# Discretizing Methods¶

class pgmpy.factors.continuous.discretize.BaseDiscretizer(name, bases, namespace, **kwargs)[source]

Base class for the discretizer classes in pgmpy. The discretizer classes are used to discretize a continuous random variable distribution into discrete probability masses.

Parameters:
• factor (A ContinuousNode or a ContinuousFactor object) – the continuous node or factor representing the distribution to be discretized.

• low (float) – the range over which the function will be discretized.

• high (float) – the range over which the function will be discretized.

• cardinality (int) – the number of states required in the discretized output.

Examples

```>>> from scipy.stats import norm
>>> from pgmpy.factors.continuous import ContinuousNode
>>> normal = ContinuousNode(norm(0, 1).pdf)
>>> from pgmpy.discretize import BaseDiscretizer
>>> class ChildDiscretizer(BaseDiscretizer):
...     def get_discrete_values(self):
...         pass
>>> discretizer = ChildDiscretizer(normal, -3, 3, 10)
>>> discretizer.factor
<pgmpy.factors.continuous.ContinuousNode.ContinuousNode object at 0x04C98190>
>>> discretizer.cardinality
10
>>> discretizer.get_labels()
['x=-3.0', 'x=-2.4', 'x=-1.8', 'x=-1.2', 'x=-0.6', 'x=0.0', 'x=0.6', 'x=1.2', 'x=1.8', 'x=2.4']
```
abstract get_discrete_values()[source]

This method implements the algorithm to discretize the given continuous distribution.

It must be implemented by all the subclasses of BaseDiscretizer.

Returns:

Return type:

A list of discrete values or a DiscreteFactor object.

get_labels()[source]

Returns a list of strings representing the values about which the discretization method calculates the probability masses.

Default value is the points - [low, low+step, low+2*step, ……… , high-step] unless the method is overridden by a subclass.

Examples

```>>> from pgmpy.factors import ContinuousNode
>>> from pgmpy.discretize import BaseDiscretizer
>>> class ChildDiscretizer(BaseDiscretizer):
...     def get_discrete_values(self):
...         pass
>>> from scipy.stats import norm
>>> node = ContinuousNode(norm(0).pdf)
>>> child = ChildDiscretizer(node, -5, 5, 20)
>>> chld.get_labels()
['x=-5.0', 'x=-4.5', 'x=-4.0', 'x=-3.5', 'x=-3.0', 'x=-2.5',
'x=-2.0', 'x=-1.5', 'x=-1.0', 'x=-0.5', 'x=0.0', 'x=0.5', 'x=1.0',
'x=1.5', 'x=2.0', 'x=2.5', 'x=3.0', 'x=3.5', 'x=4.0', 'x=4.5']
```
class pgmpy.factors.continuous.discretize.RoundingDiscretizer(name, bases, namespace, **kwargs)[source]

This class uses the rounding method for discretizing the given continuous distribution.

For the rounding method,

The probability mass is, cdf(x+step/2)-cdf(x), for x = low

cdf(x+step/2)-cdf(x-step/2), for low < x <= high

where, cdf is the cumulative density function of the distribution and step = (high-low)/cardinality.

Examples

```>>> import numpy as np
>>> from pgmpy.factors.continuous import ContinuousNode
>>> from pgmpy.factors.continuous import RoundingDiscretizer
>>> std_normal_pdf = lambda x : np.exp(-x*x/2) / (np.sqrt(2*np.pi))
>>> std_normal = ContinuousNode(std_normal_pdf)
>>> std_normal.discretize(RoundingDiscretizer, low=-3, high=3,
...                       cardinality=12)
[0.001629865203424451, 0.009244709419989363, 0.027834684208773178,
0.065590616803038182, 0.120977578710013, 0.17466632194020804,
0.19741265136584729, 0.17466632194020937, 0.12097757871001302,
0.065590616803036905, 0.027834684208772664, 0.0092447094199902269]
```
get_discrete_values()[source]

This method implements the algorithm to discretize the given continuous distribution.

It must be implemented by all the subclasses of BaseDiscretizer.

Returns:

Return type:

A list of discrete values or a DiscreteFactor object.

class pgmpy.factors.continuous.discretize.UnbiasedDiscretizer(name, bases, namespace, **kwargs)[source]

This class uses the unbiased method for discretizing the given continuous distribution.

The unbiased method for discretization is the matching of the first moment method. It involves calculating the first order limited moment of the distribution which is done by the _lim_moment method.

For this method,

The probability mass is, (E(x) - E(x + step))/step + 1 - cdf(x), for x = low

(2 * E(x) - E(x - step) - E(x + step))/step, for low < x < high

(E(x) - E(x - step))/step - 1 + cdf(x), for x = high

where, E(x) is the first limiting moment of the distribution about the point x, cdf is the cumulative density function and step = (high-low)/cardinality.

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E., Loss Models, From Data to Decisions, Fourth Edition, Wiley, section 9.6.5.2 (Method of local moment matching) and exercise 9.41.

Examples

```>>> import numpy as np
>>> from pgmpy.factors import ContinuousNode
>>> from pgmpy.factors.continuous import UnbiasedDiscretizer
# exponential distribution with rate = 2
>>> exp_pdf = lambda x: 2*np.exp(-2*x) if x>=0 else 0
>>> exp_node = ContinuousNode(exp_pdf)
>>> exp_node.discretize(UnbiasedDiscretizer, low=0, high=5, cardinality=10)
[0.39627368905806137, 0.4049838434034298, 0.13331784003148325,
0.043887287876647259, 0.014447413395300212, 0.0047559685431339703,
0.0015656350182896128, 0.00051540201980112557, 0.00016965346326140994,
3.7867260839208328e-05]
```
get_discrete_values()[source]

This method implements the algorithm to discretize the given continuous distribution.

It must be implemented by all the subclasses of BaseDiscretizer.

Returns:

Return type:

A list of discrete values or a DiscreteFactor object.

get_labels()[source]

Returns a list of strings representing the values about which the discretization method calculates the probability masses.

Default value is the points - [low, low+step, low+2*step, ……… , high-step] unless the method is overridden by a subclass.

Examples

```>>> from pgmpy.factors import ContinuousNode
>>> from pgmpy.discretize import BaseDiscretizer
>>> class ChildDiscretizer(BaseDiscretizer):
...     def get_discrete_values(self):
...         pass
>>> from scipy.stats import norm
>>> node = ContinuousNode(norm(0).pdf)
>>> child = ChildDiscretizer(node, -5, 5, 20)
>>> chld.get_labels()
['x=-5.0', 'x=-4.5', 'x=-4.0', 'x=-3.5', 'x=-3.0', 'x=-2.5',
'x=-2.0', 'x=-1.5', 'x=-1.0', 'x=-0.5', 'x=0.0', 'x=0.5', 'x=1.0',
'x=1.5', 'x=2.0', 'x=2.5', 'x=3.0', 'x=3.5', 'x=4.0', 'x=4.5']
```