Squared loss

As explained in Grokking Machine Learning

A regression error metric equal to the sum of squared differences between observed and predicted target values.

For a regression line, squared loss adds the squares of the vertical differences between the observed points and the line’s predictions. A smaller total indicates a closer fit; a larger total indicates a poorer one. section 3.4

Figure 3.19 The square error is the sum of the squares of the vertical distances from the points to the line. Note that the square error is large for the bad model on the left and small for the good model on the right.

Compare the squared distances for a poor-fitting line and a close-fitting line. section 3.4

How Grokking Machine Learning covers it

How deep it goes

Defines the metric as a sum of squared vertical distances and compares good and poor fits visually.

Examples

Compares squared distances from data points to good- and poor-fitting regression lines.

What you can do after

Evaluate a linear regression fit by interpreting the sum of squared distances from points to its line.

How it connects

Connects linear regression error to absolute error and gradient descent.

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Also explained in

• 

  liveBookmanning.com
  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AISquared error is a loss measure computed as the squared difference between a predicted and observed numeric value.
• 

  liveBookmanning.com
  Statistics Every Programmer NeedsThe sum of squared residuals is the sum of the squared differences between observed response values and their fitted values.
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  liveBookmanning.com
  Deep Learning with R, Third EditionSquared error is a discrepancy measure equal to the square of the difference between a prediction and its target.

Compare how 4 books explain squared loss →

Related concepts

• elbow methodused by · The elbow method is a heuristic for selecting model complexity or a parameter value by locating where increasing it yields diminishing improvement in an evaluation criterion.
• ordinary least squaresaddressed by · Ordinary least squares is a regression parameter-estimation method that minimizes the sum of squared residuals between observed and predicted responses.
• absolute errorcontrasts with · Absolute error is an error measure based on the nonnegative absolute difference between an observed value and its prediction, optionally aggregated across observations.
• meanaddressed by · A mean is a measure of central tendency, calculated as the arithmetic average of values or, for a random variable, as the probability-weighted average of its possible values.
• regularizationkind of · Regularization is a modeling technique that constrains or penalizes solutions during fitting or optimization to discourage undesirable complexity or behavior and improve generalization or estimation.

This explainer was generated by Manning's knowledge graph from the text of Grokking Machine Learning. The section links point to the parts of the book it draws on.