All Questions
Tagged with conditional-independence graphical-model
16
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A question of "elementary imsets" in an ADMG
In [The m-connecting imset and factorization for ADMG models] (https://doi.org/10.48550/arXiv.2207.08963), it was mentioned the notation of an "elementary imset". The definition of ...
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66
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Conditional independence statements for probabilistic motivation for linear regression
So the motivation for using the squared loss in linear regression can be written as the following (I think):
Assume $\{(\mathbf{x}_i, y_i) \mid i = 1, \dots n\}$ are repeated independent samples from ...
- 359
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756
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Intuition of conditional independence in DAGs
In the DAG above, we have $A$ conditionally independent of $E$ when $C$ and $B$ are observed (that is $A\perp E|B,C$), but not when only $C$ is observed (that is $A\not\perp E|C$). I don't have a ...
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Implications of violating Bayesian network independence assumptions during inference
Consider the example Bayesian network below where $X \perp \!\!\! \perp Y $ (X is independent of Y).
Assuming that this is the true independence structure of the process that is generating the data, ...
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113
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Quick way to determine the different independence assumptions
This question is different than my previous question in that I'm asking sort of a "meta" question.
Here's two graphical models (a Belief Network and a Markov Network):
I would like to ...
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145
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Determining unconditional independence in Markov Networks
I would like to know whether $E \perp\kern-5pt\perp A $ in the following Markov Network and would like to know if my reasoning is correct:
So, since this is a Pairwise Markov Network, it factorizes ...
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290
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Checking for conditional independence in graphical models
I would like to know whether $B \perp\kern-5pt\perp C | D,A $ and $D \perp\kern-5pt\perp A | B,C $ in the following two graphical models and would like to know if my reasoning is correct:
For the ...
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Is $C \perp\kern-5pt\perp D | A $ for the two graphical models? [duplicate]
I would like to know whether $C \perp\kern-5pt\perp D | A $ in the following two graphical models and would like to know if my reasoning is correct:
For the left model (Belief Network), here's my ...
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66
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Is $B \perp\kern-5pt\perp C | A $ for the two graphical models?
I would like to know whether $B \perp\kern-5pt\perp C | A $ in the following two graphical models and would like to know if my reasoning is correct:
For the left graphical model, which is a Belief ...
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83
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Is it always possible to find a joint distribution $p(x_1,x_2,x_3,x_4)$ consistent with these local conditional distributions?
I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.1 (p 79). The exercise is the following:
Exercise 4.1
Consider the pairwise Markov network,
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What is the most elegant way to express conditional independence on a line graph?
Consider a Markov graph
$$x_1 -x_2-x_3-...-x_t$$
In such a graphical model, we have the conditional independence property $x_{s-1} \perp x_{s+1:t} | x_s \;\forall\; x=2,...,t-1$ and $x_{1:s-1} \perp ...
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63
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Directed graphical models and independence (exercise)
Context: this is Ex. 1 in these notes http://www.stat.cmu.edu/~larry/=sml/DAGs.pdf .
The exercise asks to prove that, given a directed graphical model associated to a DAG (directed acyclic graph) $G$:
...
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Is there any work on, given a set of conditional independences, build the graphical model?
The graphical model Represents probabilistic independence.
Given a set of conditional independence assumptions, how to find the probabilistic graphical model that maximizes some metrics (e.g, minimum ...
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Bayesian structure learning: how to identify z as a collider in x-z-y structure?
In BNSL(Bayesian Network Structure Learning) problem, we are asked to learn a DAG(Directed Acyclic Graph) over a randon variable set $U$, given samples of the underlying distribution of $U$. The ...
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d-separation in Bayes Network vs separation in undirected graph
I've been teaching myself about d-separation and am trying to answer the following question. Given the graphs below, write down all conditional independence relationships involving the random variable ...
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