Gaussian Mixture GAN for Unsupervised Learning

Overview

This project implements a Gaussian Mixture GAN (GM-GAN), combining Generative Adversarial Networks (GANs) and Gaussian Mixtures to improve performance in unsupervised learning tasks, particularly for image generation. It is based on pretraining with a vanilla GAN model and further tuning using Gaussian mixtures.

Problem Definition

The GM-GAN models a mixture of Gaussians to enhance GAN's ability to generate diverse data. The key elements of the Gaussian Mixture Model (GMM) used are:

• ( K ): Number of Gaussians in the mixture.
• ( c ): Range from which the Gaussians' means are sampled.
• ( \sigma ): Scaling factor for the covariance matrices.
• ( \gamma ): Learning rate for model optimization.

Model Architecture

1. Generator: Generates data samples from a noise distribution.
2. Discriminator: Distinguishes between real and generated samples.
3. Gaussian Mixture: A Gaussian Mixture Model that refines the data generation by adding a probability distribution over multiple Gaussian components.

Loss Function

1. Generator Loss: [ L_G = \mathbb{E}[\log(1 - D(G(z)))] ]
2. Discriminator Loss: [ L_D = \mathbb{E}[\log D(x)] + \mathbb{E}[\log(1 - D(G(z)))] ] where ( D ) is the discriminator, ( G ) is the generator, and ( z ) is random noise.

Results

• Vanilla GAN FID: 39.45
• Static GM-GAN FID: 19.02 (best result on local static GM-GAN)
• Hyperparameters:
  • Batch size: 64
  • Learning rate: ( 0.0002 )
  • FID (Best Metric): 16.12 (after fine-tuning GM-GAN)

Installation

1. Clone the repository:

   git clone https://github.com/matteo-st/gan-gaussian-mixture.git
   cd yourrepo gan-gaussian-mixture
   
   

generate.py

Use the file generate.py to generate 10000 samples of MNIST in the folder samples. Example:

python3 generate.py --bacth_size 64