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

# Regression

> Learn about TabPFN's regression capabilities.

TabPFN can be applied to regression tasks using the `TabPFNRegressor` class. Instead of a single point estimate, the regressor predicts an output distribution, enabling you to generate different types of forecasts and accurately measure uncertainty in your predictions.

## Getting Started

The following shows a full example of using the `TabPFNRegressor`:

```python theme={null}
from sklearn.datasets import load_diabetes
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
from sklearn.model_selection import train_test_split
from tabpfn import TabPFNRegressor
from tabpfn.constants import ModelVersion

# Load example dataset
X, y = load_diabetes(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)

# Initialize and fit
model = TabPFNRegressor()
# To use TabPFNv2:
# model = TabPFNRegressor.create_default_for_version(ModelVersion.V2)
model.fit(X_train, y_train)

# Predict
preds = model.predict(X_test)

# Evaluate
print("MSE:", mean_squared_error(y_test, preds))
print("MAE:", mean_absolute_error(y_test, preds))
print("R²:", r2_score(y_test, preds))
```

## Understanding Predictions

The `TabPFNRegressor.predict()` method can return different types of predictions based on the `output_type` parameter.

### Point Predictions (Mean, Median, Mode)

By default, `predict()` returns the **mean** of the predicted distribution. You can also request the `median` or `mode` for different point estimates.

```python theme={null}
# Get the mean prediction (default)
mean_preds = model.predict(X_test, output_type="mean")

# Get the median prediction
median_preds = model.predict(X_test, output_type="median")

# Get the mode prediction
mode_preds = model.predict(X_test, output_type="mode")
```

### Quantile Regression

To perform quantile regression and get predictions for specific quantiles, set `output_type="quantiles"` and pass a list of desired quantiles. This is ideal for estimating prediction intervals.

```python theme={null}
# Get predictions for the 10th, 50th (median), and 90th quantiles
quantile_preds = model.predict(
    X_test,
    output_type="quantiles",
    quantiles=[0.1, 0.5, 0.9],
)

# quantile_preds is a list of arrays
# q10_preds = quantile_preds[0]
# q50_preds = quantile_preds[1]
# q90_preds = quantile_preds[2]
```

### Full Distribution

For advanced use cases, you can retrieve the full predictive distribution.

* `output_type="main"` returns a dictionary containing the mean, median, mode, and default quantiles.
* `output_type="full"` returns everything in `"main"` plus the raw logits and criterion object, allowing for custom loss calculations (see the FAQ).

```python theme={null}
# Get a dictionary of all main prediction types
main_outputs = model.predict(X_test, output_type="main")
# print(main_outputs.keys()) 
# > dict_keys(['mean', 'median', 'mode', 'quantiles'])

# Get the full distribution objects for custom analysis
full_outputs = model.predict(X_test, output_type="full")
# print(full_outputs.keys())
# > dict_keys(['mean', 'median', 'mode', 'quantiles', 'criterion', 'logits'])
```

<Accordion title="How can I apply a custom loss (e.g. MAPE, asymmetric loss) to regression?">
  `TabPFNRegressor` provides a full predictive distribution, enabling loss-aware predictions without retraining. You can compute the Bayes-optimal point prediction that minimizes the expected custom loss. This method gives flexible custom-loss predictions without modifying the model.

  ```python theme={null}
  out = reg.predict(X, output_type="full")
  criterion, logits = out["criterion"], out["logits"]

  q = np.linspace(0.01, 0.99, 101)
  samples = np.stack(
      [criterion.icdf(logits, float(x)).cpu().numpy() for x in q], axis=1
  )

  denom = np.maximum(np.abs(samples), 1e-6)
  diffs = np.abs(samples[:, :, None] - samples[:, None, :])
  exp_mape = (diffs / denom[:, :, None]).mean(axis=1)
  best_idx = exp_mape.argmin(axis=1)
  y_hat = samples[np.arange(samples.shape[0]), best_idx]
  ```
</Accordion>

## Related

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