En anglais

Too stiff, too wobbly, or just right

Computing · Machine Learning · ages 19-21

Name ______________________ Date ____________

A straight line fits curving data and misses the same way no matter how much data arrives. What is this?
- Bias
- Variance
- Overfitting
A model always predicts 0.4 while the true share is 0.5. With bias as average prediction minus truth, what is the bias?
Answer: ______________
High prediction variance at a fixed input means predictions are widely spread around their average across possible training samples.
Circle one: True False
If a model has bias at an input, its predictions at that input cannot also vary across training samples.
Circle one: True False
Which method can reduce variance by combining fitted models?
- Averaging many models over resampled data
- Fitting one fixed line without comparing samples
- Discarding observations without combining predictions
Three models have these errors on the same held-out sample: A: training 8, held-out 9; B: training 4, held-out 5; C: training 2, held-out 7. Select by the lowest held-out error. Which choice follows this rule?
- Model A, because its held-out error is 9
- Model C, because its training error is 2
- Model B, because its held-out error is 5
- Model C, because its held-out error is 7
At one fixed input, two equally likely training samples give predictions 2 and 4. Their average is 3. Prediction variance is the average squared distance from this average. What is the prediction variance?
Answer: ______________
Training error falls but held out error climbs as you add flexibility. What is happening?
- Perfect learning
- Underfitting
- Overfitting
Two models make errors: one is steady and stiff, and the other swings with samples. Which pairing is right?
- Both are bias
- Stiff is variance, swinging is bias
- Stiff is bias, swinging is variance
After collecting more representative training data, predictions at a fixed input have a smaller spread across repeated samples, but their average remains below the true mean response. Which conclusion is supported?
- Bias disappeared, since a larger sample removes every error
- Variance fell, while a negative bias remains
- Variance rose, while the average miss proves there is no bias

Answer key

For grown-ups. Fold this page away before handing over the rest.

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Bias · Steady misses from a model that is too stiff mean bias.
-0.1 · 0.4 minus 0.5 is minus 0.1, a steady underestimate.
True · Variance averages squared distances from the average prediction across training samples. High variance describes a wide spread, not a guaranteed jump after every small edit.
False · Bias concerns the average prediction relative to the true mean response. Variance concerns the spread around that average. A model can have both at the same input.
Averaging many models over resampled data · Bagging averages predictions from models fitted to bootstrap samples of training data. It can reduce variance when their sampling errors differ.
Model B, because its held-out error is 5 · Compare held-out errors 9, 5 and 7. The lowest is 5, so select model B. Model C's lower training error does not change the stated selection rule.
1 · The distances from 3 are -1 and 1. Squaring gives 1 and 1. Their average is (1 + 1) / 2 = 1.
Overfitting · Falling training error with rising held-out error suggests overfitting: added flexibility is not improving performance on the held-out data.
Stiff is bias, swinging is variance · A systematic average miss indicates bias. Changes in predictions across training samples indicate variance. One model can have both.
Variance fell, while a negative bias remains · The smaller spread across training samples means lower prediction variance. The average remains below the true mean response, so bias is still negative.