Questions tagged [probabilistic-graphical-models]

For questions about (probabilistic) graphical models (PGMs), which are probabilistic models where a graph represents the conditional dependencies between random variables. If the graph is a directed acyclic graph (DAG), the graphical model is often called a Bayesian network or Belief network. If the graph is undirected, it's often called a Markov network or Markov random field.

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Why are Directed Graphical Models considered ML methods?

Consider the following problem. The probability of being born in countries [1,2,3,4] is given by [a, b, c, d] respectively. This is a categorical problem. Now, assume that the height of a person ...
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What is the primary advantage of viewing RNN as a directed graphical model?

While reading the chapter titled "Sequence Modeling: Recurrent and Recursive Nets" from the textbook named Deep Learning by Ian Goodfellow et al, I came across a subsection 10.2.3 titled &...
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For the VAE, should the input, output and latent variable code be random variables?

For a variational autoencoder, we have input $x$ (assume 1 data point for now, like an image), a latent code sampled from the decoder, $z$, and an output $\hat{x}$. If I were to draw a diagram for the ...
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What is the difference between Probabilistic Graphical models and Graph Neural networks?

While going over PGMs and GNNs, it seems like both leverage the graph data structure. The former has been used to represent causal associations (among other things), while the latter has a varied set ...
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In the original GAN paper, why is it mentioned that you can sample deep directed graphical models without a Markov chain?

In the original GAN paper (table 2), why is it mentioned that you can sample deep directed graphical models without a Markov chain (well, they say without difficulties, but others list MCMC as a ...
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In the original GAN paper, why is it claimed that variational inference is used in deep undirected models for inference?

In the original GAN paper (table 2), why is it claimed that variational inference is used in deep undirected models for inference? I was under the impression that they used Gibbs Sampling, MCMC-based ...
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In Probabilistic Graphical Model (written by Daphne Koller), what's the meaning of "parameter" in representation of the distribution?

I just started to read the PGM book written by Daphne Koller. In the chapter of Bayesian Network Representation(Chapter 3), there are some descriptions about the standard parameterization of the joint ...
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In RL as probabilistic inference, why do we take a probability to be $\exp(r(s_t, a_t))$?

In section 2 the paper Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review the author is discussing formulating the RL problem as a probabilistic graphical model. They ...
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How do I derive the gradient of the log-likelihood of an RBM?

In a Restricted Boltzmann Machine (RBM), the likelihood function is: $$p(\mathbf{v};\mathbf{\theta}) = \frac{1}{Z} \sum_{\mathbf{h}} e^{-E(\mathbf{v},\mathbf{h};\mathbf{\theta})}$$ Where $E$ is the ...
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Purpose of the hidden variables in a Restricted Boltzmann Machine

From the part titled Introducing Latent Variables under subsection 2.2 in this tutorial: Introducing Latent Variables. Suppose we want to model an $m$-dimensional unknown probability distribution $q$ ...
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How to make sense of label propagation formula in graph neural networks?

In the label propagation algorithm in section 3.2.3, we know the label of some nodes and we want to predict the label for the rest of the nodes whose labels we don't know. The update formula for this ...
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Deriving hyperparameter updates in Online Interactive Collaborative Filtering

I've been going through "Online Interactive Collaborative Filtering Using Multi-Armed Bandit with Dependent Arms" by Wang et al. and am unable to understand how the update equations for the ...
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What is a conditional random field?

I new in machine learning, especially in Conditional Random Fields (CRF). I have read several articles and papers and in there is always associated with HMM and sequences classification. I don't ...
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How do probabilistic graphical models factor into modern machine learning?

I just finished the three-part series of Probabilistic Graphical Models courses from Stanford over on Coursera. I got into them because I realized there is a certain class of problem for which the ...
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What does a hybrid Bayesian network contain?

The field of artificial intelligence is so vast. There are many methodologies for handling continuous data, and I have just read about the hybrid Bayesian network. I just want to know that what a ...
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