EasyDeepLearn

MAP vs MLE — key difference.

medium

Answer

  • MLE: θ̂ = argmax p(D  ∣  θ)p(D\; \mid \;{\theta}).
  • MAP: θ̂ = argmax p(θ  ∣  D)  =  argmax⁡p({\theta}\; \mid \;D)\; = \;\operatorname{argmax} p(D  ∣  θ)  ⋅  p(θ)p(D\; \mid \;{\theta})\; \cdot \;p({\theta}).
  • MAP adds a prior — reduces to MLE with uniform prior.
  • In log space, MAP = MLE + log-prior term → acts as regularization.
  • L2 regularization = Gaussian prior; L1 = Laplace prior.
  • Not fully Bayesian: gives a point estimate, not the full posterior.
Check yourself — multiple choice
  • Same as MLE
  • MAP: argmax posterior = argmax likelihood + log-prior → MLE with regularization (L2 = Gaussian prior, L1 = Laplace prior)
  • Fully Bayesian
  • Random

MAP = MLE + log-prior; L2 = Gaussian prior, L1 = Laplace prior.

#estimation#bayesian

Practise Statistics Fundamentals

215 interview questions in this topic.

Read the lessonFlashcardsTake the quiz

Related questions