Probablistic Machine Learning course projects related to topic Modelling using LDA, Variational Inference and Autoencoders
Lab1: In this Lab, we find clusters in Twitter data, i.e. grouping tweets with similar content. For this purpose, we first describe a mixture model for categorical data. Secondly, we use the expectation-maximization (EM) algorithm to find the maximum likelihood (ML) estimate of the parameters of our model
Lab2: In this Lab, we continue working with the CMM and Twitter data-set presented in Lab 1. We will use different versions of the Gibbs sampling algorithm to find the posterior distribution of the cluster assignments 
Lab3: In this lab,we continue working with the CMM and Twitter data-set presented in Lab1. We will use Bayesian nonparametric (BNP) to assume (a priori) infinite number of mixture components K. In practice, we will only be able to ”see” a finite number, K+, of components K+ < N - 1 << 1 which is constrained by the number of observations in our data-set. Again,we will rely on the Gibbs sampling algorithm to infer the posterior distribution of the unknownvariables and parameters in our model
Lab4: In this Lab, we explore two different applications of Hidden Markov Models (HMMs) i)Part-Of-Speech (POS) tagging and ii) Human Activity Recognition (HAR). We will learn how to obtain the MLE of the parameters 
Lab5: In this Lab we implement Coordinate acsent Mean-field Variational inference (CAVI) and derive Evidence Lower bound for Gaussian Mixture model. Specifically we
1.Generate a synthetic dataset from a GMM with 3 clusters and 1000 datapoints per cluster.
2.Derive the formula of the ELBO for this model.
3.Implement the CAVI updates for the model.
4.Run the algorithm and plot the results at convergence.
Lab6: In this Lab we will generate synthetic data and then we will use it to learn how to apply Stochastic Gradient Descent (SGD) and Amortized Variational Inference with neural networks. We will use the package pytorch, which allow us to perform automatic differentiation.
Lab7: In this Lab we will focus on the problem of density estimation. We will use the well-known MNIST dataset to train a Variational Autoencoder that will learn to approximate the distribution of the data and consequently, will be able to generate 'realistic' images. We will use the package pytorch, which allow us to perform automatic differentiation