Page 2 of 8~112 min topic

Loss functions

Define the regression loss workbench input contract

Page 2 hardens the boundary around the regression loss workbench so bad inputs fail before the interesting algorithm runs.

~14 min this pageData contract

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Define what may enter

The accepted input remains: predicted vs true numeric targets for a tiny regression set. Keep parsing and normalization in functions that do not score, train, or call a model. That split lets a test fail the boundary without blaming the core logic. The user-facing decision stays: compare MSE vs MAE on the same residual set to see which outlier hurts more.

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Reject at the boundary

import math
def valid(a,b): return len(a)==len(b)>0 and all(math.isfinite(x) for x in a+b)
print(valid([1,2],[1.2,1.8])); assert not valid([1],[1,2])

Expected evidence: True, while the unequal arrays assertion passes. If the contract is silent on a bad value, later debugging will look like an algorithm bug when it is really a data bug.

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Keep transforms testable

Write one assertion for a neighboring valid input to the regression loss workbench so tightening the boundary does not over-reject. Document field names and types the way a teammate would need them on day two of loss-functions—not as comments you plan to delete.

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Lab notebook: name the fields

List every field in y_true/y_pred arrays including one large outlier and mark each as required, optional, or forbidden. Required fields must fail loudly when missing; optional fields need defaults you can quote in a test; forbidden fields (secrets, raw PII, path escapes) must never be accepted silently. This list is the contract for the regression loss workbench.

Add one sentence about encoding, units, or timezones if relevant to predicted vs true numeric targets for a tiny regression set. Contracts that ignore units create “correct” programs that still ship wrong decisions when someone tries to compare MSE vs MAE on the same residual set to see which outlier hurts more.

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Worked judgment

Write the error string you want for the most likely bad input. Prefer ValueError('threshold out of range')-style messages over generic invalid input. The contract’s job is to make shape mismatch between y_true and y_pred, or silent NaN loss harder to confuse with a model or algorithm bug later.

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Why this stage matters for the regression loss workbench

At the data contract stage for loss-functions, the job is narrower than finishing a product demo. You are creating one progressive evidence piece about y_true/y_pred arrays including one large outlier that later pages inherit without redefining success. Keep that fixture small enough to inspect by hand, keep outputs copy-pasteable as text, and refuse to narrate this baseline as if it were a production SLA: mean prediction residual before any model.

For this page specifically, success looks like malformed inputs rejected with field-named errors while still centering the user decision to compare MSE vs MAE on the same residual set to see which outlier hurts more. If you cannot point to a file, command, or assertion that proves that for the regression loss workbench, stay on this page instead of advancing.

Glossary: loss function · Glossary: gradient descent

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Before you start

Why this matters

Invent one malformed input that the regression loss workbench might accidentally accept. Predict the exception or rejection message. After you run the contract code, compare your prediction with the real failure text.

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Page assessment

Answer from memory. Completion is saved from this evidence, not from opening the next page.

1. Which malformed values die before core logic?
2. Can transform and prediction/search be tested separately?
3. Does the error name the violated field or shape?
4. Is the accepted input still exactly: predicted vs true numeric targets for a tiny regression set?

All responses are required.