Prediction Error

A Prediction Error is a model error that represents the difference between a predicted value and the actual value in a predictive modeling task.

• AKA: Forecast Error, Model Error, Estimation Error, Predictive Deviation, Residual.
• Context:
  • It can typically be calculated as the difference between predicted output and true output for a given instance.
  • It can typically be measured using various error metrics depending on the prediction task type.
  • It can typically arise from model bias, model variance, or irreducible error in the data.
  • It can typically be analyzed to understand model performance and identify improvement opportunities.
  • It can typically guide model selection, hyperparameter tuning, and feature engineering decisions.
  • It can often vary across different data regions, time periods, or input distributions.
  • It can often be decomposed into systematic error and random error components.
  • It can often indicate overfitting when training error is low but test error is high.
  • It can often be reduced through ensemble methods, regularization, or data augmentation.
  • It can often have different cost implications depending on error direction and magnitude.
  • It can range from being a Classification Error to being a Regression Error, depending on its task type.
  • It can range from being a Training Prediction Error to being a Test Prediction Error, depending on its data partition.
  • It can range from being a Point Prediction Error to being an Interval Prediction Error, depending on its prediction type.
  • It can range from being a In-Sample Prediction Error to being an Out-of-Sample Prediction Error, depending on its evaluation context.
  • It can range from being a Systematic Prediction Error to being a Random Prediction Error, depending on its error pattern.
  • It can be minimized through optimization algorithms during model training.
  • It can be estimated through cross-validation, bootstrap methods, or holdout validation.
  • It can be visualized using residual plots, error distributions, and learning curves.
  • It can be weighted differently in cost-sensitive learning and weighted regression.
  • ...
• Example(s):
  • Classification Errors, such as:
    • Binary Classification Error: wrong class in two-class problem.
    • Multi-Class Classification Error: wrong category in multi-class problem.
    • False Positive Classification: incorrectly predicting positive class.
    • False Negative Classification: incorrectly predicting negative class.
  • Regression Errors, such as:
    • Absolute Error: |predicted - actual| value.
    • Squared Error: (predicted - actual)² value.
    • Percentage Error: relative error as percentage.
    • Logarithmic Error: error in log-transformed space.
  • Time Series Prediction Errors, such as:
    • Forecast Error: incorrect future value prediction.
    • Lag Error: temporal misalignment in prediction.
    • Trend Error: incorrect direction prediction.
    • Seasonal Error: incorrect seasonal pattern prediction.
  • Probabilistic Prediction Errors, such as:
    • Calibration Error: probability estimate deviation.
    • Log Loss Error: logarithmic scoring error.
    • Brier Score Error: quadratic scoring error.
  • Structured Prediction Errors, such as:
    • Sequence Prediction Error: error in sequence labeling.
    • Graph Prediction Error: error in network prediction.
    • Tree Prediction Error: error in hierarchical structure.
  • Domain-Specific Prediction Errors, such as:
    • Medical Diagnosis Error: incorrect disease prediction.
    • Financial Forecast Error: incorrect market prediction.
    • Weather Prediction Error: incorrect weather forecast.
    • Demand Forecast Error: incorrect demand prediction.
  • Aggregated Prediction Errors, such as:
    • Mean Absolute Error (MAE): average absolute errors.
    • Mean Squared Error (MSE): average squared errors.
    • Root Mean Squared Error (RMSE): square root of MSE.
    • Mean Absolute Percentage Error (MAPE): average percentage errors.
  • ...
• Counter-Example(s):
  • Correct Prediction, which matches the true value.
  • Perfect Prediction, with zero error.
  • Model Uncertainty, which quantifies prediction confidence rather than error.
  • Bias-Variance Tradeoff, which is a theoretical concept rather than actual error.
  • Training Loss, which is optimization objective rather than prediction error.
  • Gradient, which is derivative rather than error.
  • Feature Importance, which measures relevance rather than error.
• See: Classification Error, Regression Error, Model Error, Statistical Model Assessment Task, Mean Absolute Error (MAE) Measure, Mean Squared Error (MSE) Measure, Cross-Validation, Model Performance Metric, Residual Analysis, Error Analysis, Decision Tree Training System, Interpolation Task, Extrapolation Task, System Predictability Measure, Model Evaluation Method, Error Weighting Metric.

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