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1answer
16 views

Hidden Markov Model with conditional observations

I am looking for a research paper that basically describes a hidden markov model that has multiple observations, and some observations that have conditional dependencies. For example, please consider ...
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1answer
35 views

simply demostration on conditioned probability

I don't find the answer of this simply problem: how can I algebrically demonstrate that, with 3 variable A,B,C $ \sum\limits_C P(B|C)P(C|A)=P(B|A)$ under condition that $P(A,B,C)=P(A|C)P(B|C)P(C)$ ...
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0answers
20 views

How are deterministic/logical nodes represented mathematically in directed graphical models?

Various software for performing inference on graphical models support logical(a.k.a deterministic) nodes. PyMc, Winbugs, Smile are the ones I'm aware of. Based on the different inference methods ...
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2answers
62 views

Learning to map vectors to vectors

Say we want to learn a function: $f(\mathbf{x} \in \mathbf{R}^p) \rightarrow \mathbf{y} \in \mathbf{R}^q$ where $\mathbf{x}$ and $\mathbf{y}$ are vectors representing time series. We have multiple ...
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1answer
32 views

identifying latent variables in this model

I have been trying to understand EM and I am having a hard time understanding what a latent variable is. In particular, I am having issues in identifying whether in a particular model that I am using, ...
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0answers
34 views

Log linear models advantages

What are the advantages of log linear representation in opposite of table representation? Is it simply computational issue ( avoid overflowing)? For example, in a markov network A-B we can represent ...
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0answers
19 views

What is the correct definition for completness in d-separation in directed graphical models?

I was reading Koller's book of probabilistic graphical models and in section 3.3.2 she discusses what properties should hold for d-separation as a method for determining independence. She tries to ...
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2answers
112 views

What does the notation $(\textbf{X} \perp \textbf{Y} , \textbf{W}\mid \textbf{Z})$ mean?

I was reading Koller's and Friedman's Probabilistic Graphical Models book and became confused about some of its notation because of a set of notes that either contradict it or express it differently. ...
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1answer
30 views

LASSO or other regularized regression with censored (missing) data

Here is my problem. I am looking at various time series curves. Let's call them total spend aggregated over all customers on various products versus time. At any given time, I want to predict the ...
1
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1answer
121 views

Smoother lines for ggplot2

This question probably has a simple solution, still the thing is I've written a code to plot mortality in 2 different groups and that is, death in obese patients vs not obese. Now their are 2 groups ...
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1answer
20 views

Graphical Model Equivalent of Matrix Pseudoinverse

The may sound like a strange question but I was wondering if a Pseudoinverse of a matrix could be found using SVD whether there was a graphical modelling equivalent that could be used to estimate the ...
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1answer
22 views

Markov blanket conditional distribution derivation

I am trying to derive the formula for the conditional distribution for a variable in a Bayesian network: $$p(x_j|x_{-j})=p(x_j|x_{pa(j)})\prod_{k\in ch(j)}p(x_k|x_{pa(k)})$$ I understand D-separation ...
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0answers
36 views

Assumptions implied by “pairwise marginal” parameterization of MRF

I'm trying to understand the assumptions of different parameterizations in a Markov network. In this case, I'm trying to understand the assumptions (and effects) that result from parameterizing ...
2
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1answer
43 views

What is max-sum / max-product variant of loopy BP computing?

In (Nowazin and Lampert, Structured Learning and Prediction in Computer Vision, p. 29.), they say that in the max-sum variant of loopy belief propagation, the "variable max-beliefs are no longer ...
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0answers
24 views

How to design an energy function in a factor graph model?

When designing a factor graph, the designer needs to specify the structure of the graph (encoding independence assumptions), and the form and parameterization of the energy functions for the ...
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0answers
10 views

Does anyone know how to make this infograph with R? [closed]

This picture was posted on a Brazilian newspaper called "Folha de São Paulo". The graph relates each candidate's name with their allied political parties
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0answers
30 views

Possible inferences from a graph pattern

So, I had a weighted dynamic graph having info about 10 consecutive timesteps ( basically 10 files ). Now, I had to mine out patterns in the weight and structure of the complete graph. I did that. The ...
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0answers
22 views

A Graphical Model for Fellegi-Sunter Record Linkage

I am trying to understand the Fellegi-Sunter Probability Model for Record Linkage problem. I am following the thesis at: http://www.inf.ed.ac.uk/publications/thesis/online/IM080663.pdf in order to ...
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1answer
32 views

Difference between graphical model and markov chain

Representing causality using fuzzy cognitive maps presents a cognitive model which is a graphical model consisting of weighted directed graph. To me it looks like a state transition machine. Can ...
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1answer
48 views

Can Someone Explain How Factor Multiplication Works with Factor Graphs?

I'm taking the Probablistic Graphical Model course here: https://class.coursera.org/pgm-003/ This class uses the concept of Factors extensively with regards to graphical models: ...
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1answer
40 views

Explaining away

I am brushing up on graphical models, and doing the following problem 3.3 from the book PGM by Kophler. An alarm A can be set off by either Burglary B or earthquake E. Prove that if $P(a^1| b^1, e^1) ...
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0answers
72 views

Example on Hidden Markov Model

I was studying Hidden Markov Model(HMM) recently. I was looking to cross check what I understood. I found a code on Forward-Backward and Viterbi is given in simple Python terms in Wikipedia. I ...
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0answers
30 views

Python alternative to Factorie

Is there alternative / replacement in Python of Factorie (http://factorie.cs.umass.edu/index.html) - In particular I am looking for a tool in Python that allows me to create arbitrarily structured ...
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0answers
51 views

graphical methods / deep architectures for collaborative filtering

Having read "Restricted Boltzmann Machines for Collaborative Filtering" (Salakhutdinov et. al. 2007), I'm wondering if there has been any follow-up work on applying graphical and/or deep architectures ...
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0answers
31 views

How to run two motion plots together in R? [closed]

I'm doing a real recreation of the annual tree growth from tree-ring measurements, and I have many problems working with graphs and their margins. I have done the two graphs separately and these work ...
1
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1answer
44 views

normalization in max-sum algorithm (loopy belief propagation)

I was implementing the max sum algorithm for a general graph (i.e., the ones with a cycle). I updated the messages as indicated in ...
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0answers
14 views

Why calculating partition function is important in graphical models?

Consider a graphical model as specified at [1] Eq (1) and (2). Why calculating the partition function is important in graphical models? Why do we need it? I was under the impression that people ...
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0answers
54 views

Difference between fuzzy graphical network , Markov model and Bayesian network

Referring to this answer Difference between Bayesian network and neural network and causal inference, I have come across other graphical models (1) Fuzzy Cognitive Map and (2) Neuro-Fuzzy (3) Fuzzy ...
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2answers
57 views

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 ...
0
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1answer
20 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
216 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
14 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
12 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
16 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
18 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 $R$: ...
3
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1answer
119 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 ...
0
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1answer
31 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? ...
0
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1answer
39 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
45 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 ...
0
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1answer
25 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
47 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
25 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
131 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 ...
1
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2answers
93 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
14 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 ...
1
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0answers
132 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 ...
3
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1answer
94 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
69 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 ...
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2answers
176 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 ...