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Mix a clean signal with noise

BOTIE

Build one forward noising step. Scale the clean sample by the square root of alpha and the noise by the square root of one minus alpha, then combine them.
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Use a copy of the example to try your own data. Keep the problem's assumptions in mind, and predict the effect of a change before checking the output. You can also add another branch to compare two ways of doing the calculation.

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Context for this challenge

Build one forward noising step. Scale the clean sample by the square root of alpha and the noise by the square root of one minus alpha, then combine them.

Botie can construct a controlled noisy sample before attempting to learn how to reverse the corruption.

Use square-root alpha for the clean branch and square-root one-minus-alpha for the noise branch, then add them.

Examples and results
Clean sample
  1. 01
  2. 10
Standard-normal noise draw
  1. 00
  2. 11
Retained signal fraction
0.8
Required result
  1. 00.8944
  2. 10.4472
Try a fresh construction

This clears this draft, including its undo history. Earlier successful attempts stay recorded. Build again without opening hints to record an independent attempt.

Stuck? Inspect a worked construction

The tools below form one possible solution. You can assemble it, follow its signals, and undo that change to return to your own construction.

Assumptions and test precision

This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out. Numerical tests allow a difference of 0.001. Lists and structures must also have the right shape.

Noise pulls against the clean sample

This check uses the pieces from “Combine separately scaled signal and noise”.

BOTIE

Botie has a clean two-coordinate sample and a noise draw that points against it. Apply the forward noising step with retained signal fraction 0.36. Use square roots for both scale factors.
Clean sample
  1. 02
  2. 1-1
Standard-normal noise draw
  1. 0-1
  2. 12
Retained signal fraction
0.36

Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.

Build a construction in the workspace above first. This case will test those pieces.

Why is knowing the noisy vector alone insufficient to undo these supplied examples?

Forward corruption is explicit arithmetic; learning a reverse process requires information about the data distribution.

This is a small construction problem. The lesson explains the assumptions and the parts of the full method that this example leaves out.

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