MMD DRO

class dro.src.linear_model.mmd_dro.MMD_DRO(input_dim, model_type, fit_intercept=True, solver='MOSEK', sampling_method='bound')

Bases: BaseLinearDRO

MMD-DRO (Maximum Mean Discrepancy - Distributionally Robust Optimization) Implementation with flexible sampling methods and model types.

Reference: <https://arxiv.org/abs/2006.06981>

Initialize MMD-DRO with kernel-based ambiguity set.

Parameters:

• input_dim (int) – Dimension of input features. Must match training data.

• model_type (str) –

  Base model type. Supported:

  • 'svm': Support Vector Machine (hinge loss)

  • 'logistic': Logistic Regression (log loss)

  • 'ols': Ordinary Least Squares (L2 loss)

  • 'lad': Least Absolute Deviation (L1 loss)

• sampling_method (str) –

  Supported:

  • 'bound'

  • 'hull'

• fit_intercept (bool)

• solver (str)

Raises:

ValueError –

• If model_type not in supported list

• If input_dim ≤ 0

• If sampling_method is invalid

• If n_certify_ratio < 1

Example:

>>> model = MMD_DRO(input_dim=128, model_type='svm')
>>> model.sampling_method = 'hull' 
>>> model.eta = 0.5  

update(config)

Update MMD-DRO model configuration.

Parameters:

config (Dict[str, Any]) –

Configuration dictionary containing optional keys:

• eta (float):

  MMD radius controlling distributional robustness. Must satisfy \(\eta > 0\). Defaults to current value.

• sampling_method (str):

  Ambiguity set sampling strategy. Valid options:

  • 'bound': Sample on MMD ball boundary

  • 'hull': Sample within convex hull

• n_certify_ratio (float):

  Ratio of certification samples to training data size. Must satisfy \(0 < ext{ratio} \leq 1\). Defaults to current ratio.

Raises:

ValueError –

• If eta is non-positive

• If sampling_method not in {‘bound’, ‘hull’}

• If n_certify_ratio ∉ (0, 1]

• If config contains unrecognized keys

Return type:

None

Example:

>>> model = MMD_DRO(input_dim=10, model_type='svm')
>>> model.update({
...     'eta': 0.5,              
...     'sampling_method': 'hull' 
... })

fit(X, y)

Fit the MMD-DRO model to the data.

Parameters:

• X (numpy.ndarray) – Training feature matrix of shape (n_samples, n_features). Must satisfy n_features == self.input_dim.

• y (numpy.ndarray) –

  Target values of shape (n_samples,). Format requirements:

  • Classification: ±1 labels

  • Regression: Continuous values

Returns:

Dictionary containing trained parameters:

• theta: Weight vector of shape (n_features,)

Return type:

Dict[str, Any]