The purpose of this project is to demonstrate the implementation and results of the optimization of a probabilistic model. Since this model has two continuous latent variables, multiple quantities can be inferred by bayesian inference and marginalization.
Figure 1: Exploration of latent space w (left) on a regular grid on [-2, 2] x [-2, 2]. Each cell belongs to a 2D conditional probability distribution p(x|w).
Bayesian inference can also be performed for a shape X, so that the posterior distributions for p(w|X) were calculated for all ten shapes from the data set (right).
The maximal values match to the locations of the shapes on the left side.
Figure 2: Bayesian inference on the shape-model. The posterior distributions p(z|x, w) (right) for samples x from a shape of a digit (left) can be approximately evaluated.
For basic usage and more functionality demonstration have a look at the jupyter notebook. You can also contact me for details regarding the model and the optimization objective derivation.