The multiple choice is in between brackets.

The expectation maximization algorithm can be used to fit [ Select ] ["only multivariate normal distributions", "many hidden variable models", "only Gaussian mixture models", "only Bernoulli distributions"] to data. The EM algorithm finds a [ Select ] ["local maximum", "global maximum", "local minimum", "global minimum"] for the [ Select ] ["log-likelihood", "mean squared error loss", "mean absolute error loss", "hinge loss"] of the data.

Imagine that we apply the algorithm as in the slides. One part of the algorithm is to compute the responsibilities, these represent the [ Select ] ["maximum likelihood for a single instance", "minimum likelihood for a single instance", "conditional probability on the hidden variable", "optimal number of components"] given the [ Select ] ["current best guess for the value of the hidden variable z.", "locally optimal model parameters", "globally optimal model parameters", "current best guess for the model parameters"] . Computing the responsibilities is called the [ Select ] ["backward step", "maximization step", "forward step", "expectation step"] .

The next step of the algorithm is to re-compute [ Select ] ["the model parameters", "the responsibilities", "only the weights of the components", "only the means of the components"] given [ Select ] ["only the means of the components", "only the covariances of the components", "the model parameters", "the responsibilities"] . This step is called the [ Select ] ["forward step", "maximization step", "expectation step", "backward step"] .

To prove that the EM algorithm converges, we decompose the log-likelihood into two terms. One is a function we called L(q, ), the other is the [ Select ] ["cross entropy between p(z|x, ) and q(z|x)", "KL divergence between p(z|x, ) and q(z|x)", "cross entropy between p(x|z, ) and q(z|z)", "KL divergence between p(x|z, ) and q(x|z)"] .