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raccourcis clavier

The Problem

We need to predict a continuous numeric value (price, temperature, probability) but the relationship between inputs and output is complex.

Core Idea

Supervised learning task where the goal is to predict a continuous numeric output variable from input features.

How It Works

  1. Collect labeled data: features X and continuous target y
  2. Choose regression model: linear regression, decision trees, neural networks, etc.
  3. Define loss function: typically mean squared error (MSE) or mean absolute error (MAE)
  4. Train: find model parameters that minimize average prediction error
  5. Predict: for new inputs, compute continuous output value

Visual Explanation

G Features (X) Features (X) Regression Model Regression Model Features (X)->Regression Model Continuous Prediction (ŷ) Continuous Prediction (ŷ) Regression Model->Continuous Prediction (ŷ) Targets (y) Targets (y) Loss (MSE/MAE) Loss (MSE/MAE) Targets (y)->Loss (MSE/MAE) Optimize Optimize Loss (MSE/MAE)->Optimize Prediction (ŷ) Prediction (ŷ) Prediction (ŷ)->Loss (MSE/MAE)

Key Properties

  • Continuous output: predicts values on a real-valued scale (not categories)
  • Probabilistic: can model uncertainty via prediction intervals
  • Interpretable: linear regression coefficients show feature importance directly
  • Metric-dependent: MSE penalizes large errors more than MAE

Connections

Edge Cases & Gotchas

  • Heteroscedasticity: error variance changes with input values (violates OLS assumptions)
  • Multicollinearity: correlated features distort coefficient estimates
  • Outliers: heavily influence linear regression (consider robust regression)
  • Non-linearity: linear regression fails when true relationship is curved