> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Quantile regressors

> Conditional quantile estimators, used by SPCI

### `QuantileRegressor`

Bases: <code>[ArrayModel](#conformalforecast._model.ArrayModel)</code>, <code>[ABC](#abc.ABC)</code>

Quantile regression model used by SPCI.

Trained on autoregressive residual data: given the last `w` residuals,
predict the quantile distribution of the next residual. Subclasses can
wrap any quantile-regression library (QRF, LightGBM quantile, neural
quantile networks, etc.).

#### `QuantileRegressor.fit`

```python theme={null}
fit(X, y)
```

Fit the regressor.

## Parameters

X : NDArray, shape (n\_samples, w)
Training features. Each row is a window of `w` past residuals.
y : NDArray, shape (n\_samples,)
Training targets (the next residual after each window).

#### `QuantileRegressor.predict_quantile`

```python theme={null}
predict_quantile(X, q)
```

Predict the `q`-quantile of the conditional distribution.

## Parameters

X : NDArray, shape (n\_samples, w)
q : float in (0, 1)

## Returns

NDArray, shape (n\_samples,)

#### `QuantileRegressor.predict_quantiles`

```python theme={null}
predict_quantiles(X, qs)
```

Predict several quantiles at once.

SPCI asks for `2 * beta_grid_size` quantiles per `(series, horizon)`
cell while searching for the width-minimizing `beta`. Most quantile
libraries answer a whole list in one traversal of the fitted model, which
is dramatically cheaper than one call per level -- for
`quantile-forest`, 42 separate calls measured 52.2 ms against 1.23 ms
batched. That loop dominated SPCI's `interval()` outright: the
measured \~53 ms per cell was essentially all quantile calls.

The default implementation loops over :meth:`predict_quantile`, so a
custom regressor only has to implement the scalar method. Override this
when the backend can do better.

## Parameters

X : NDArray, shape (n\_samples, w)
qs : NDArray, shape (n\_quantiles,)
Levels in `(0, 1)`.

## Returns

NDArray, shape (n\_samples, n\_quantiles)
Column `j` is the `qs[j]`-quantile.

### `QRFQuantileRegressor`

Bases: <code>[QuantileRegressor](#conformalforecast.quantile_regressors.base.QuantileRegressor)</code>

Quantile Random Forest regressor (Meinshausen 2006).

Default quantile estimator for SPCI per Xu & Xie (2023). Wraps the
`quantile-forest` package, exposing a clean two-method interface.

## Notes

The `quantile-forest` package is an optional dependency. The import is
deferred to :meth:`fit` (not construction) so that a
:class:`QRFQuantileRegressor` -- including one built as
:class:`~conformalforecast.methods.spci.SequentialPredictiveConformalInference`'s
default `regressor` -- can be constructed, and its schema generated via
`model_json_schema()`, without `quantile-forest` installed. Calling
:meth:`fit` without it installed raises :class:`ImportError`.

#### `QRFQuantileRegressor.fit`

```python theme={null}
fit(X, y)
```

Fit the forest on autoregressive residual windows.

## Parameters

X : NDArray, shape (n\_samples, n\_features)
Training features. Each row is a window of past residuals,
optionally concatenated with exogenous features.
y : NDArray, shape (n\_samples,)
The next residual after each window.

## Raises

ImportError
If `quantile-forest` is not installed. Deferred to here (rather
than construction) so this class stays constructible -- and its
schema generable -- without the `[spci]` extra.

#### `QRFQuantileRegressor.predict_quantile`

```python theme={null}
predict_quantile(X, q)
```

Predict the `q`-quantile of the conditional residual distribution.

## Parameters

X : NDArray, shape (n\_samples, n\_features)
q : float in (0, 1)

## Returns

NDArray, shape (n\_samples,)

## Raises

RuntimeError
If called before :meth:`fit`.

#### `QRFQuantileRegressor.predict_quantiles`

```python theme={null}
predict_quantiles(X, qs)
```

Predict several quantiles in a single traversal of the forest.

`quantile-forest` accepts a list of levels and answers them from one
pass over the leaf distributions, which is why this override exists:
SPCI's beta search asks for \~42 levels per cell, and one call per level
measured 42x slower on a fitted forest.

## Parameters

X : NDArray, shape (n\_samples, n\_features)
qs : NDArray, shape (n\_quantiles,)

## Returns

NDArray, shape (n\_samples, n\_quantiles)

## Raises

RuntimeError
If called before :meth:`fit`.


## Related topics

- [Methods](/conformalforecast/methods.html.md)
- [Sequential predictive conformal inference](/conformalforecast/docs/methods/spci.html.md)
- [Architecture](/conformalforecast/docs/concepts/architecture.html.md)
- [Exogenous features](/conformalforecast/docs/capabilities/exogenous.html.md)
- [conformalforecast](/conformalforecast/index.html.md)