naive_cauchy_expansion
Bases: transformation
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).
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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 | Type | Description |
---|---|---|
name |
str, default = 'naive_cauchy_expansion'
|
Name of the naive cauchy expansion function. |
Methods:
Name | Description |
---|---|
__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. |
Source code in tinybig/expansion/probabilistic_expansion.py
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__init__(name='naive_cauchy_expansion', *args, **kwargs)
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 | Type | Description | Default |
---|---|---|---|
name |
The name of the naive cauchy expansion function. |
'naive_cauchy_expansion'
|
Source code in tinybig/expansion/probabilistic_expansion.py
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 $$ D = m d, $$ where \(d\) 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
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 $$ \begin{equation} \kappa(\mathbf{x} | \boldsymbol{\theta}) = \left[ \log P\left({\mathbf{x}} | \theta_1\right), \log P\left({\mathbf{x} } | \theta_2\right), \cdots, \log P\left({\mathbf{x} } | \theta_d\right) \right] \in {R}^D \end{equation} $$
Parameters:
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. |