parametric model
In plain wordsA model whose shape is fixed in advance by a set number of adjustable settings, like a straight line's slope and intercept. More data refines those settings but never adds new ones.
A statistical or machine-learning model described by a fixed, finite set of parameters whose number does not grow with the amount of training data; learning amounts to estimating those parameters, after which the training data can be discarded. Examples include linear regressionlinear regression, n.: Fitting a straight line (or flat surface) through data points to predict one number from others — say, a house's price from its floor area — choosing the line that keeps prediction errors smallest., logistic regressionlogistic regression, n.: A simple, widely used method for yes-or-no predictions that outputs a probability — say, a 70% chance a customer cancels — by passing a weighted sum of inputs through an S-shaped curve., naive Bayesnaive Bayes, n.: A simple, fast way of sorting items into categories using probabilities, which pretends that each clue is independent of the others. It is the classic technique behind early email spam filters., linear discriminant analysislinear discriminant analysis, n.: A statistical method for telling known groups apart. It finds the weighted mix of measurements on which groups differ most relative to their spread, then uses it to sort new items or compress many measurements into a few. and Gaussian mixture models with a fixed number of components. The fixed functional form is a strong inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases.: parametric models are fast, data-efficient and interpretable when the assumed form is roughly right, but stay biased however much data is collected when it is wrong. In classical statistics 'parametric' also describes methods that assume the data come from a known family of distributions, such as the normal, as t-tests do. Neural networks are formally parametric, but with millions to trillions of parametersparameter, n.: One of the adjustable numbers inside an AI model that are tuned during training. Large language models have billions of them, and together they store what the model has learned. they behave in many respects like flexible nonparametric models.
A parametric model assumes the shape up front; with only 80 observations, that assumption is worth making.
Origin
The parametric–nonparametric distinction took shape in 1940s statistics, when methods free of assumptions about distributional parameters were named 'non-parametric' (earliest known use: Jacob Wolfowitz, 1942). The machine-learning usage, contrasting fixed-size models with models that grow with the data, became standard in textbooks of the 1990s–2000s.
Related
- nonparametric modelnonparametric model, n.: A model that lets the data decide how complex it becomes: the more examples it gets, the more detail it can capture — for instance, one that predicts by comparing a new case with every stored example.
- linear regressionlinear regression, n.: Fitting a straight line (or flat surface) through data points to predict one number from others — say, a house's price from its floor area — choosing the line that keeps prediction errors smallest.
- logistic regressionlogistic regression, n.: A simple, widely used method for yes-or-no predictions that outputs a probability — say, a 70% chance a customer cancels — by passing a weighted sum of inputs through an S-shaped curve.
- inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases.
- parameterparameter, n.: One of the adjustable numbers inside an AI model that are tuned during training. Large language models have billions of them, and together they store what the model has learned.
- bias–variance tradeoffbias–variance tradeoff, n.: The balancing act between models too simple to capture a pattern and models so flexible that they also learn the noise. The best predictions usually come from somewhere in between.
- nonparametric modelnonparametric model, n.: A model that lets the data decide how complex it becomes: the more examples it gets, the more detail it can capture — for instance, one that predicts by comparing a new case with every stored example.
Mentioned in
modelmodel, n.: A simplified working version of something. In AI it usually means the trained program, a big set of learned numbers, that takes an input and produces an answer, prediction or piece of content., nonparametric modelnonparametric model, n.: A model that lets the data decide how complex it becomes: the more examples it gets, the more detail it can capture — for instance, one that predicts by comparing a new case with every stored example., parameterparameter, n.: One of the adjustable numbers inside an AI model that are tuned during training. Large language models have billions of them, and together they store what the model has learned.