## models.HierarchicalStacking


Hierarchical stacking (Yao, Pirš, Vehtari and Gelman, 2022): model


Usage


``` python
models.HierarchicalStacking()
```


weights that vary with covariates, `w = softmax(alpha + B x)` against the last model as reference, so a model can be trusted in one part of the portfolio and not another. The priors are those of BayesBlend's `HierarchicalBayesStacking`; sampled by NUTS.

Scale continuous covariates (BayesBlend divides by twice the standard deviation) and dummy-code discrete ones before fitting, with the dummies first.

With `partial_pooling`, each model's slopes on the discrete covariates, and separately on the continuous ones, are drawn around a model-level mean, itself drawn around a global mean. A scale of 0 removes a level: `tau_mu_global=0` fixes the global mean at 0, `tau_mu_*=0` pools completely and `tau_sigma_*=0` sets every slope to its model's mean. BayesBlend warns that pooling needs at least three covariates. `adaptive` multiplies the prior scales by `N**lambda` with `lambda ~ Exponential(adaptive)`, weakening them as the data grow.


## Parameters


`discrete: int = ``0`  
Number of leading covariates that are dummy codes.

`alpha_loc: float = 0.0, 1.0`  

`alpha_scale: float = 0.0, 1.0`  

`beta_loc: float = 0.0, 1.0`  
Slope prior without pooling.

`beta_scale: float = 0.0, 1.0`  
Slope prior without pooling.

`partial_pooling: bool = ``False`  

`tau_mu_global: float = ``1.0`  

`tau_mu_discrete: float = ``1.0`  

`tau_mu_continuous: float = ``1.0`  

`tau_sigma_discrete: float = ``1.0`  
Pooling scales, BayesBlend's defaults.

`tau_sigma_continuous: float = ``1.0`  
Pooling scales, BayesBlend's defaults.

`adaptive: float`  
Rate of the exponential prior on `lambda` (BayesBlend uses 4).

`chains: int = 4, 1000, 1000`  

`tune: int = 4, 1000, 1000`  

`draws: int = 4, 1000, 1000`  

`seed: int = ``0`  


## Examples

``` python
>>> from prospicio.models import HierarchicalStacking
>>> x = [i / 99 - 0.5 for i in range(100)]
>>> a = [-0.5 if v < 0 else -2.0 for v in x]
>>> b = [-2.0 if v < 0 else -0.5 for v in x]
>>> fit = HierarchicalStacking(chains=2, tune=300, draws=300).fit([a, b], [x])
>>> w = fit.weights([[-0.4, 0.4]])
>>> w[0][0] > 0.7 and w[1][0] < 0.3
```

True


## Methods

| Name | Description |
|----|----|
| [fit()](#fit) | Samples the intercepts and slopes. |

------------------------------------------------------------------------


#### fit()


Samples the intercepts and slopes.


Usage


``` python
fit(lpd, covariates)
```


##### Parameters


`lpd: list of list of float`  
One list per model, one held-out log density per observation.

`covariates: list of list of float`  
One list per covariate, one value per observation.


##### Returns


`StackingFit`