7135CEM – Modelling and Optimisation under Uncertainty

7135CEM Assignment Help

Modelling and Optimisation under Uncertainty Assignment help

Context
During this module, you learned about different advanced machine learning techniques, associated concepts and applications. We explored the Gaussian process model, which is computationally efficient method for Regression, Classification, optimization, etc. We have also covered the Bayesian networks as promising tools for modelling the data with complex dependency structure. Finally, you have learned how to use Dirichlet Latent processes for unsupervised learning applications, particularly text mining.
In this assignment, you will have to select an application related to a regression, classification, modelling un-structured data, or text mining problem, and explore how best to apply the machine learning algorithms to solve it. The selected application for each of the methods mentioned above should have the following features:

1. Gaussian Process regression and Classification: The application selected for any of these two methods must consist of at least four input variables and a single output variable. You must also implement Gaussian process classification by appropriately define a threshold on the output variable to create a binary or multiple classes first, and then apply the Gaussian process classification on the categorized output.

2. Bayesian network: If you are choosing an application for this method, this application must consist of at least eight random variables. The random variables could be all discrete or continuous or hybrid.

3. There is no restriction on selecting the application to apply the Latent Dirichlet allocation model for topic modelling.

There are some potential projects listed below, which could be studied to get some ideas. However, I strongly recommend you to come up with your own idea(s) by reviewing these project and some other relevant and recent articles.

1. This dataset from the UCI repository is quite interesting. The task is to predict the depth in the body (effectively, the depth along the spine) given the properties of a two-dimensional “slice” of the body. The hard part about this problem is that it is actually the output causing the input rather than the other way around. I have not had luck designing a good regression method for this data. Can you do this?

2. Find a Bayesian interpretation of elastic net regularization, and compare this method for regression against “standard” Bayesian regression (with a Gaussian prior) on a dataset of your choosing.

3. Probabilistic PCA using Gaussian Process is a Bayesian interpretation of the classical PCA algorithm for dimensionality reduction. Implement Gaussian Process based PPCA in Python, R or Matlab, and compare its performance with other methods (such as “standard” PCA) on a dataset of your choosing.

4. Bayesian optimization is very important issue with a wide range of applications. However, this was not fully studied during lectures, but it can be easily implemented using Gaussian Process. The Python codes and some examples can be found here!

5. The squared exponential covariance is widely used for Gaussian process regression. It is probably used in 90+% of all GP publications. That said, it is widely believed to be “too smooth” for many real-world regression tasks. Compare the squared exponential

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