Bayesian on English AI Terms Dictionary

Spike-and-slab regression

Sat, 18 Jul 2026 10:16:41 +0000

Definition

Spike-and-slab regression is a Bayesian statistical technique used for variable selection and sparse modeling. It employs a mixture prior distribution consisting of two components: a ‘spike’ (typically a narrow distribution centered at zero) representing null effects, and a ‘slab’ (a broader distribution) representing significant effects. This approach allows the model to automatically determine which predictors are relevant by shrinking irrelevant coefficients toward zero while retaining large estimates for important ones, effectively performing feature selection within a probabilistic framework.

Probabilistic numerics

Sat, 18 Jul 2026 10:11:27 +0000

Definition

Probabilistic numerics applies Bayesian methods to traditional numerical problems like integration, differentiation, and linear algebra. Instead of providing point estimates, it outputs probability distributions over the solution, quantifying epistemic uncertainty arising from finite computational resources. This enables more robust decision-making in scientific computing and machine learning by acknowledging and propagating numerical errors alongside model uncertainties.

Summary

A field treating numerical computation problems as statistical inference tasks to quantify uncertainty in results.

Inductive Probability

Sat, 18 Jul 2026 10:02:49 +0000

Definition

Inductive probability quantifies how likely a hypothesis is true given observed evidence, acknowledging that conclusions are probable rather than certain. It forms the basis of Bayesian inference, where prior beliefs are updated with new data. This concept is fundamental in statistical learning and decision-making under uncertainty, allowing AI systems to reason about partial information and update their confidence levels as more data becomes available.

Summary

A measure of the degree to which evidence supports a hypothesis, distinct from deductive certainty.

Inferential theory of learning

Sat, 18 Jul 2026 10:02:49 +0000

Definition

This theory posits that learning is essentially a process of probabilistic inference. Instead of memorizing data, the learner maintains a probability distribution over possible models or hypotheses. As new data arrives, Bayes’ theorem is used to update these probabilities, refining the model’s understanding of the underlying structure. It emphasizes generalization through uncertainty quantification rather than point estimates.

Summary

A framework where learning is viewed as Bayesian inference, updating beliefs about hypotheses based on observed data.

Prior

Sat, 18 Jul 2026 09:35:30 +0000

Definition

A ‘prior’ represents existing beliefs or historical data regarding a variable before incorporating new observations. In Bayesian inference, the prior is combined with the likelihood of the observed data to compute the posterior distribution. This concept is crucial in machine learning for regularization, where priors encode assumptions about model complexity or sparsity. Choosing an appropriate prior can significantly influence model behavior, especially when data is scarce.

Summary

In Bayesian statistics, a probability distribution expressing knowledge or belief about a parameter before observing new evidence or data.