maximum a posteriori estimation

A point estimate that adds a priorprior, n.: What you believe, and how strongly, before looking at the evidence in front of you. In AI it also means built-in assumptions that steer what a system learns. to maximum likelihood estimationmaximum likelihood estimation, n.: Tuning a model's settings until the real data it learns from looks as likely, and so as unsurprising, to the model as possible. Most AI training, including the pretraining of chatbots, is a version of this.: it picks the parameter values that make likelihoodlikelihood, n.: A score for a possible explanation of some data: how probable that explanation, or that setting of a model, would have made the data actually seen. × prior largest — the peak, or mode, of the posteriorposterior, n.: What you believe after weighing new evidence against what you believed before. It is the updated belief that Bayes' theorem produces. — by minimizing the negative log-likelihoodlog-likelihood, n.: The logarithm of how probable a model finds the observed data. Taking logs turns a product of many tiny probabilities into a manageable sum; training usually minimizes its negative. minus the log-prior. Under a flat prior it coincides with maximum likelihood, and unlike full Bayesian inferenceBayesian inference, n.: Reasoning that treats unknowns as uncertain beliefs and updates them with evidence using Bayes' theorem. The result is not one answer but a range of answers, each with a probability. it discards everything about the posterior except that peak. The log-prior acts as a regularizer: a zero-mean Gaussian prior on weights gives L2 regularizationregularization, n.: Any technique that stops a model from memorizing its training examples too closely — often by penalizing complexity — so that it works better on new data. (ridge regressionridge regression, n.: Linear regression with a built-in brake: it fits the data while also keeping the weights small, which makes predictions more stable when there are many overlapping inputs., weight decayweight decay, n.: A training rule that shrinks every weight slightly at each step, like a small tax on large numbers. It keeps models simpler and usually helps them work better on new data.), and a Laplace prior gives L1 (the lassolasso, n.: A version of linear regression that keeps only the most useful inputs: it penalizes the total size of the weights so that many become exactly zero, leaving a simpler model.). MAP estimates are cheap, needing only standard optimization, but they carry no uncertainty and, unlike the posterior itself, depend on how the parameters are represented. In sequence generation, 'MAP decoding' means searching for the single most probable output, which greedy decodinggreedy decoding, n.: The simplest way for a language model to write: always pick the single most likely next word. It is fast and predictable but can produce dull or repetitive text. and beam searchbeam search, n.: A search method that keeps several of the best partial answers at each step, rather than only the single best, to find a better overall result without trying every possibility. approximate.

Adding weight decay turns our maximum likelihood fit into a MAP estimate under a Gaussian prior.