Bayes’ Rule – Hidden Markov Models Speech Recognition
Bayes’ rule was studied in class, and taught us some interesting probabilistic principles. Namely, it set up a basis to study all sorts of conditional probabilities. Furthermore, Bayes’ rule can be extended to form Bayesian networks. These networks combine many sources of knowledge into various inferences. These inferences can be visually represented as a sequential graph, with some nodes pointing at others where a casual relationship exists. This graph will be in the form of a DAG (directed acyclic graph). Once we’ve defined a set of beliefs in the form of a graph, we can calculate all probabilities using their joint distributions.
We can apply Bayes’ rule heavily towards the forwards backwards propogation in a hdiden Markov model. One the forward propogation side, we calculate the probability of an event occuring given all of its parent nodes (nodes pointing to the current node). On the backwards propogation cycle, we calculate the probability of all its children occuring (AKA the remaining observations), given the current event. These two distributions are combined using Bayes’ rule.
Bayesian inferences can be used on evolutionary topics in order to predict how the gene distribution evolves over time, as Charles Darwin predicted so long ago. Specifically, one example of bayesian inference is on the evolution of a phenotype distribution of a certain tree species. More commonly in industry, hidden markov models (HMMs) are used in speech recognition algorithms. The leaders of industry such as Google and Baidu still employ HMMs as the basis for some of their algorithms. One major advancement, though not recent, was that hidden Markov models can be parameter-tuned using the expectation maximization algorithm. Then these hidden Markov models can also be converted into Gaussian mixture models, which are very useful for representing the relationships between the states of the hidden Markov model.