ppLasso: Generalized linear point process modeling using lasso...
In ppstat: Point Process Statistics

Description Usage Arguments Details Value Note Author(s) References See Also

The function ppLasso fits a generalized linear point process model with a lasso penalization on all parameters.

1	ppLasso(formula, data, family, support = 1, N = 200, Delta, ...)

`formula`	an object of class `formula`. A symbolic description of the model to be fitted. Kernel terms are treated in a special way and other terms are treated as in `pointProcessModel`. See ‘Details’.
`data`	an object of class `MarkedPointProcess` containing the point process data as well as any continuous process data.
`family`	an object of class `Family`. Specification of the general model family containing the specification of the phi function, which links the linear predictor process to the predictable intensity process. The default value is `Hawkes("identity")`, but also `Hawkes("log")` is allowed.
`support`	a `numeric` vector. Specifies the support of the filter functions as the interval from `support[1]` to `support[2]`. If `support` is of length 1 the support is the interval from 0 to `support[1]`. The default value is 1.
`N`	a `numeric`. The number of basis function evaluations used in the support. Default value 200.
`Delta`	a `numeric`. Basis functions are evaluated at `Delta`-grid values in the support. If missing, `Delta` is set to the length of the support divided by `N`. If specified, overrides the use of `N`.
`...`	additional parameters that are passed on to `pointProcessModel`.

The function provides an interface for using the glmnet function from the suggested package glmnet to fit a model with the lasso penalization on the parameter vector.

With family = Hawkes("identity") (the default) ppLasso uses a quadratic contrast function for estimation, as considered in Hansen, Reynaud-Bouret and Rivoirard, and the different parameters are weigthed according to the criteria derived in that paper. With family = Hawkes("log") the likelihood is used. A one-dimensional tuning parameter remains to be selected, which is currently done by an ad hoc degrees-of-freedom computation.

A model of class PointProcessModel.

With family = Hawkes("identity") the model returned may have filter functions taking negative values. No approximate standard errors are currently computed.

Niels Richard Hansen Niels.R.Hansen@math.ku.dk.

N. R. Hansen, P. Reynaud-Bouret and V. Rivoirard. Lasso and probabilistic inequalities for multivariate point processes. arXiv:1208.0570

pointProcessModel

ppstat documentation built on May 2, 2019, 5:26 p.m.