reid#
- hidimstat.desparsified_lasso.reid(beta_hat, residual, tolerance=0.0001, multioutput=False, stationary=True, method='median', order=1)[source]#
Residual sum of squares based estimators for noise standard deviation estimation.
This implementation follows the procedure described in Fan et al.[1] and Reid et al.[2]. The beta_hat should correspond to the coefficient of Lasso with cross-validation, and the residual is based on this model.
For group, the implementation is based on the procedure from Chevalier et al.[3].
- Parameters:
- beta_hatndarray, shape (n_features,) or (n_task, n_features)
Estimated sparse coefficient vector from regression.
- residualndarray, shape (n_samples,) or (n_samples, n_task)
Residuals from the regression model.
- tolerancefloat, default=1e-4
Threshold for considering coefficients as non-zero.
- multioutputbool, default=False
If True, handles multiple outputs (group case).
- stationarybool, default=True
Whether noise has constant magnitude across time steps.
- method{‘median’, ‘AR’}, (default=’simple’)
Covariance estimation method: - ‘median’: Uses median correlation between consecutive time steps - ‘AR’: Uses Yule-Walker method with specified order
- orderint, default=1
Order of AR model when method=’AR’. Must be < n_task.
- Returns:
- sigma_hat_raw or covariance_hatfloat or ndarray
For single output: estimated noise standard deviation For multiple outputs: estimated (n_task, n_task) covariance matrix
Notes
Implementation based on Reid et al.[2] for single output and Chevalier et al.[3] for multiple outputs.
References