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This is article 22 in Reading Stanford CS109, covering Summer 2026 Lecture 21: Comparing Classifiers (Jul 29), taught by Chris Gregg. It follows the official worksheet, answer key, and LLM guide.
This is L2: a four-page worksheet with P1–P8 plus a Platt challenge, a five-page key omitting only the P8 pset7 solution, and a three-page six-concept guide. Current slides are unavailable and video is Canvas-gated.
P1: Logistic Regression refresher
For θ=[-1,3,-1] and x=[1,1,1], z=1 and ŷ=0.7311. With y=1, ∂LL/∂θ₁=x₁(y-ŷ)=0.2689, so ascent increases θ₁. Negative θ₂ pushes predictions away from class 1.
P2: Brute-force Bayes and Naive Bayes
m binary features require O(2^m) cells: about 4.2 million assignments at m=22, and 2^100≈1.3×10^30 at 100. Data is the binding constraint: 467 samples can populate at most 467 cells.
Naive Bayes assumes conditional independence:
P(x₁,…,xₘ|y)=∏ⱼP(xⱼ|y)This reduces parameters to O(m). The assumption is usually imperfect but makes estimation feasible.
P3: A Beta prior prevents a zero-probability veto
Thirty positives in 100 examples with prior Beta(3,4) yield posterior Beta(33,74) and mean 33/107≈0.3084. The prior's pseudo-rate exceeds 0.30, hence the upward nudge. If a feature is never 1 among positives, MLE assigns zero and one unseen value vetoes the entire positive-class product; a prior supplies a small nonzero probability.
P4: Train, test, baselines, and overfitting
For 99.8% accuracy, first ask whether it is train or test. Random Forest has the largest table gap, 0.8726 versus 0.8500, but a two-point advantage still needs test size and a bootstrap interval. The always-positive baseline already scores 0.5887. XOR demonstrates a linear boundary's limit; interaction features can change separability in expanded space.
P5: Calibration is not accuracy
Observed positive fractions are 0.08,0.30,0.52,0.75,0.70. The 0.9 bucket is badly overconfident and has threshold accuracy 0.70. Under Bin(100,0.9):
P(X=70)=C(100,70)0.9^70 0.1^30 ≈ 1.8×10^-8That is not plausible sampling noise. A model that always outputs the base rate can be perfectly calibrated while having no discrimination.
P6: Precision, recall, and error costs
TP=40,FP=10,FN=20,TN=130 gives accuracy 0.85, precision 0.80, and recall 2/3. Always-negative still gets 0.70 accuracy but zero recall. Lowering a threshold usually raises recall and lowers precision. The correct priority in fraud or medical screening follows false-positive and false-negative costs.
P7: Fairness is not one number
Selection rates are 0.30 and 0.50; their 0.60 ratio fails the 80% rule. Positive-prediction correctness is 48/60=0.80 versus 70/100=0.70, a 0.10 gap that passes relaxed calibration at ε=0.2. Passing one criterion and failing another means “fair” requires an explicit definition. Removing a protected column also fails when correlated proxies reconstruct demographic signal.
P8: Decision-tree entropy
The root has 40/80 positives and entropy 1 bit. With p_left=17/52 and p_right=23/28:
H_left ≈ 0.912
H_right ≈ 0.677
E[H_child] ≈ 0.830
information gain ≈ 0.170 bitsP8 is a pset7 item omitted from the public key; these values follow the public prompt.
Optional challenge: Platt recalibration
For q=σ(ap̂-0.5), p̂=0.9,a=2 gives q=σ(1.3)≈0.7858. On held-out pairs:
LL(a)=Σᵢ[yᵢlog qᵢ+(1-yᵢ)log(1-qᵢ)]
∂LL/∂a=Σᵢp̂ᵢ[yᵢ-σ(ap̂ᵢ-0.5)]Optimize by gradient ascent. Calibration must use held-out validation data because training-set probabilities are optimistically distorted.
How to use the LLM Learning Guide
Work through brute-force Bayes, Naive Bayes, train/test evaluation, calibration, precision/recall, and fairness. Solve first, then ask for the first erroneous step and identify the error cost or fairness definition behind every metric choice.
Material boundaries
- The worksheet has P1–P8 plus a challenge; the five-page key omits only P8.
- The three-page guide has six concepts and no extra problem.
- Current slides are unavailable and video is Canvas-gated.
Course video sources
Verified the official Summer 2026 archive: the course is recorded and its syllabus says recordings are available through Canvas. The archived homepage's Videos link redirects to Stanford Canvas login and requires course access. None of the lectures in the 2022 Stanford Online public playlist matches this lecture's title, so no public player is provided and recordings from other offerings are not passed off as this one.
Official sources:
- CS109 Summer 2026 — Canvas lecture recordings (login required)
- CS109 Summer 2026 — archived official schedule
- CS109 Summer 2026 — archived syllabus and recording policy
- Stanford Online CS109 2022 public playlist (different offering, supplementary)
Checked: 2026-10-10.
Update Log
- 2026-10-10: Added explicit video status and checked recording sources and access notes.
- 2026-10-10: Rechecked video status. Confirmed Summer 2026 recordings need Canvas sign-in and the 2022 public playlist has no matching lecture; status unchanged and check date added.
References
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