Regression and AI in practice
Introduced| English | Meaning |
|---|---|
| regression/rɪˈɡreʃn/ | A statistical method for modelling how a response variable is related to one or more explanatory variables. |
| classification/ˌklæsɪfɪˈkeɪʃn/ | Arranging items or organisms into groups according to shared features or a defined system. |
| linear regression/ˈlɪnɪə rɪˈɡreʃn/ | A method of modelling a response using a linear combination of explanatory variables and fitted coefficients. |
| OCR/ˌəʊ siː ˈɑː/ | OCR |
Predicting a number, not a name
- Ask a model "is this email spam?" and it must choose from a fixed set of answers. Ask it "what will this house sell for?" and there is no set to choose from: the answer is a number, and being out by a thousand pounds is nearly right.
- Those are two different tasks, and mixing them up is the commonest mistake in this topic. Both are supervised learning; only the shape of the answer differs.
- This lesson is regression 回归 against classification 分类, how linear regression 线性回归 chooses its line, and how real products chain trained models into a pipeline.
Regression and classification
- Classification predicts a category from a fixed set: cat or dog, spam or not spam, which of ten digits.
- Regression predicts a number on a continuous scale: a house price, tomorrow's temperature, how long a journey will take.
- Both are supervised: both learn from labelled examples. The choice between them is decided by one question: is the answer a label or a number?
- The distinction changes how you measure success. A classifier is right or wrong; a regressor is a certain distance out, which is why their loss functions differ.
The difference between regression and classification is that regression predicts:
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Regression outputs a continuous number (price, temperature); classification outputs a category.
Regression predicts a continuous number (a price, a temperature), while classification predicts a category (cat vs dog).
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Number out = regression; category out = classification — the two main kinds of supervised prediction.
Worked example: which task is which
- Predicting which of five customer types a shopper belongs to. Classification: the answer is one of a fixed set of categories.
- Predicting how much that shopper will spend next month. Regression: the answer is a number, and being close counts as nearly right.
- Predicting whether a machine will fail in the next week. Classification: yes or no. Predicting how many days until it fails. Regression.
- The same underlying data can feed either. Read the question being asked, not the subject matter.
Match each prediction task to its kind.
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The same data can feed either. Read the question: a label from a fixed set, or a number on a scale.
Linear regression
- Linear regression fits a straight line, or a flat surface when there are several inputs:
- The coefficients are chosen to minimise the sum of the squared errors between the line's predictions and the actual training values.
- Squared, for two reasons the exam accepts: errors above and below the line then cannot cancel out, and a large error is penalised much more than several small ones.
The line that leaves the least total squared distance
Fitting a regression line
Drag the controls. Linear regression draws the straight line that makes the squared distances to the data points as small as possible — then it predicts a number for any new input.
Linear regression chooses its coefficients to:
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It fits the line/hyperplane that makes the squared differences from the data points as small as possible.
Why does linear regression minimise the sum of the SQUARED errors rather than the errors themselves?
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Both reasons are accepted. Without squaring, a line could have a huge error above and below and still score zero.
When a straight line is the right model
- Use linear regression when the relationship looks roughly linear and you want a model a human can read: each coefficient says how much that input matters, and in which direction.
- When the data curves, the same idea still applies with a different model: polynomial regression, a decision tree, or a neural network. In every case the recipe is the same, choose a model, define a loss, minimise it.
- That recipe is what connects this lesson to the last one: gradient descent is simply how the minimising is done when there is no formula for the answer.
AI in a real product
- Real systems rarely use one model. They chain several trained models into a pipeline, each doing one step.
- Face identification at a door: a camera captures a face, image recognition converts it into a numerical representation, and that is matched against the representations of registered people.
- Reading a sign aloud for a traveller: image recognition locates the text, OCR 光学字符识别 turns the pixels into characters, machine translation converts the words, and text-to-speech produces the audio.
- The exam gives a scenario and asks which models are used, in order. Name the stage and what it produces for the next one.
Match each AI idea to what it means.
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Training fits the model once; inference is the quick prediction each time a user interacts.
A "read a sign aloud" feature typically chains which models?
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Several trained models form a pipeline: find the text, extract characters, translate, then speak.
Put the stages of an app that reads a foreign sign aloud in order.
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Several trained models chained together, each handing its output to the next. Name the stage and what it produces.
Worked example: training against inference
- A phone app recognises a plant from a photograph instantly, yet training its model took weeks on many machines. Explain why.
- Training repeatedly runs forward and backward passes over a very large labelled dataset, adjusting millions of weights over many epochs. That is what took weeks.
- Inference, using the trained model, is a single forward pass through a network whose weights are now fixed: multiply, add, activate, layer by layer, once.
- The intelligence lives in the learned weights, which is why the finished model is small enough and fast enough to ship on a phone.
Using a trained model to make a prediction requires only a single ____ pass.
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Training repeats forward and backward passes over a huge dataset; inference runs the fixed weights once, which is why it is instant.
Marks that slip away
- Classification gives a category, regression gives a number. Both are supervised; that is not the difference.
- Linear regression minimises the sum of squared errors, not "the total distance". Say squared, and say why.
- A pipeline answer must give the stages in order and say what each hands to the next.
- Training is repeated forward and backward passes; inference is one forward pass. Do not describe training when the question asks about use.
You've got it
- classification predicts a category, regression predicts a number; both are supervised, and the question's answer shape decides which
- linear regression fits $y = m_1x_1 + \ldots + c$ by minimising the sum of squared errors, so errors cannot cancel and large ones are penalised heavily
- curved data needs another model, but the recipe is unchanged: choose a model, define a loss, minimise it
- real products chain models: image recognition, OCR, translation and text-to-speech; training is many forward and backward passes, inference is one forward pass