Squared loss
Squared loss is the square of the difference between a predicted or fitted value and its target or observation, often summed across data points.
Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI
Squared error is a loss measure computed as the squared difference between a predicted and observed numeric value.
- How it is used
- Guides regression fitting by defining the residual-sum-of-squares objective for linear models and a gradient signal for boosting.
- How deep it goes
- Connects the objective to linear-regression coefficients and boosting gradients, without deriving the squared-loss formula.
- Examples
- Uses a scikit-learn linear-regression pipeline with RMSE scoring and a from-scratch gradient-boosting regression loop.
- What you can do after
- Apply it via scikit-learn and XGBoost by selecting regression objectives and interpreting squared-error-based training workflows.
Read how Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI explains squared loss →
Statistics Every Programmer Needs
The sum of squared residuals is the sum of the squared differences between observed response values and their fitted values.
- How it is used
- Uses squared residuals to fit linear regression and evaluate how closely predictions match observed responses.
- How deep it goes
- Derives SSE through residuals and SST–SSR decomposition, but stops short of discussing optimization algorithms or loss-function variants.
- Examples
- Uses marathon stage1 and stage2 times, fitted values, a sum-of-squares table, and NumPy calculations.
- What you can do after
- Evaluate regression fit by calculating SSE directly from residuals and validating it against SST minus SSR.
Read how Statistics Every Programmer Needs explains squared loss →
Grokking Machine Learning
A regression error metric equal to the sum of squared differences between observed and predicted target values.
- How it is used
- Measures how well a linear regression model’s line fits the observed data points.
- 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.
Deep Learning with R, Third Edition
Squared error is a discrepancy measure equal to the square of the difference between a prediction and its target.
- How it is used
- Trains a linear classifier by providing a differentiable discrepancy between predictions and binary targets.
- How deep it goes
- Defines the formula and implements averaging, then applies gradient updates without deriving the gradients mathematically.
- Examples
- Uses two synthetic two-dimensional point classes, R/TensorFlow code, loss logs, and a plotted decision boundary.
- What you can do after
- Apply via TensorFlow and R by defining squared loss and minimizing it with gradient-based parameter updates.
Read how Deep Learning with R, Third Edition explains 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.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.