Lab: train a model yourself

This is where it all comes together. Below is a complete, if tiny, machine learning system: a dataset, a model $f_{w,b}(x) = wx + b$, a cost $J(w,b)$ and an optimiser, gradient descent. Everything a large model does, this does too, just with two parameters instead of billions.

How the lab works

• Left, the data and the model. Pick a preset dataset, or tap empty space to add a house and tap a point to remove it (the buttons do the same from the keyboard). The blue line is the current model.
• Middle, the contour map of $J(w, b)$. The trail shows every step gradient descent has taken. Click the map to choose a different starting point.
• Right, the loss curve. The cost after every iteration.
• Controls. Set the start values and $\alpha$, then Step one iteration at a time or Run. Reset goes back to the start. Show the answer draws the exact best line (computed directly with a formula) so you can check what gradient descent found.

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This lab is a complete learning system: data, a line, a cost, and gradient descent.

Challenges

The lab ticks these off as you complete them:

1. Train to $J < 0.1$ on the House prices preset. Start from $w = 0$, $b = 0$ with $\alpha = 0.1$ and press Run. Compare your line with Show the answer.
2. Find a learning rate that diverges. Raise $\alpha$ a little at a time. What does the path on the contour map look like just before it blows up, and just after?
3. Converge in under 100 iterations. You’ll need a well-chosen $\alpha$, and maybe a better starting point.
4. See the effect of an outlier. Load the One outlier preset and train. One badly priced house drags the whole line toward it, because squaring makes its large error count a lot. Remove it and train again.
5. Fit your own data. Add at least three houses of your own and train a model on them.

Questions to think about

• Starting points: does gradient descent always reach the same line, wherever you start? (For this bowl-shaped cost, it should. Why?)
• Why does the loss curve drop steeply at first and then flatten?
• On the Flat — no trend preset, what value does $w$ end up near, and what does that mean about how price depends on size in that data?

Section 1 quiz

You’ve finished the first section. This quiz covers everything from what machine learning is to choosing a learning rate; each answer comes with an explanation.

Self-check · 10 questions

Section 1 quiz: regression and gradient descent

1. Which problem is the best candidate for machine learning?

Estimating a used car's price from its age, mileage and modelSorting invoices by dateConverting kilograms to poundsCalculating compound interest

2. A hospital has thousands of scans, each labelled by doctors as healthy or not. A model learns to label new scans. This is…

Unsupervised clusteringSupervised classificationSupervised regressionReinforcement learning

3. Which of these is an unsupervised learning task?

Predicting a house price from past salesFinding groups of similar customers with no labelsTranslating sentences from paired examplesDiagnosing disease from labelled scans

4. For $f_{w,b}(x) = 1.5x + 1$, what is $\hat{y}$ when $x = 2$?

33.545

5. Two training examples: $(1, 2)$ and $(2, 2)$. For the model $w = 1, b = 0$, what is $J(w,b)$?

0.250.512

6. A point on the contour map of $J(w,b)$ lies on the smallest ring around the centre. What does that tell you about its line?

It has a cost close to the minimum, so it fits the data nearly as well as possibleIt has the steepest slopeIt passes through the originIt's the starting point of gradient descent

7. What does the learning rate $\alpha$ control in gradient descent?

The size of each stepThe number of training examplesThe shape of the cost functionThe direction of each step

8. At the minimum of $J$, what is the slope $\frac{\partial J}{\partial w}$, and what does gradient descent do there?

Zero, so w stops changingNegative, so w increasesOne, so w decreases by alphaVery large, so it takes a big step

9. You train with $\alpha = 1.0$ and the cost goes 5, 20, 80, 320… What should you do first?

Start from a different wTrain for more iterationsLower the learning rate, for example to 0.3 or 0.1Add more data

10. Why is batch gradient descent called batch?

It trains several models at onceIt runs in the backgroundIt updates one parameter at a timeEach step uses all m training examples to compute the slopes

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