ml
Loss Functions
Regression (MSE, RMSE, MAE, MAPE, Huber, R²) and classification (BCE, Hinge, Focal, KL) — per-sample breakdown, outlier sensitivity, loss landscape SVG.
Mode
Loss vs Residual (δ = 1.0)
—— MSE (e²)—— MAE (|e|)—— Huber
Outlier Sensitivity — extra sample impact on aggregate loss
—— MSE—— MAE—— Huber
Regression Losses
MSE0.3033
RMSE0.5508
MAE0.4
MAPE17.24%
Huber (δ=1.0)0.1483
R²0.8295
Samples (n)6
Per-Sample Breakdown
#yŷe²|e|Huber
111.10.010.10.005
22.52.30.040.20.02
333.50.250.50.125
44.240.040.20.02
554.80.040.20.02
623.21.441.20.7
MSE = Σe²/n · MAE = Σ|e|/n · MAPE = 100×Σ|e/y|/n
Huber: ½e² if |e|≤δ, else δ(|e|−δ/2) · R² = 1 − SSres/SStot
BCE = −Σ[y·log(p̂)+(1-y)·log(1-p̂)]/n · Focal = −(1-p_t)^γ log(p_t)
Huber: ½e² if |e|≤δ, else δ(|e|−δ/2) · R² = 1 − SSres/SStot
BCE = −Σ[y·log(p̂)+(1-y)·log(1-p̂)]/n · Focal = −(1-p_t)^γ log(p_t)