API#

This page contains API documentation for the classes.

Terms#

Terms are used in GAMs to model the features. For instance, we can use Spline and Categorical as follows:

terms = Spline("age") + Categorical("sex")

This constructs a TermList, which can be passed to a GAM.

model = GAM(terms)

Here are all the available terms:

`Intercept`()	An intercept term.
`Linear`([feature, penalty, by, constraint])	A linear term.
`Categorical`([feature, penalty, by, ...])	A Categorial term.
`Spline`([feature, penalty, l2_penalty, by, ...])	A Spline term.
`Tensor`(splines, *[, by])	A Tensor term.

A TermList is a subclass of list, designed to hold terms.

Link functions relate linear predictions \(\eta_i = X_i \beta\) to the expected values \(\mu_i\) of an exponential family distribution.

\[\begin{split}y_i &\sim \operatorname{ExpFam}(\mu_i, \phi) \\ g(\mu_i) &= \eta_i = X_i \beta\end{split}\]

For instance, if you believe the features multiply together to create \(\mu_i\), you can model this with the Log link as

\[\begin{split}y_i &\sim \operatorname{Normal}(\mu_i, \phi) \\ \log(\mu_i) & = X_i \beta\end{split}\]

This implies that \(\mu_i = \exp(X_i \beta) = \exp(X_{ij} \beta_j)\)

`Identity`()	Identity link: \(g(\mu) = \mu\)
`Log`()	Log link: \(g(\mu) = \log(\mu)\)
`Logit`([low, high])	Logit link: \(g(\mu) = \log(\mu / (1 - \mu))\)
`Softplus`([a])	Softplus link: \(g(\mu) = \log(\exp(a \mu) - 1)/a\)

`Normal`([scale])	Normal Distribution
`Poisson`([scale])	Poisson Distribution
`Binomial`([trials, scale])	Binomial Distribution
`Gamma`([scale])	Gamma Distribution
`InvGauss`([scale])	Inverse Gaussian Distribution
`Exponential`([scale])	Exponential Distribution
`Bernoulli`([scale])	Bernoulli Distribution

`GAM`([terms, distribution, link, ...])	Initialize a Generalized Additive Model (GAM).
`ExpectileGAM`([terms, expectile, ...])	Initialize an ExpectileGAM.