Estimators

Online GAMLSS

rolch.OnlineGamlss

The online/incremental GAMLSS class.

init

__init__(distribution, forget: float = 0.0, method: str = 'ols', do_scale: Union[Dict, bool] = True, expect_intercept: Union[Dict, bool] = True, estimation_kwargs: Optional[Dict] = None, max_it_outer: int = 30, max_it_inner: int = 30, abs_tol_outer: float = 0.001, abs_tol_inner: float = 0.001, rel_tol_outer: float = 1e-05, rel_tol_inner: float = 1e-05, rss_tol_inner: float = 1.5)

Initialise the online GAMLSS Model

Parameters:

Name	Type	Description	Default
`distribution`	`Distribution`	The parametric distribution	required
`forget`	`float`	The forget factor. Defaults to 0.0.	`0.0`
`method`	`str`	The estimation method. Defaults to "ols".	`'ols'`
`do_scale`	`Optional[Dict]`	Whether to scale the input matrices. Defaults to None, which implies that all inputs will be scaled. Note that the scaler assumes that the first column of each \(X\) contains the intercept.	`True`
`estimation_kwargs`	`Optional[Dict]`	Dictionary of estimation method kwargs. Defaults to None.	`None`
`max_it_outer`	`int`	Maximum outer iterations for the RS algorithm. Defaults to 30.	`30`
`max_it_inner`	`int`	Maximum inner iterations for the RS algorithm. Defaults to 30.	`30`
`abs_tol_outer`	`float`	Absolute tolerance on the Deviance in the outer fit. Defaults to 1e-3.	`0.001`
`abs_tol_inner`	`float`	Absolute tolerance on the Deviance in the inner fit. Defaults to 1e-3.	`0.001`
`rel_tol_outer`	`float`	Relative tolerance on the Deviance in the outer fit. Defaults to 1e-20.	`1e-05`
`rel_tol_inner`	`float`	Relative tolerance on the Deviance in the inner fit. Defaults to 1e-20.	`1e-05`
`rss_tol_inner`	`float`	Tolerance for increasing RSS in the inner fit. Defaults to 1.5.	`1.5`

fit

fit(y: np.ndarray, x0: np.ndarray, x1: Optional[np.ndarray] = None, x2: Optional[np.ndarray] = None, x3: Optional[np.ndarray] = None, sample_weights: Optional[np.ndarray] = None, beta_bounds: Dict[int, Tuple] = None)

Fit the online GAMLSS model.

Note

The user is only required to provide the design matrix \(X\) for the first distribution parameters. If for some distribution parameter no design matrix is provided, ROLCH will model the parameter using an intercept.

Note

The provision of bounds for the coefficient vectors is only possible for LASSO/coordinate descent estimation.

Parameters:

Name	Type	Description	Default
`y`	`ndarray`	Response variable \(Y\).	required
`x0`	`ndarray`	Design matrix for the 1st distribution parameter \(X_\mu\)	required
`x1`	`Optional[ndarray]`	Design matrix for the 2nd distribution parameter \(X_\sigma\). Defaults to None.	`None`
`x2`	`Optional[ndarray]`	Design matrix for the 3rd distribution parameter \(X_\nu\). Defaults to None.	`None`
`x3`	`Optional[ndarray]`	Design matrix for the 4th distribution parameter \(X_\tau\). Defaults to None.	`None`
`sample_weights`	`Optional[ndarray]`	User-defined sample weights. Defaults to None.	`None`
`beta_bounds`	`Dict[int, Tuple]`	Bounds for the \(eta\) in the coordinate descent algorithm. The user needs to provide a `dict` with a mapping of tuples to distribution parameters 0, 1, 2, and 3 potentially. Defaults to None.	`None`

predict

predict(x0: np.ndarray, x1: Optional[np.ndarray] = None, x2: Optional[np.ndarray] = None, x3: Optional[np.ndarray] = None, what: str = 'response', return_contributions: bool = False) -> np.ndarray

Predict the distibution parameters given input data.

Parameters:

Name	Type	Description	Default
`x0`	`ndarray`	Design matrix for the 1st distribution parameter \(X_\mu\)	required
`x1`	`Optional[ndarray]`	Design matrix for the 2nd distribution parameter \(X_\sigma\). Defaults to None.	`None`
`x2`	`Optional[ndarray]`	Design matrix for the 3rd distribution parameter \(X_\nu\). Defaults to None.	`None`
`x3`	`Optional[ndarray]`	Design matrix for the 4th distribution parameter \(X_\tau\). Defaults to None.	`None`
`what`	`str`	Predict the response or the link. Defaults to "response".	`'response'`
`return_contributions`	`bool`	Whether to return a `Tuple[prediction, contributions]` where the contributions of the individual covariates for each distribution parameter's predicted value is specified. Defaults to False.	`False`

Raises:

Type	Description
`ValueError`	Raises if `what` is not in `["link", "response"]`.

Returns:

Type	Description
`ndarray`	np.ndarray: Predicted values for the distribution.

update

update(y: np.ndarray, x0: np.ndarray, x1: Optional[np.ndarray] = None, x2: Optional[np.ndarray] = None, x3: Optional[np.ndarray] = None, sample_weights: Optional[np.ndarray] = None)

Update the fit for the online GAMLSS Model.

Warning

Currently, the algorithm only takes single-step updates. Batch updates are planned for the first stable version.

Note

The beta_bounds from the initial fit are still valid for the update.

Parameters:

Name	Type	Description	Default
`y`	`ndarray`	Response variable \(Y\).	required
`x0`	`ndarray`	Design matrix for the 1st distribution parameter \(X_\mu\)	required
`x1`	`Optional[ndarray]`	Design matrix for the 2nd distribution parameter \(X_\sigma\). Defaults to None.	`None`
`x2`	`Optional[ndarray]`	Design matrix for the 3rd distribution parameter \(X_\nu\). Defaults to None.	`None`
`x3`	`Optional[ndarray]`	Design matrix for the 4th distribution parameter \(X_\tau\). Defaults to None.	`None`
`sample_weights`	`Optional[ndarray]`	User-defined sample weights. Defaults to None.	`None`