How deeply does Deep Learning with R, Third Edition cover squared loss?

Defines the formula and implements averaging, then applies gradient updates without deriving the gradients mathematically.

Squared loss

As explained in 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.

Squared loss measures prediction error by squaring the difference between each prediction and its target. Averaging these squared differences produces one loss value for training. section 3.3.2

Training a linear classifier

A linear classifier predicts two-dimensional points with prediction = matmul(input, W) + b. On 2,000 synthetic points from two classes, minimizing squared loss with batch gradient updates reduces the loss from 4.5364 to 0.0289 over 40 steps. Predictions above 0.5 separate the classes. section 3.3.2

mean_squared_error <- function(targets, predictions) {
  per_sample_losses <- tf$square(targets - predictions)  #1
  tf$reduce_mean(per_sample_losses)  #2
}

The implementation squares elementwise target-prediction differences, then averages the per-sample losses. section 3.3.2

How Deep Learning with R, Third Edition covers it

Cover of Deep Learning with R, Third Edition

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Also explained in

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

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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 Deep Learning with R, Third Edition. The section links point to the parts of the book it draws on.