🔬 RMSLE (Root Mean Squared Logarithmic Error)

RMSLE (Root Mean Squared Logarithmic Error)#

RMSE on log-scaled values, penalising under-prediction and easing large magnitudes.

Important

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What it is#

Root Mean Squared Logarithmic Error is RMSE computed on the logarithms of the predictions and actuals — the root-mean-square of the differences in log space:

\[\text{RMSLE} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\big(\log(\hat{y}_i + 1) - \log(y_i + 1)\big)^2}.\]

The +1 lets it handle zeros.

What the log changes#

Taking logs turns absolute errors into relative ones, so a fixed percentage miss costs the same whether the value is small or huge — making RMSLE robust to scale and to large outliers. It also becomes asymmetric: it penalizes under-prediction more than over-prediction.

When to use it#

RMSLE suits positive, right-skewed targets that span orders of magnitude — prices, counts, demand — and situations where under-forecasting is the costlier mistake. Its limits: it can’t take negative values, and its log scaling makes the raw number less intuitive than RMSE.

Theme: Model Evaluation & Uncertainty · All terminology

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Mind map — connected ideas

Root Mean Squared Error (RMSE) · Mean Absolute Error (MAE) · MASE (Mean Absolute Scaled Error) · Mean Absolute Percentage Error (MAPE) · WAPE (Weighted Absolute Percentage Error) · Outlier

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More in Model Evaluation & Uncertainty

Average Absolute Error (AAE) · Baseline Heuristics · Bootstrap · Bootstrap Confidence Intervals (CIs) · Coverage · Cramér’s V · DeLong’s Test · KS Statistic (Kolmogorov–Smirnov Statistic) · Likelihood Ratio (LR) · Mann–Whitney U Test (also called the Wilcoxon rank-sum test) · MASE (Mean Absolute Scaled Error) · Mean Absolute Error (MAE) · Mean Absolute Percentage Error (MAPE) · Mean Squared Error (MSE)