How Machine Learning Learns

Machine learning sounds mysterious and is mostly arithmetic done a staggering number of times. Once you see one small model learn, every bigger one is the same idea with more numbers.

The parts

Every machine learning project has the same ingredients.

• Training data: a pile of past examples. For a spam filter, 100,000 old emails.
• Features: the inputs the model looks at for each example. Number of links, whether the sender is in your contacts, whether the subject line says FREE in capitals.
• Labels: the right answer for each example. This email was spam; that one wasn't. Somebody had to supply those answers, often by clicking "report spam."
• A model: a formula with adjustable numbers in it (called parameters or weights). At the start, the numbers are guesses.
• A loss: a score for how wrong the model is. Lower is better.

Training means: make a guess for every example, measure the loss, nudge the adjustable numbers to make the loss a little smaller, and repeat until it stops improving. That's it. The rest is engineering.

A worked toy example

The invented Pine Hollow Neighborhood Association wants to predict turnout at its meetings so it can rent enough chairs. It has records from five meetings: how many flyers volunteers posted, and how many people came.

Flyers is the feature. Attendance is the label. The model is a straight line:

predicted people = (slope x hundreds of flyers) + starting point

The slope and the starting point are the two adjustable numbers. Training means finding values that fit the five meetings best.

Step 1: a first guess and its loss

Say we guess slope 15 and starting point 12. For March (1 hundred flyers) the model predicts 15 x 1 + 12 = 27 people. Real: 30. Error: 3.

We need one number for "how wrong overall." The most common choice is mean squared error: square each error so negatives don't cancel positives and big misses count extra, then average.

Sum of squared errors: 9 + 64 + 9 + 324 + 169 = 575. Divide by 5 meetings: a loss of 115.

Step 2: nudge and re-measure

Every guess was too low, so the slope should go up. Try slope 18, keeping the starting point at 12.

Sum: 80. Divide by 5: a loss of 16. Down from 115. For this data, slope 18 and starting point 12 happen to be the best possible straight line; no other pair of numbers gets the loss lower. A computer finds that by making many small nudges, each one in the direction that shrinks the loss. Lesson 4 explains how it knows which direction.

The trained model says: each extra 100 flyers brings about 18 more people, and about 12 show up no matter what (the regulars). Not bad for five rows.

Overfitting: the model that memorized

A fancier model can hit all five meetings exactly. A curved formula with five adjustable numbers can bend through every point, for a training loss of zero. Looks perfect. Now the association holds three more meetings the model never saw.

On the new meetings, the straight line's mean squared error is (4 + 0 + 100) / 3, about 35. The curve's is about 7,500, almost all from predicting that 600 flyers will produce negative 20 people. That is overfitting. The curve learned the noise in five meetings (May was a little light, maybe it rained) instead of the pattern. It looks brilliant on the data it studied and falls apart on anything new.

Why the test set exists

Builders guard against this with a test set. Before training, they lock away a slice of the data, often 10 to 20 percent. The model never sees it during training. At the end, they score the model on the locked slice. That score is the honest one, because it is the closest thing to the future.

If a company tells you its model is "98 percent accurate," the first question is: accurate on what? On its training data, that number means little. On a held-back test set from the same source, it means something. On fresh data from your town, collected after the model was built, it means the most.

Where real models get their data

A spam filter's labels come from millions of users clicking "report spam." A credit model's labels come from who actually paid back loans. A medical imaging model's labels come from doctors marking scans. Every one of those label sources has gaps. If the old loan records come from a bank that rarely lent in certain neighborhoods, the model has little data on those neighborhoods and may score them poorly for that reason alone. When the world shifts (a pandemic, a new scam, a new road), a model trained on the old world keeps predicting the old world. This is called drift, and it is why serious teams re-test models on a schedule.