combinatorial_normal_expansion
Bases: combinatorial_expansion
The combinatorial normal data expansion function.
It performs the combinatorial normal 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 combinatorial normal probabilistic expansion can be represented as follows: $$ \begin{equation} kappa(\mathbf{x} | \boldsymbol{\theta}) = \left[ \log P\left({\mathbf{x} \choose 1} | \theta_1\right), \log P\left({\mathbf{x} \choose 2} | \theta_2\right), \cdots, \log P\left({\mathbf{x} \choose d} | \theta_d\right) \right] \in {R}^D \end{equation} $$ where term \(P\left({{x}} | \theta_d\right)\) in the above expansion denotes the probability density function of the multivariate normal distribution with hyper-parameter \(\theta_d\), $$ \begin{equation} P\left(x | \theta_d\right) \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma}), \end{equation} $$ where the hyper-parameter \(\theta_d = (\mathbf{\mu}, \mathbf{\Sigma})\) covers the mean vector \(\mathbf{\mu}\) and variance matrix \(\mathbf{\Sigma}\).
For combinatorial normal probabilistic expansion, its output expansion dimensions will be \(D = \sum_{i=1}^d {m \choose i}\), where \(d\) denotes the combinatorial expansion order parameter.
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 = 'combinatorial_normal_expansion'
|
The name of the combinatorial normal expansion function. |
d |
int, default = 2
|
The combinatorial expansion order. |
with_replacement |
bool, default = False
|
The with_replacement tag for the random combination. |
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/combinatorial_expansion.py
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__init__(name='combinatorial_normal_expansion', d=1, with_replacement=False, *args, **kwargs)
The initialization method of the combinatorial normal probabilistic expansion function.
It initializes a combinatorial normal 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 |
str
|
The name of the combinatorial normal probabilistic expansion function. |
'combinatorial_normal_expansion'
|
d |
int
|
The order of random combinations. |
1
|
with_replacement |
bool
|
The replacement boolean tag. |
False
|
Source code in tinybig/expansion/combinatorial_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 combinatorial expansion function, the expansion space dimension will be $$ D = \sum_{i=1}^d {m \choose i}. $$
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/combinatorial_expansion.py
forward(x, device='cpu', with_replacement=False, *args, **kwargs)
The forward method of the combinatorial normal probabilistic expansion function.
It performs the combinatorial data expansion of the input data and returns the expansion result as $$ \begin{equation} \kappa(\mathbf{x}) = \left[ {\mathbf{x} \choose 1}, {\mathbf{x} \choose 2}, \cdots, {\mathbf{x} \choose d} \right] \in {R}^D. \end{equation} $$
Parameters:
Name | Type | Description | Default |
---|---|---|---|
x |
Tensor
|
The input data vector. |
required |
device |
The device to perform the data expansion. |
'cpu'
|
|
with_replacement |
bool
|
The replacement boolean tag. |
False
|
Returns:
Type | Description |
---|---|
Tensor
|
The expanded data vector of the input. |