ExpFamilyPCA.jl Documentation
ExpFamilyPCA.jl is a Julia package for performing exponential principal component analysis (EPCA). ExpFamilyPCA.jl supports custom objectives and includes fast implementations for several common distributions.
Installation
To install the package, use the Julia package manager. In the Julia REPL, type:
using Pkg; Pkg.add("ExpFamilyPCA")Quickstart
using ExpFamilyPCA
indim = 5
X = rand(1:100, (10, indim)) # data matrix to compress
outdim = 3 # target compression dimension
poisson_epca = PoissonEPCA(indim, outdim)
X_compressed = fit!(poisson_epca, X; maxiter=200, verbose=true)
Y = rand(1:100, (3, indim)) # test data
Y_compressed = compress(poisson_epca, Y; maxiter=200, verbose=true)
X_reconstructed = decompress(poisson_epca, X_compressed)
Y_reconstructed = decompress(poisson_epca, Y_compressed)Supported Distributions
| Distribution | ExpFamilyPCA.jl | Objective | Link Function $g(\theta)$ |
|---|---|---|---|
| Bernoulli | BernoulliEPCA | $\log(1 + e^{\theta - 2x\theta})$ | $\frac{e^\theta}{1 + e^\theta}$ |
| Binomial | BinomialEPCA | $n \log(1 + e^\theta) - x\theta$ | $\frac{ne^\theta}{1 + e^\theta}$ |
| Continuous Bernoulli | ContinuousBernoulliEPCA | $\log\left(\frac{e^\theta - 1}{\theta}\right) - x\theta$ | $\frac{\theta - 1}{\theta} + \frac{1}{e^\theta - 1}$ |
| Gamma¹ | GammaEPCA or ItakuraSaitoEPCA | $-\log(-\theta) - x\theta$ | $-\frac{1}{\theta}$ |
| Gaussian² | GaussianEPCA or NormalEPCA | $\frac{1}{2}(x - \theta)^2$ | $\theta$ |
| Negative Binomial | NegativeBinomialEPCA | $-r \log(1 - e^\theta) - x\theta$ | $\frac{-re^\theta}{e^\theta - 1}$ |
| Pareto | ParetoEPCA | $-\log(-1 - \theta) + \theta \log m - x\theta$ | $\log m - \frac{1}{\theta + 1}$ |
| Poisson³ | PoissonEPCA | $e^\theta - x\theta$ | $e^\theta$ |
| Weibull | WeibullEPCA | $-\log(-\theta) - x\theta$ | $-\frac{1}{\theta}$ |
¹: For the Gamma distribution, the link function is typically based on the inverse relationship.
²: For Gaussian, also known as Normal distribution, the link function is the identity.
³: The Poisson distribution link function is exponential.