Probabilistic Graphical Models : Bayesian Networks

#MachineLearning​​​ #GraphicalModels #BayesianNetworks #ArtificialNeuralNetworks #DeepLearning #ANN #SupervisedLearning​​​ #DataScience​​​ #ExplainableAI #GenerativeModels #MarkovChain

[@aryanshrajsaxena6961]

This channel is drastically underrated

[@VijayChakravarty-pz4qv]

In the example used, we had the structure of the Bayesian network given and then we could estimate the parameters using BPE. I have read that we can do three things in Bayesian Networks...parameter learning, structure learning and latent structure learning. How do we go about predicting the structure of the Bayesian Network if the parameters are given instead?

[@siddharthsethi7773]

Does Probabilistic Graphical Model have some connection with Decision Trees as if we can use Probabilistic Graphical Model to find which data set plays an important role in predicting the output same as in Decision Trees where we find Entropy and Information gain. Are these two somewhere related?

[@EvolutionaryIntelligence]

The only connection is that both use boxes and arrows! In Decision Trees, there is no notional of conditional dependence. You just start from the root node and follow the appropriate leaves to get to your conclusion. But Probabilistic Graphical Models are used to model conditional probabilities and are generative in nature, whereas Decision Trees are purely discriminative.

[@VatsalyaSharan]

Is there any way to decrease the correlation by certain design choices of our model Or are these correlations completely determined by the datasets we use?

[@EvolutionaryIntelligence]

These correlations are determined by the datasets, but you can compute them incorrectly if you are using the wrong model. And thats why model selection becomes very important in these problems.

[@EvolutionaryIntelligence]

@Prashant Shukla 16139 Bayesian Networks have no relation with Naive Bayes classifier. If the graph structure of a Bayesian Network is not known apriori, estimating it from data is an NP-hard problem and you could look at this paper for some of the useful algorithms: link.springer.com/article/10.1007/s13748-019-00194-y

[@varshanhs7654]

What is the difference between Bayesian Network and Bayesian Belief Network?

[@lucaswehmuth]

How did you get the value of P(W = T) ?

[@EvolutionaryIntelligence]

By summing over the relevant conditional probabilities.

[@lucaswehmuth]

@@EvolutionaryIntelligence Which are?

[@EvolutionaryIntelligence]

@@lucaswehmuth
By using the chain rule of probability theory, we can write:
P(C, S, R, W) = P(C) * P(S|C) * P(R|C,S) * P(W|C,S,R)
This can be simplified by using the conditional independence relationships described in the video through the graph:
P(C, S, R, W) = P(C) * P(S|C) * P(R|C) * P(W|S,R)
Now the numerator in the expression at time 17:14 is obtained by summing over various possibilities of R and C. For the denominator, you need to additionally sum over the possibilities of S as well.