Week 8 and 9
In the week 8 and 9, I implemented DirichletProcessGaussianMixture. But its behavior looks similar to BayesianGaussianMixture. Both of them can infer the best number of components. DirichletProcessGaussianMixture took a slightly more iteration than BayesianGaussianMixture to converge on Old-faith data set, around 60 iterations.
If we solve Dirichlet Process Mixture by Gibbs sampling, we don’t need to specify the truncated level T. Only the concentration parameter $\alpha$ is enough. In the other hand, with variational inference, we still need to specify the maximal possible number of components, i.e., the truncated level.
At the first, the lower bound of DirichletProcessGaussianMixture seems a little strange. It is not always going up. When some clusters disappear, it goes down a little bit, then go up straight. I think it is because the estimation of the parameters is ill-posed when these clusters have data samples less than the number of features. I did the math derivation of Dirichlet process mixture models again, and found it was a bug on the coding of a very long equation.
I also finished the code of BayesianGaussianMixture for ‘tied’, ‘diag’ and ‘spherical’ precision.
My mentor pointed out the style problem in my code and docstrings. I knew PEP8 convention, but got no idea where was also a convention for docstring, PEP257. It took me a lot of time to fix the style problem.
Progress report 2
During the last 5 weeks (since the progress report 1), I finished the
GaussianMixutrewith four kinds of covariance- Most test cases of
GaussianMixutre BayesianGaussianMixturewith four kinds of covarianceDirichletProcessGaussianMixture
Although I spent some time on some unsuccessful attempts, such as decoupling out observation models and hidden models as mixin classes, double checking DP equations, I did finished the most essential part of my project and did some visualization. In the following 4 weeks, I will finish all the test cases for BayesianGaussianMixture and DirichletProcessGaussianMixture, and did some optional tasks, such as different covariance estimators and incremental GMM.