core.bound.McAllesterBound 

 1import math
 2
 3from torch import Tensor
 4
 5from core.bound import AbstractBound
 6from core.utils.kl import inv_kl
 7
 8
 9class McAllesterBound(AbstractBound):
10    """
11    Implements a McAllester PAC Bayes bound.
12    """
13
14    def __init__(self, bound_delta: float, loss_delta: float):
15        super().__init__(bound_delta, loss_delta)
16
17    def calculate(
18        self,
19        avg_loss: float,
20        kl: Tensor | float,
21        num_samples_bound: int,
22        num_samples_loss: int,
23    ) -> tuple[Tensor | float, Tensor | float]:
24        """
25        Calculates the PAC Bayes bound.
26
27        Args:
28            avg_loss (float): The loss averaged using Monte Carlo sampling.
29            kl (Union[Tensor, float]): The Kullback-Leibler divergence between prior and posterior distributions.
30            num_samples_bound (int): The number of data samples in the bound dataset.
31            num_samples_loss (int): The number of Monte Carlo samples.
32
33        Returns:
34            Tuple[Union[Tensor, float], Union[Tensor, float]]:
35                A tuple containing the calculated PAC Bayes bound and the upper bound of empirical risk.
36        """
37        empirical_risk = inv_kl(
38            avg_loss, math.log(2 / self._loss_delta) / num_samples_loss
39        )
40        risk = empirical_risk + math.sqrt(
41            (kl + math.log((2 * math.sqrt(num_samples_bound))) / self._bound_delta)
42            / (2 * num_samples_bound)
43        )
44        return risk, empirical_risk
class McAllesterBound(core.bound.AbstractBound.AbstractBound): 
10class McAllesterBound(AbstractBound):
11    """
12    Implements a McAllester PAC Bayes bound.
13    """
14
15    def __init__(self, bound_delta: float, loss_delta: float):
16        super().__init__(bound_delta, loss_delta)
17
18    def calculate(
19        self,
20        avg_loss: float,
21        kl: Tensor | float,
22        num_samples_bound: int,
23        num_samples_loss: int,
24    ) -> tuple[Tensor | float, Tensor | float]:
25        """
26        Calculates the PAC Bayes bound.
27
28        Args:
29            avg_loss (float): The loss averaged using Monte Carlo sampling.
30            kl (Union[Tensor, float]): The Kullback-Leibler divergence between prior and posterior distributions.
31            num_samples_bound (int): The number of data samples in the bound dataset.
32            num_samples_loss (int): The number of Monte Carlo samples.
33
34        Returns:
35            Tuple[Union[Tensor, float], Union[Tensor, float]]:
36                A tuple containing the calculated PAC Bayes bound and the upper bound of empirical risk.
37        """
38        empirical_risk = inv_kl(
39            avg_loss, math.log(2 / self._loss_delta) / num_samples_loss
40        )
41        risk = empirical_risk + math.sqrt(
42            (kl + math.log((2 * math.sqrt(num_samples_bound))) / self._bound_delta)
43            / (2 * num_samples_bound)
44        )
45        return risk, empirical_risk

Implements a McAllester PAC Bayes bound.

McAllesterBound(bound_delta: float, loss_delta: float) 
15    def __init__(self, bound_delta: float, loss_delta: float):
16        super().__init__(bound_delta, loss_delta)
def calculate( self, avg_loss: float, kl: torch.Tensor | float, num_samples_bound: int, num_samples_loss: int) -> tuple[torch.Tensor | float, torch.Tensor | float]: 
18    def calculate(
19        self,
20        avg_loss: float,
21        kl: Tensor | float,
22        num_samples_bound: int,
23        num_samples_loss: int,
24    ) -> tuple[Tensor | float, Tensor | float]:
25        """
26        Calculates the PAC Bayes bound.
27
28        Args:
29            avg_loss (float): The loss averaged using Monte Carlo sampling.
30            kl (Union[Tensor, float]): The Kullback-Leibler divergence between prior and posterior distributions.
31            num_samples_bound (int): The number of data samples in the bound dataset.
32            num_samples_loss (int): The number of Monte Carlo samples.
33
34        Returns:
35            Tuple[Union[Tensor, float], Union[Tensor, float]]:
36                A tuple containing the calculated PAC Bayes bound and the upper bound of empirical risk.
37        """
38        empirical_risk = inv_kl(
39            avg_loss, math.log(2 / self._loss_delta) / num_samples_loss
40        )
41        risk = empirical_risk + math.sqrt(
42            (kl + math.log((2 * math.sqrt(num_samples_bound))) / self._bound_delta)
43            / (2 * num_samples_bound)
44        )
45        return risk, empirical_risk

Calculates the PAC Bayes bound.

Arguments:
  • avg_loss (float): The loss averaged using Monte Carlo sampling.
  • kl (Union[Tensor, float]): The Kullback-Leibler divergence between prior and posterior distributions.
  • num_samples_bound (int): The number of data samples in the bound dataset.
  • num_samples_loss (int): The number of Monte Carlo samples.
Returns:

Tuple[Union[Tensor, float], Union[Tensor, float]]: A tuple containing the calculated PAC Bayes bound and the upper bound of empirical risk.