Exam practice

1. The new district’s height and slope are measured, and scaled the same way as the examples’ (for example to 0–1 by min–max scaling).
2. Its distance from every training example is worked out: the square root of (gap in height)² + (gap in slope)².
3. The examples are sorted from nearest to farthest, and the 3 nearest are taken.
4. Their labels vote: the belt that most of them have is the answer. (If all three differ, the nearest one’s belt is given.)

No rules are written in advance: the answer comes only from the examples.

A to B: gaps 0.30 and 0.40. √(0.30² + 0.40²) = √(0.09 + 0.16) = √0.25 = 0.5.
A to C: gaps 0.30 and 0.10. √(0.30² + 0.10²) = √(0.09 + 0.01) = √0.10 ≈ 0.32.
C is nearer to A.

The pocket money’s numbers are much bigger: a gap of Rs 1,000 counts as much as a gap of 1,000 cm in height, which is impossible. So pocket money decides the distance almost on its own, and height hardly counts. Fix it by scaling both features to the same range before measuring, for example with min–max scaling: (value − lowest) ÷ (highest − lowest), which turns both into numbers from 0 to 1.

Accuracy = 17 ÷ 20 × 100% = 85%.
Always saying Hill gets the 12 Hill districts right: 12 ÷ 20 × 100% = 60%. This is the baseline.
The model beats the baseline by 25 percentage points, so it has learned something from its features. But 85% alone would have sounded better than it is: the comparison shows how much of it is real learning.

The rows must add up to 30: 7 + 17 = 24 districts in the first two rows, so the Terai row has 6, all said Terai: ? = 6.
Right answers are on the diagonal: 5 + 13 + 6 = 24. Accuracy = 24 ÷ 30 × 100% = 80%.
Its most common mistake is calling Hill districts Mountain (3 times). It never confuses Mountain and Terai: they are far apart in height.

Each example is tested in turn by a model trained on all the other examples. So every example is tested once, and never by a model that has it as an example. The accuracy is the number right out of all the examples.
With only 77 examples, a test set of 15 is small, and its score jumps a lot depending on which districts it happens to get (from 80% to 100% in this unit). Leave-one-out uses all 77 for testing and 76 for training each time, so the score is steadier and no data is wasted.

With height and slope scaled, Bhaktapur’s nearest neighbors are Kathmandu (Hill), Dang and Chitwan (Terai), or in the widget’s training set Dang, Kailali (Terai) and Udayapur (Hill): two Terai votes to one. Bhaktapur is mostly the flat floor of the Kathmandu Valley, so its average slope (10°) is as low as that of Terai districts with some hills, and its height (1,378 m) is between.
The program is not at fault: it did exactly what nearest neighbors should. The features can’t tell a flat valley high in the hills from flat plains, at least when slope counts as much as height (with height alone, Bhaktapur is placed correctly). The label is correct: Bhaktapur is in the Hill belt.

• Source: heights from the Shuttle Radar Topography Mission (2000), rain from CHELSA’s climate model, people from the 2021 census, belts from the government’s grouping.
• Quality: the rain is a model’s estimate, weakest high in the mountains where there are few gauges; the heights had gaps in steep valleys that were filled by estimating; the census is a few years old.
• Representativeness: only 77 examples, 16 of them Mountain; whole districts only, so it can’t be used for a single village.
• Bias: each district has one label though its land spans several belts (Gorkha has Manaslu but is Hill); the model learns people’s decisions.
• Privacy: no single person is in it, only totals; the census office keeps each household’s answers secret by law.

Any three, with reasons, such as:

• Who is in it, and who is missing? If the bank lent mostly to people in cities, or mostly to men, the model has few examples of village farmers or women, and may treat them unfairly (representativeness).
• Do the labels carry old unfairness? If the bank turned people away in the past for reasons that weren’t fair, the model learns those decisions as if they were right (bias in the labels).
• What features does it use, and could any stand in for something unfair? A home address can stand in for caste, ethnicity or wealth.
• Is the data still true? Twenty-year-old loans may say little about today’s incomes and prices (quality).
• Did customers agree, and is their data kept safe? Loan records are private, and a leak harms real people (privacy).

• i.Rules. The rule is known and must be followed exactly (marks ≥ the pass mark), and students must be able to see why. A model could only make mistakes a rule never would.
• ii.Nearest neighbors (or a decision tree). A small table: two features, a few hundred examples. Nearest neighbors needs no rules to be known, is quick at this size, and can show which grains it compared with. A neural network would need far more data for no gain.
• iii.A neural network. Speech is a sound wave with thousands of numbers every second; nobody can write rules or choose features for it by hand. Neural networks trained on many hours of recorded Nepali speech do this, though they need large data, and must be tested on speakers from every part of Nepal.

Benefits (any two): better weather and flood forecasts (GraphCast learned from decades of weather records); help for doctors finding disease in medical images; translation and voice typing in more languages; useful tools such as search and maps.
Harms (any three): people’s writing, photos and faces used without their consent (Clearview AI’s billions of face photos, fined €30.5 million in the Netherlands); surveillance, when collected data is used to follow people; leaks that expose private data; low-paid and harmful labeling work (workers in Kenya paid under $2 an hour); bias against people who are less online and so less in the data; electricity and water used by data centers.