I spent the past week working on the nonparametric regression problem assigned by Professor Verma, and gained a better understanding in multivariate Gaussians and the effect of using kernel functions to define covariance matrices. I was stuck on the part where I had to generate a periodic posterior function, as I could not produce a positive semidefinite covariance matrix.

For my research project, I have also started to build a Gaussian Mixture Model as a measure of structural integrity for the clusters of the transformed data, but came across an issue when implementing the EM algorithm. Specifically, I was not able to implement the Expectation step without reducing the exponents in both the numerator and denominator to zero, and converting the expression to log is not feasible given that the denominator is a sum of exponents (as opposed to products). I tried looking for other implementat For my research project, I have also started to build a Gaussian Mixture Model as a measure of structural integrity for the clusters of the transformed data, but came across an issue when implementing the EM algorithm. Specifically, I was not able to implement the Expectation step without reducing the exponents in both the numerator and denominator to zero, and converting the expression to log is not feasible given that the denominator is a sum of exponents (as opposed to products).