Bias-variance tradeoff: cheatsheet

The two failure modes

Term	Meaning	Fix
Bias (underfit)	model too simple to capture the pattern	more flexible model, more features
Variance (overfit)	model too sensitive to specific training sample	simpler model, more data, regularization, averaging
Irreducible noise	inherent randomness; hard floor	nothing

Total error = bias^2 + variance + irreducible noise.

The U-curve

Complexity	Bias	Variance	Test error
Too simple	high	low	high (underfit)
Sweet spot	moderate	moderate	LOW
Too complex	low	high	high (overfit)

The diagnostic (the capability)

Training error	Test error	Diagnosis	Try
high	high (similar)	high bias / underfit	add complexity
low	high (big gap)	high variance / overfit	simplify, more data, regularize
low	low (small gap)	good fit	ship it

Regularization

Type	Penalty	Effect
Ridge (L2)	sum of squared coefficients	shrinks all toward zero, lowers variance
Lasso (L1)	sum of absolute coefficients	shrinks; can drive some to zero (feature selection)

Where each method sits

Method	Default bias	Default variance	Tends to
Linear / logistic regression	high	low	underfit on complex problems
Deep unpruned tree	low	high	overfit
Random forest	low	low	sweet-spot (averages out variance)
Boosting (long run)	low	rising	can overfit; needs tuning
SVM (soft margin C)	dial	dial	both directions

Pitfalls

Pitfall	Reality
”Training accuracy = quality”	training fit is not generalization
Only adding data	fixes variance, does little for bias
Only adding complexity	fixes bias, raises variance
Ignoring noise floor	nothing beats irreducible noise