prob.rst

Representation of Probability

To represent and modifies probabilities such as

P(x, y|z),

one can define an instance of :class:`Prob` and change its attributes.

Examples

The probabiity

\sum_{w}P(v|y)[P(w|z)P(x|y)P(u)]

is composed of two parts: P(v|y) and a product P(w|z)P(x|y)P(u) and then they are sumed on w. We first define the first part:

from ylearn.causal_model.prob import Prob

var = {'v'}
conditional = {'y'} # the conditional set
marginal = {'w'} # sum on w

Now we continue to define the second part, the product,

p1 = Prob(variables={'w'}, conditional={'z'})
p2 = Prob(variables={'x'}, conditional={'y'})
p3 = Prob(variables={'u'})
product = {p1, p2, p3}

The final result is

P = Prob(variables=var, conditional=conditional, marginal=marginal, product=product)
P.show_latex_expression()

>>> :math:`\sum_w P(v|y)[P(u)][P(w|z)][P(x|y)]`

An instance of :class:`Prob` can also output the latex code

P.parse()

>>> '\\sum_{w}P(v|y)\\left[P(u)\\right]\\left[P(w|z)\\right]\\left[P(x|y)\\right]'

.. py:class:: ylearn.causal_model.prob.Prob(variables=set(), conditional=set(), divisor=set(), marginal=set(), product=set())

    Probability distribution, e.g., the probability expression

    .. math::

        \sum_{w}P(v|y)[P(w|z)P(x|y)P(u)].

    We will clarify below the meanings of our variables with this example.

    :param set, default=set() variables: The variables (:math:`v` in the above example) of the probability.
    :param set, default=set() conditional: The conditional set (:math:`y` in the above example) of the probability.
    :param set, default=set() marginal: The sum set (:math:`w` in the above example) for marginalizing the probability.
    :param set, default=set() product: If not set(), then the probability is composed of the first probability
            object :math:`(P(v|y))` and several other probabiity objects that are all saved
            in the set product, e.g., product = {P1, P2, P3} where P1 for :math:`P(w|z)`,
            P2 for :math:`P(x|y)`, and P3 for :math:`P(u)` in the above example.

    .. py:method:: parse

        Return the expression of the probability distribution.

        :returns: Expression of the encoded probabiity
        :rtype: str

    .. py:method:: show_latex_expression

        Show the latex expression.