The PROBABILISTIC justification for the least-squares cost assumes the noise ε⁽ⁱ⁾ in y⁽ⁱ⁾ = θᵀx⁽ⁱ⁾ + ε⁽ⁱ⁾ is
ABernoulli(p)
BUniform on [0, 1]
CIid Gaussian N(0, σ²)
DExponential with rate 1
Answer & Solution
Correct answer: C. Iid Gaussian N(0, σ²)
Under iid Gaussian noise N(0, σ²), maximising the likelihood is equivalent to minimising the sum of squared errors — that's why least-squares is 'the' regression loss.
Keep practising Linear Regression and Supervised Learning
Browse all Linear Regression and Supervised Learning questions for Claude, or explore more Aifoundations topics.
Related questions
Split batch from stochastic descentThe resulting per-example log-likelihood is, up to constantsClosed-form normal equations require XᵀX to beLogistic regression uses which hypothesis function?The design matrix X for n training examples with d features (plus intercept) has shapeThe closed-form 'normal equations' solution for least-squares linear regression isThe LMS (Widrow–Hoff) update rule on a single training example is'Α' in θⱼ := θⱼ − α·∂J/∂θⱼ is called the