Before we start, here is the one map to keep in your head. Every exercise lives on one of these five
stages, and the arrows are why we call it a loop, not a line.
We will only ever need three little tools. Let us re-state each in plain words before any symbol
is used, so a reader who has never seen them can still follow.
Order: Scoping → Data → Modeling → Deployment → Monitoring.
The stage that first quantifies worth is Scoping (it uses Tool 1, the expected-value formula).
WHAT this looks like: the leftmost box in the figure above, before you ever touch data.
Recall Solution
(a) ::: Data drift
(b) ::: Canary deployment
(c) ::: Shadow deployment
See Deployment strategies (shadow, canary, blue-green) and Data drift and concept drift.
Plug into Tool 1:
E[Value]=0.7×200,000−50,000−40,000=140,000−90,000=$50,000.
WHY this step: we price feasibility (0.7) and ongoing cost (40k) in one number.
\mathbb{E}[\text{Value}] = +\50{,}000 > 0$ → green-light in scoping.
Recall Solution
Set E[Value]=0 and solve for psuccess:
psuccess⋅200,000−90,000=0⇒psuccess=200,00090,000=0.45.
WHY this step: at break-even the payoff exactly covers all fixed costs. Any feasibility
psuccess>0.45 makes it worthwhile. Answer: ==0.45==.
Tool 2:
Avoidable bias=9−1=8%,Variance=12−9=3%.
Bias (8%) ≫ variance (3%), so the biggest lever is the model / features (bigger
model, better architecture, richer features), not more data. See
Bias-variance decomposition.
Recall Solution
Avoidable bias=5−4=1%,Variance=15−5=10%.
Now variance (10%) dominates. The lever is more / cleaner data and regularization — attack
the generalization gap, not the model size.
Recall Solution
Avoidable bias=3−5=−2%.
A negative avoidable bias is meaningless as a "gap to close." WHAT it really means:
TrainErr<HLP, so the model beats humans on the training set — the classic
signature of overfitting (it memorized noise). See
Human-level performance and Bayes error. The real signal now lives entirely in the variance
term (11−3=8%): fix generalization.
(a) ::: Data drift — the inputs P(x) changed (new vocabulary); the ruleP(y∣x) is fine.
(b) ::: Jump back to Stage 2 (Data) — collect + label the new inputs, then retrain. Retraining
on old data cannot help because old data lacks the new inputs.
(c) ::: Shadow deployment — the new model runs on live traffic with output ignored, so you
compare silently and spot the mismatch before it reaches users. See
Model monitoring and observability.
Recall Solution
(a) ::: Concept drift — same P(x), but P(y∣x) changed (same input, new correct answer).
(b) ::: Relabeling new data under the new policy helps; the old labels are now wrong, so you
must re-label to the new concept and retrain. This is why concept drift is nastier than data
drift — even your history is stale.
(a) ::: Model B. The north-star is the business metric subject to the satisficing
constraint. Model A violates latency (130>100 ms), so its higher accuracy is disqualified —
a fast 96% beats a too-slow 99%. This is a scoping decision.
(b) ::: Shadow deployment at the "Shadow" automation level: A runs on live traffic, its output
is logged but never used, so you compare A vs B silently with zero user risk. See
Deployment strategies (shadow, canary, blue-green).
Recall Solution
(a) Tool 1:
E[Value]=0.55×300,000−60,000−50,000=165,000−110,000=$55,000>0.
Build it — positive expected value even after pricing the ongoing monitoring team.
(b) ::: Data-centric. The dominant error category (60%) is noisy labels, so relabeling that
one category (fixing the data for a fixed model) is the 80/20 move — clean data generalizes better.
See Data-centric vs model-centric AI.
Recall
One-line self-check: which single formula would you use for each of — "is it worth building?",
"where do I spend the week?", "which arrow after a production drop?"
Answer ::: Tool 1 (expected value); Tool 2 (bias/variance gaps); Tool 3 (data vs concept drift).