Contents
What is stochastic variational inference?
2. Stochastic Variational Inference. We derive stochastic variational inference, a stochastic optimization algorithm for mean-field vari- ational inference. Our algorithm approximates the posterior distribution of a probabilistic model with hidden variables, and can handle massive data sets of observations.
What is stochastic variation?
The adjective “stochastic” implies the presence of a random variable; e.g. stochastic variation is variation in which at least one of the elements is a variate and a stochastic process is one wherein the system incorporates an element of randomness as opposed to a deterministic system.
What variational family is used in mean field approximation method?
In the mean-field approximation (a common type of variational Bayes), we assume that the unknown variables can be partitioned so that each partition is independent of the others. Using KL divergence, we can derive mutually dependent equations (one for each partition) that define the shape of Q.
How to use stochastic variational inference in mixture modeling?
To match the data we generated, we’ll use K = 3 mixture components in D = 2 dimensions. We’ll use stochastic variational inference to fit the mixture model.
How is the call method used in Bayesian Gaussian mixture?
In the call method, we’ll use TensorFlow to set up two computations. First, the log likelihood of each datapoint in the batch, given the model and the current value of the variational posterior’s variables. And second, the sum of the Kullback–Leibler divergence between the variational posteriors and their priors.
Which is the log likelihood of a Gaussian mixture?
First, the log likelihood of each datapoint in the batch, given the model and the current value of the variational posterior’s variables. And second, the sum of the Kullback–Leibler divergence between the variational posteriors and their priors. class GaussianMixtureModel(tf.keras.Model): “””A Bayesian Gaussian mixture model.
How to model a Gaussian mixture in TF 2.0?
The recommended way to feed data through a model in TF 2.0 is to use the tf.data API (as opposed to the old feed_dict mechanism). So, let’s create a TF Dataset which contains the data points from above. Let’s model the data-generating distribution with a Bayesian Gaussian mixture model.