382 (HEAD) from trunk to branch, resolving conflicts

[gkronber]

r16389: merged branch back to trunk

[gkronber]

We could also change the ERC-view to produce LR models with confidence intervals. Right now it still produces 'traditional-style' LR models (represented as symbolic expression trees).

[gkronber]

r16390: deleted branch after trunk reintegration

[gkronber]

r16392: fixed failing unit test

[fholzing]

Please note: A View for the Linear Regression Model is missing.

[mkommend]

r16415: Fixed used variables in LinearRegressionModel.

[mkommend]

r16437: Merged r16392 into stable.

This changeset has already been released, because it caused conflicts as it affects functionality implement in other tickets (#2904).

[mkommend]

r16443: Changed variable impact unit tests to use new LR methods.

[gkronber]

r16448: changed LR to produce two solutions: symbolic representation and solution with prediction intervals.

It is not straight-forward to implement the model with prediction intervals as a symbolic regression model.

[gkronber]

Reverted unintended change to ticket.

[gkronber]

r16449: added a view for LR models with prediction intervals

[abeham]

Reviewed r16389, r16415, r16448:16449

• trunk/HeuristicLab.Algorithms.DataAnalysis/3.4/Linear/LinearRegression.cs
  • obsolete method uses allocation of double[] coefficients which is unnecessary as it will be assigned by alglib.lrunpack

The two-fold approach of having a solution with confidence and a generic one that can be simplified is not so nice. The comment mentions that There is no clean way to implement the new model class for LR as a symbolic model. Have you considered introducing subclasses LinearSymbolicRegressionModel and LinearSymbolicRegressionSolution that would calculate covariation matrix and confidence bounds by assuming the given tree represents a linear model and throwing exception in case the assumption is violated?

Another option to consider would be to create the symbolic model on the fly from the confidence-based one when "Simplify Model" or "Export to Excel" is hit.

Anyway, this can be performed at a later date.

[abeham]

r17074: merged to stable

[gkronber]

Replying to abeham:

Have you considered introducing subclasses LinearSymbolicRegressionModel and LinearSymbolicRegressionSolution that would calculate covariation matrix and confidence bounds by assuming the given tree represents a linear model and throwing exception in case the assumption is violated?

Another option to consider would be to create the symbolic model on the fly from the confidence-based one when "Simplify Model" or "Export to Excel" is hit.

Anyway, this can be performed at a later date.

Probably, the first option is possible. We should create a new ticket for this.

[gkronber]

r16443 has not been merged to stable

[gkronber]

r17163: merged r16443 from trunk to stable

[gkronber]

r17168: update mergeinfo: r16392 has been merged to stable already (see r16437)