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"""Implement lattice interface.""" |
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from overrides import overrides |
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import numpy as np |
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from abc import ABCMeta, abstractmethod |
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class Lattice(metaclass=ABCMeta): |
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"""Abstract base class representing a complemented lattice.""" |
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@classmethod |
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@abstractmethod |
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def join(cls, probs1: np.ndarray, probs2: np.ndarray) -> np.ndarray: |
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return NotImplemented |
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@classmethod |
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@abstractmethod |
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def meet(cls, probs1: np.ndarray, probs2: np.ndarray) -> np.ndarray: |
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return NotImplemented |
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@classmethod |
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@abstractmethod |
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def join_reduce(cls, probs: np.ndarray) -> np.ndarray: |
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return NotImplemented |
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@classmethod |
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@abstractmethod |
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def meet_reduce(cls, probs: np.ndarray) -> np.ndarray: |
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return NotImplemented |
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class Product(Lattice): |
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"""Lattice where meet=prod and sum is defined accordingly. |
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Equivalent to assuming independence, more or less. |
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""" |
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eps = 1e-9 |
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@classmethod |
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@overrides |
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def join(cls, probs1: np.ndarray, probs2: np.ndarray) -> np.ndarray: |
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return probs1 + probs2 - cls.meet(probs1, probs2) |
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@classmethod |
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@overrides |
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def meet(cls, probs1: np.ndarray, probs2: np.ndarray) -> np.ndarray: |
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return probs1 * probs2 |
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@classmethod |
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@overrides |
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def join_reduce(cls, probs: np.ndarray) -> np.ndarray: |
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"""Assumes disjoint events.""" |
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return np.sum(probs, axis=-1) |
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@classmethod |
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@overrides |
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def meet_reduce(cls, probs: np.ndarray) -> np.ndarray: |
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return np.prod(probs, axis=-1) |
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@classmethod |
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def comp(cls, probs): |
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return 1 - probs |
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@classmethod |
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def normalize(cls, probs): |
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"""Normalize a distribution by dividing by the total mass.""" |
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return probs / np.sum(probs + cls.eps, axis=-1) |
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