leaspy.utils.distributions

Module defining useful distribution for ordinal noise model.

Classes

MultinomialDistribution	Class for a multinomial distribution with only one sample based on the Multinomial torch distrib.
MultinomialCdfDistribution	Class for a multinomial distribution with only sample method.

Functions

discrete_sf_from_pdf(pdf)	Compute the discrete survival function values from a discrete probability density.
compute_ordinal_pdf_from_ordinal_sf(ordinal_sf[, ...])	Compute the probability density of an ordinal model from its survival function.

Module Contents

discrete_sf_from_pdf(pdf)

Compute the discrete survival function values from a discrete probability density.

For a discrete variable with levels l=0..L the survival function is \(P(X>l)=P(X\ge l+1)\) for l=0..L-1. This function assumes the last dimension of pdf indexes the discrete levels.

Parameters:

pdftorch.Tensor or np.ndarray

The discrete probability density.

Returns:

np.ndarray

The discrete survival function values.

Parameters:

pdf (Union[Tensor, ndarray])

Return type:

Tensor

compute_ordinal_pdf_from_ordinal_sf(ordinal_sf, dim_ordinal_levels=3)

Compute the probability density of an ordinal model from its survival function.

Given the survival function probabilities \(P(X>l)=P(X\ge l+1)\) for l=0..L-1, compute \(P(X=l)\) for l=0..L.

Parameters:

ordinal_sftorch.FloatTensor

Survival function values : ordinal_sf[…, l] is the proba to be superior or equal to l+1 Dimensions are:

• 0=individual

• 1=visit

• 2=feature

• 3=ordinal_level [l=0..L-1]

• [4=individual_parameter_dim_when_gradient]

dim_ordinal_levelsint, default = 3

The dimension of the tensor where the ordinal levels are.

Returns:

ordinal_pdftorch.FloatTensor (same shape as input, except for dimension 3 which has one more element)

ordinal_pdf[…, l] is the proba to be equal to l (l=0..L)

Parameters:

• ordinal_sf (Tensor)

• dim_ordinal_levels (int)

Return type:

Tensor

class MultinomialDistribution(probs, **kwargs)

Bases: torch.distributions.Multinomial

Class for a multinomial distribution with only one sample based on the Multinomial torch distrib.

Parameters:

probstorch.Tensor

The pdf of the multinomial distribution.

Attributes:

arg_constraints: ClassVar

Returns a dictionary from argument names to Constraint objects that should be satisfied by each argument of this distribution. Args that are not tensors need not appear in this dict.

classmethod from_sf(sf, **kws)

Generate a new MultinomialDistribution from its survival function instead of its probability density function.

Parameters:

pdftorch.Tensor

The input probability density function.

**kws

Additional keyword arguments to be passed for instance initialization.

Parameters:

sf (Tensor)

class MultinomialCdfDistribution(sf, *, validate_args=True)

Bases: torch.distributions.Distribution

Class for a multinomial distribution with only sample method.

Parameters:

sftorch.Tensor

Values of the survival function [P(X > l) for l=0..L-1 where L is max_level] from which the distribution samples. Ordinal levels are assumed to be in the last dimension. Those values must be in [0, 1], and decreasing when ordinal level increases (not checked).

validate_argsbool, optional (default True)

Whether to validate the arguments or not (None for default behavior, which changed after torch >= 1.8 to True).

Attributes:

cdftorch.Tensor

The cumulative distribution function [P(X <= l) for l=0..L] from which the distribution samples. The shape of latest dimension is L+1 where L is max_level. We always have P(X <= L) = 1

arg_constraintsdict

Contains the constraints on the arguments.

Parameters:

• sf (Tensor)

• validate_args (Optional[bool])

arg_constraints: ClassVar

Returns a dictionary from argument names to Constraint objects that should be satisfied by each argument of this distribution. Args that are not tensors need not appear in this dict.

cdf

Returns the cumulative density/mass function evaluated at value.

Args:

value (Tensor):

classmethod from_pdf(pdf, **kws)

Generate a new MultinomialDistribution from its probability density function instead of its survival function.

Parameters:

pdftorch.Tensor

The input probability density function.

**kws

Additional keyword arguments to be passed for instance initialization.

Parameters:

pdf (Tensor)

sample()

Multinomial sampling.

We sample uniformly on [0, 1( but for the latest dimension corresponding to ordinal levels this latest dimension will be broadcast when comparing with cdf.

Returns:

torch.Tensor

Vector of integer values corresponding to the multinomial sampling. Result is in [[0, L]]

Return type:

Tensor