Minimalpar

Minimalpar is a principle and set of methods used in statistics and data analysis to obtain models with the smallest possible number of free parameters while maintaining acceptable predictive accuracy or explanatory power. The term highlights parsimony: simpler models are preferred when they perform comparably to more complex ones.

Formally, minimalpar can be described as solving an optimization problem that seeks to minimize the sparsity or the count of nonzero parameters subject to a constraint on fitting error. In practice, this is implemented through regularization, model selection, or description-length criteria that penalize model complexity. Common approaches include sparse regularization (for example, L1 penalties), information criteria such as AIC and BIC, and minimum description length methods, often used with cross-validation to assess generalization.

Applications span various domains, including statistics, machine learning, signal processing, econometrics, and control theory. It is used to derive interpretable models, reduce overfitting, and improve robustness when data are limited or noisy. The concept is closely related to, but distinct from, ideas such as model selection, sparsity, and parsimony in model design.

History and terminology: The broader idea of favoring simple parameterizations has a long-standing presence in statistical theory. The specific label minimalpar appears in contemporary discussions and literature as a concise way to refer to approaches that formalize minimal parameter representations within constrained optimization frameworks.

See also: parsimony, sparse modeling, regularization, minimum description length, information criteria such as AIC and BIC, cross-validation.