lp_fn

probly.losses.torch.lp_fn(alpha: Tensor, y: Tensor, p: float = 2.0) → Tensor

Lp calibration loss from [Tsi19].

Implements the Lp calibration loss for predictive uncertainty estimation in Information Robust Dirichlet Networks.

The loss is computed using the expectation-based formulation:

F_i = ( E[(1 - p_c)^p] + Σ_{j≠c} E[p_j^p] )^(1/p)

Parameters:

• alpha – Dirichlet concentration parameters, shape (B, K), must be > 0.

• y – One-hot encoded class labels, shape (B, K).

• p – Lp norm exponent controlling calibration strength (default: 2.0).

Returns:

Scalar Lp calibration loss summed over the batch.

Raises:

ValueError – If alpha contains non-positive values or if shapes do not match.