Pareto EPCA

Math

Name	`ParetoEPCA`
$G(\theta)$	$-\log(-1 - \theta) + \theta \log m$
$g(\theta)$	$\log m - \frac{1}{\theta + 1}$
$\mu$ Space^[1]	$\mathbb{R} \setminus \{ \log{m} \}$
$\Theta$ Space	negative
Appropriate Data	heavy-tail
$m$	$m > 0$ (minimum value)

Documentation

ExpFamilyPCA.ParetoEPCA — Function

ParetoEPCA(indim::Integer, outdim::Integer, m::Real; options::Options = Options(μ = 2, A_init_value = 2, A_lower = 1 / indim, V_init_value = -2, V_upper = -1))

Pareto EPCA.

Arguments

indim::Integer: Dimension of the input space.
outdim::Integer: Dimension of the latent (output) space.
m::Real: A known parameter of the Pareto distribution representing the minimum value in the support.
options::Options: Optional parameters for model initialization:
- μ: Default value 2.
- A_init_value: Initial value for matrix A (default: 2).
- A_lower: Lower bound for matrix A (default: 1 / indim).
- V_init_value: Initial value for matrix V (default: -2).
- V_upper: Upper bound for matrix V (default: -1).

Returns

epca: An EPCA subtype for the Pareto distribution.

source

Tip

If your compression converges to a constant matrix, try processing your data to reduce the maximum (e.g., divide your data by a large constant, take the logarithm).

1$\mu$ space refers to the space of valid regularization parameters, not to the expectation parameter space.