It performs the naive cauchy probabilistic expansion of the input vector, and returns the expansion result.
The class inherits from the base expansion class (i.e., the transformation class in the module directory).
...
Notes
For input vector , its naive cauchy probabilistic expansion can be represented as follows:
κ(x∣θ)=[logP(x∣θ1),logP(x∣θ2),⋯,logP(x∣θd)]∈RD
where denotes the probability density function of the cauchy distribution with hyper-parameter ,
P(x∣θd)=P(x∣x0,γ)=πγ[1+(γx−x0)2]1.
For naive cauchy probabilistic expansion, its output expansion dimensions will be ,
where denotes the number of provided distribution hyper-parameters.
By default, the input and output can also be processed with the optional pre- or post-processing functions
in the gaussian rbf expansion function.
classnaive_cauchy_expansion(transformation):r""" The naive cauchy data expansion function. It performs the naive cauchy probabilistic expansion of the input vector, and returns the expansion result. The class inherits from the base expansion class (i.e., the transformation class in the module directory). ... Notes ---------- For input vector $\mathbf{x} \in R^m$, its naive cauchy probabilistic expansion can be represented as follows: $$ \begin{equation} \kappa(\mathbf{x} | \boldsymbol{\theta}) = \left[ \log P\left({\mathbf{x}} | \theta\_1\right), \log P\left({\mathbf{x} } | \theta\_2\right), \cdots, \log P\left({\mathbf{x} } | \theta\_d\right) \right] \in {R}^D \end{equation} $$ where $P\left({{x}} | \theta_d\right)$ denotes the probability density function of the cauchy distribution with hyper-parameter $\theta_d$, $$ \begin{equation} P\left(x | \theta_d\right) = P(x | x\_0, \gamma) = \frac{1}{\pi \gamma \left[1 +\left( \frac{x-x\_0}{\gamma} \right)^2 \right]}. \end{equation} $$ For naive cauchy probabilistic expansion, its output expansion dimensions will be $D = md$, where $d$ denotes the number of provided distribution hyper-parameters. By default, the input and output can also be processed with the optional pre- or post-processing functions in the gaussian rbf expansion function. Attributes ---------- name: str, default = 'naive_cauchy_expansion' Name of the naive cauchy expansion function. Methods ---------- __init__ It performs the initialization of the expansion function. calculate_D It calculates the expansion space dimension D based on the input dimension parameter m. forward It implements the abstract forward method declared in the base expansion class. """def__init__(self,name='naive_cauchy_expansion',*args,**kwargs):r""" The initialization method of the naive cauchy probabilistic expansion function. It initializes a naive cauchy probabilistic expansion object based on the input function name. This method will also call the initialization method of the base class as well. Parameters ---------- name: str, default = 'naive_cauchy_expansion' The name of the naive cauchy expansion function. Returns ---------- transformation The naive cauchy probabilistic expansion function. """super().__init__(name=name,*args,**kwargs)defcalculate_D(self,m:int):r""" The expansion dimension calculation method. It calculates the intermediate expansion space dimension based on the input dimension parameter m. For the naive cauchy probabilistic expansion function, the expansion space dimension will be $$ D = m d, $$ where $d$ denotes the number of provided distribution hyper-parameters. Parameters ---------- m: int The dimension of the input space. Returns ------- int The dimension of the expansion space. """returnmdefforward(self,x:torch.Tensor,device='cpu',*args,**kwargs):r""" The forward method of the naive cauchy probabilistic expansion function. It performs the naive cauchy probabilistic expansion of the input data and returns the expansion result as $$ \begin{equation} \kappa(\mathbf{x} | \boldsymbol{\theta}) = \left[ \log P\left({\mathbf{x}} | \theta\_1\right), \log P\left({\mathbf{x} } | \theta\_2\right), \cdots, \log P\left({\mathbf{x} } | \theta\_d\right) \right] \in {R}^D \end{equation} $$ Parameters ---------- x: torch.Tensor The input data vector. device: str, default = 'cpu' The device to perform the data expansion. Returns ---------- torch.Tensor The expanded data vector of the input. """b,m=x.shapex=self.pre_process(x=x,device=device)x=x.to('cpu')cauchy_dist_1=torch.distributions.cauchy.Cauchy(torch.tensor([0.0]),torch.tensor([1.0]))cauchy_x_1=cauchy_dist_1.log_prob(x)expansion=cauchy_x_1assertexpansion.shape==(b,self.calculate_D(m=m))returnself.post_process(x=expansion,device=device).to(device)
The initialization method of the naive cauchy probabilistic expansion function.
It initializes a naive cauchy probabilistic expansion object based on the input function name.
This method will also call the initialization method of the base class as well.
def__init__(self,name='naive_cauchy_expansion',*args,**kwargs):r""" The initialization method of the naive cauchy probabilistic expansion function. It initializes a naive cauchy probabilistic expansion object based on the input function name. This method will also call the initialization method of the base class as well. Parameters ---------- name: str, default = 'naive_cauchy_expansion' The name of the naive cauchy expansion function. Returns ---------- transformation The naive cauchy probabilistic expansion function. """super().__init__(name=name,*args,**kwargs)
calculate_D(m)
The expansion dimension calculation method.
It calculates the intermediate expansion space dimension based on the input dimension parameter m.
For the naive cauchy probabilistic expansion function, the expansion space dimension will be
D=md,
where denotes the number of provided distribution hyper-parameters.
Parameters:
Name
Type
Description
Default
m
int
The dimension of the input space.
required
Returns:
Type
Description
int
The dimension of the expansion space.
Source code in tinybig/expansion/probabilistic_expansion.py
defcalculate_D(self,m:int):r""" The expansion dimension calculation method. It calculates the intermediate expansion space dimension based on the input dimension parameter m. For the naive cauchy probabilistic expansion function, the expansion space dimension will be $$ D = m d, $$ where $d$ denotes the number of provided distribution hyper-parameters. Parameters ---------- m: int The dimension of the input space. Returns ------- int The dimension of the expansion space. """returnm
forward(x,device='cpu',*args,**kwargs)
The forward method of the naive cauchy probabilistic expansion function.
It performs the naive cauchy probabilistic expansion of the input data and returns the expansion result as
κ(x∣θ)=[logP(x∣θ1),logP(x∣θ2),⋯,logP(x∣θd)]∈RD
Parameters:
Name
Type
Description
Default
x
Tensor
The input data vector.
required
device
The device to perform the data expansion.
'cpu'
Returns:
Type
Description
Tensor
The expanded data vector of the input.
Source code in tinybig/expansion/probabilistic_expansion.py
defforward(self,x:torch.Tensor,device='cpu',*args,**kwargs):r""" The forward method of the naive cauchy probabilistic expansion function. It performs the naive cauchy probabilistic expansion of the input data and returns the expansion result as $$ \begin{equation} \kappa(\mathbf{x} | \boldsymbol{\theta}) = \left[ \log P\left({\mathbf{x}} | \theta\_1\right), \log P\left({\mathbf{x} } | \theta\_2\right), \cdots, \log P\left({\mathbf{x} } | \theta\_d\right) \right] \in {R}^D \end{equation} $$ Parameters ---------- x: torch.Tensor The input data vector. device: str, default = 'cpu' The device to perform the data expansion. Returns ---------- torch.Tensor The expanded data vector of the input. """b,m=x.shapex=self.pre_process(x=x,device=device)x=x.to('cpu')cauchy_dist_1=torch.distributions.cauchy.Cauchy(torch.tensor([0.0]),torch.tensor([1.0]))cauchy_x_1=cauchy_dist_1.log_prob(x)expansion=cauchy_x_1assertexpansion.shape==(b,self.calculate_D(m=m))returnself.post_process(x=expansion,device=device).to(device)