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Modeling user behavior in a system

Consider a system, where each user enters the system, performs a series of predefined actions, and then exits. For instance, consider a system with 5 predefined action. The action log of some user is ...
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1answer
14 views

Can graphical models represent independence besides conditional independence?

In a graphical model, two random variables are conditional independent given their common ancestors. Can graphical models represent independence besides conditional independence?
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3answers
194 views

Why are directed graphical models called Bayesian?

Why are directed graphical models called Bayesian,while those undirected not? Does that mean that Bayesian analysis is involved in the directed ones, and not in those undirected?
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0answers
12 views

Minimal I-maps induced by sets of scopes. Clarification needed

I have a question about Prop. 9.1 on page 307 in "Probabilistic Graphical Models" (link to google books) (Koller / Friedman). I don't see why $\mathcal{H}_{\Phi}$ is a minimal I-map: If I have only ...
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0answers
8 views

Neighborhood in Gaussian graphical models

A gaussian random vector $X$ can be represented using a graph where two nodes $a$ and $b$ are connected $\Leftrightarrow X_a$ is dependent on $X_b$ given all the remaining random variables. I have two ...
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1answer
15 views

Cycles in gaussian graphical models

I understand examples where two nodes can be dependent but conditionally independent given their common cause. For instance the common cause is high temperature, and the children nodes are high ...
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0answers
16 views

Maximizing expectations vs Mode maximization

In many statistical problems, I see the following formulation for maximizing rewards: Assuming that my total reward $R$ is the sum of individual rewards $R$: ...
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1answer
82 views

How to compute marginals in Sum-Product Networks?

This should be fairly easy, but for some reason i'm having hard time getting it to work and I've spent a long time trying to figure it out myself. In the last paragraph of page 4 of the original ...
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1answer
23 views

How do you calculate the amount of parameters needed to be estimated?

I don't quite understand this. A question was, pretend we have 4 predictors and all of them are binary - for the Naive Bayes method, how many parameters are there to estimate in the training step? ...
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1answer
34 views

factorGraph approximations: Splitting variables

I am reading Chris Bishop's chapter on Expectation Propagation and there is the bit on how approximating factor graphs as shown in the images. So, the original joint distribution can be written as: ...
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0answers
11 views

Determine if Clique tree is calibrated

A, B 0 0 50 0 1 10 1 0 20 1 1 50 2 0 15 2 1 15 The above table defines the clique potential $\phi_1(A,B)$. B C 0 0 62.5 0 1 12.5 1 0 12.5 1 1 62.5 The above table defines the clique ...
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0answers
18 views

Learning Conditional Random Fields using EM Algorithm (from unaligned data)

I am trying to learn CRF from the unaligned data in Natural Language Understanding application. There is one paper in this field which does exactly the same, Learning conditional random fields from ...
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1answer
23 views

How can a probability distribution P not factorize over a graph H when P satisfies the independencies implied by H

How can a probability distribution P not factorize over a graph H when P satisfies the all the global independencies implied by H? Here's an example: Let $X_1, \dots X_4$ be 4 random variables that ...
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0answers
40 views

directed bayesian network and factor graphs

I have a directed bayesian given by the figure below. In the figure the circles are random variables and the shaded ones are observed. The rectangular nodes are constants representing the hyper ...
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0answers
20 views

How different is training a factor graph with discriminative features?

Many of the people define graphical models with factors, each with 'conditional probability tables' (CPT) and perform inference on them. But more realistic case is when you can't define full ...
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2answers
50 views

Why use factor graph for Bayesian inference?

I don't understand why converting a Bayesian network into a factor graph is good for Bayesian inference? My questions are: What is the benefit of using factor graph in Bayesian reasoning? What ...
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2answers
56 views

Does this graphical model describe a hidden Markov model?

I'm facing the problem of visual tracking in computer vision. I have some observation (image blobs by background subtraction) produced by some moving object, and the task is to infer the state ...
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0answers
13 views

Loss specific belief propagation

We know standard Belief Propagation finds the parameters which maximize probability of posterior. Is there any way to use BP, for loss specific inference? For example, let's say someone wants to ...
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0answers
49 views

Easy to follow tutorial on using Markov Random Fields for classifying pixels in gray-scale images

I am trying to learn how to use Markov Random Fields for classifying pixels in an image. Could someone please direct me to a simple tutorial demonstrating how this is done. The tutorial needs to ...
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1answer
75 views

Graphical Models and Explaining Away?

So I have fundamental confusion about graphical models. Suppose the following graphical model is given: Now the question is do we have the following equality?: ...
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1answer
53 views

Bayesian network to factor graph

I have a bayesian network with conditional probabilities as given by the diagram and I have converted it to factor graph. I just sort of read about factor graphs. Can someone be kind enough to let me ...
3
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2answers
139 views

What is the relationship between graphical models and hierarchical Bayesian models?

I've searched a good bunch of literature but have failed to find an exact distinction between the two. My impression is that in the Machine Learning literature you'll find allusions to hierarchical ...
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0answers
10 views

How to connect nodes in full conditional model of GRN?

I have problem in intuitive understanding of full conditional model in building gene regulatory network. it's basically asking that "can correlation between two genes be explained by all other genes ...
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2answers
83 views

Do edges in directed acyclic graph represent causality?

I am studying Probabilistic Graphical Models, a book for self-study. Do edges in a directed acyclic graph (DAG) represent causal relations? What if I want to construct a Bayesian network, but I am ...
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1answer
105 views

Difference of Prediction between Graph Representation and Data Matrix Representation

In data mining, data can be usually represented in different forms such as records of a matrix, graphs or ordered data. While we find in research different papers addressing methods or solutions for ...
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1answer
67 views

How to quickly build an interactive diagram modeling relationships between nodes from file input?

I hope this finds someone with the right expertise here. I am currently working with a data set on product information that has - a defined search tree structure - product types - synonyms for ...
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0answers
31 views

Probabilities from Graphical Model

I am trying to derive some probabilities from the following graphical model and I am having some difficulty. The model is actually a complete bipartite graph with two sets of nodes C and W. The graph ...
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0answers
15 views

How can I model random graphs (trees) with deterministic constraints?

I have been trying to represent a tree structure as a random graph, but so far my research has led to variations of random graph models and I can't see studies which may help me leverage some of the ...
2
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1answer
93 views

At what point does LDA (Latent Dirichlet Allocation) not make sense to use?

I was wondering if anyone could provide some intuition about when the "documents" in LDA are too small for it to provide any benefit. For instance, I have seen papers where people have you used ...
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0answers
24 views

When to use Bayesian parameter learning, when others?

Is there any general suggestion as when to use Bayesian, and when other inference approaches?! For example in the case of CRFs, when to use ML [1] and when to use Bayesian approach [2] ? [1] ...
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0answers
40 views

Bounds (or model) for estimating probability from generating process

I was curious if there was any bounds or approaches to getting good estimates for a probability from the following generating process. Suppose we have 2 sets of objects $A$ and $B$ where both sets ...
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1answer
92 views

Parameters and parameter estimation in graphical models

I try to understand parameter estimation and learning problems at Graphical Models, especially in directed ones (Bayesian Networks). But first of all, I try to understand what exactly a parameter ...
3
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1answer
63 views

Confusion in Expectation Propagation energy function

I have two questions in Energy function of expectation propagation. 1. Seeing the video of [1] (slide 24 of the second part), Minka says that, the evidence is the following: $$ Z = \left( \int ...
2
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1answer
58 views

Confusion: different definitions of MAP estimation in Graphical Models (MRFs)

The "classical" MAP estimation: $$\hat\theta = \arg\max_{\theta}P(\theta|\mathbf{x})$$ where $\mathbf{x}$ are the observations and $\theta$ are the parameters. In this book chapter (page 6, second ...
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22 views

Why marginals in graphical models matter?

Many of the algorithms (like subset sum) find "marginals" in graphical models. But it is not really clear to me why marginals matter. I am asking this, since when one is doing inference they do on the ...
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0answers
42 views

Why Bayesian Networks? Why Markov Networks?

Undirected Graphical Models are usually known as "Markov Networks" and Directed Graphical Models are known as "Bayesian Networks". This is naming is not very clear to me. It might be because of some ...
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2answers
162 views

Predicting the edges of a graph

I have a dataset of paired relations, indicating whether $a$ is in relation with $b$. It is better to consider this dataset as a graph where each node has a numerical value as its feature. Let's say ...
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2answers
1k views

Interpreting the residuals vs. fitted values plot for verifying the assumptions of a linear model

Consider the following figure from Faraway's Linear Models with R (2005, p. 59). The first plot seems to indicate that the residuals and the fitted values are uncorrelated, as they should be in a ...
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0answers
82 views

Bayesian Networks: Does the d-Separation Property originate from the basic Markov Property?

I asked the following question in order to gain some intuitive understanding about the d-Separation property in Bayesian Networks a while ago: Understanding d-separation theory in causal Bayesian ...
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0answers
98 views

Good libraries for working with probabilistic graphical models?

Could someone recommend some well-maintained and up-to-date libraries for working with probabilistic graphical models? I noticed that there are some libraries for R listed here and one for C++, but ...
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1answer
37 views

Fixed point iterations for expectation propagation using energy minimization

EP Primal In 1, it is finding the EP iterations by solving a saddle-point problem on the energy function. First, the primal is claimed to be $$ \min_{\hat{p}_i} \max_{q} \left[ \sum_i ...
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1answer
20 views

The junction tree theorem

In [1] (Page 31,equation 2.12 ) it is claiming that in a graph which is processed by the junction tree algorithm, the joint distribution of the variables could be found by $$ p(x_1, ..., x_m) = ...
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22 views

Junction tree theorem on cycles

In page 31 of David Sontag's 2010 MIT PhD thesis 1 (Approximate Inference in Graphical Models using LP Relaxations) we read that: The junction tree theorem guarantees that every joint distribution ...
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2answers
45 views

Which toolbox for Belief Propagation and other inference methods in graphical models?

Which open-source software (toolbox) do you think is the best for modelling graphical models (e.g. factor graphs), and doing inference on them? (the language doesn't matter)
3
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1answer
53 views

In message-passing methods, what is the actual content of the messages?

In message-passing methods, factors and random variables exchange messages that typically encode marginals, but as much as I look at their formulas, I still don't understand what those messages ...
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2answers
185 views

Understanding d-separation theory in causal Bayesian networks

I am trying to understand the d-Separation logic in Causal Bayesian Networks. I know how the algorithm works, but I don't exactly understand why the "flow of information" works as stated in the ...
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3answers
88 views

How to train in models, with efficient inferences, like belief-propagation ?

There are many papers that are devoted to efficient inference in graphical models. Though many of these paper don't explicitly talk about the learning (training, etc) problem. For example: ...
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1answer
64 views

Sign of the unnormalized log likelihood in Ising model

Here is a section of Machine Learning: a Probabilistic Perspective by Kevin Patrick Murphy I don't understand in (19.18) why there is a negative sign. For me, $\log ...
7
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1answer
119 views

regarding conditional independence and its graphical representation

When studying covariance selection, I once read the following example. With respect to the following model: Its covariance and inverse covariance matrix are given as follows, I do not understand ...
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1answer
24 views

Are MRFs with edges to all observed data possible?

I have been discussing the following issue with a colleague of mine and I can't seem to wrap my head around it. I have a computer vision background, so I'm mostly familiar with 2D MRFs/CRFs for image ...