Lowparameterization

Lowparameterization is the design and use of models or representations that describe a system with relatively few parameters or degrees of freedom. The central aim is parsimony: capturing essential structure while limiting flexibility, which can improve interpretability and generalization, particularly when data are scarce, noisy, or expensive to obtain. It contrasts with high-parameterization or overparameterized models that can fit complex patterns but risk overfitting and require larger data sets.

Common approaches include choosing simple parametric families, enforcing structural constraints such as invariances or symmetries, and using dimensionality reduction or low-rank representations to summarize data with few factors. Examples are linear models with a small feature set, Gaussian or exponential family models, and low-rank matrix factorization where a matrix is approximated by products of small factors. Regularization and informative priors can further shrink parameters or reduce effective degrees of freedom, while physics-based or domain-informed models embed known relationships to limit parameter count. In machine learning, lowparameterization can also be achieved through shared representations in multi-task learning or through using a compact basis of features.

The trade-offs include potential underfitting and reduced expressivity if the chosen parameterization is too restrictive. The approach is often most effective when prior knowledge, data limitations, or the need for interpretability justify a simpler model, and it complements model selection, identifiability, and robust inference practices.