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14 views

Intuition for understanding latent variables

I am having difficulty understanding and proving the GMM/LDA model, for I think I do not really understand latent variables. To be more exact, I cannot understand the latent variable z_k(categorical ...
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2answers
24 views

Names for some canonical directed causal graphs/illustrations of some canonical causal relationships?

Certain names are used for structures or node relationships that appear in acyclic, directed graphs (DAGs). Often these DAGs are interpreted causally. Here's a partial list for relationships that ...
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0answers
6 views

Probabilistc Inference for Hybrid Models

I am looking for a library that can solve (calculate the MAP estimate) of the variables in a probable graphical model in which some variables are discrete and some are continuous. I understand that ...
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0answers
15 views

How do v-structures in graphical models reflect real world data?

I understand d-separation and how v-structures in graphical models work. What i don't understand is how they relate to real world multivariate data. I don't see how v-structures can be separated from ...
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0answers
7 views

Need a statistic for comparing “strength” of Markov blankets in a Bayesian network

Working with Bayesian networks. I take a given network structure and fit its parameters on data. I am looking for a statistic based on those parameter estimates that allows me to compare Markov ...
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0answers
73 views

How to do inference over two steps in a graphical model simultaneously?

I have observed data $D$ about a physical object described by $M$. I would like to determine the posterior distribution of $M$ given $D$, or $p(M|D)$. Now I can't infer this directly because unknown ...
3
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0answers
61 views

Missing values with Community structure in networks?

Is there a way to predict Missing values with Community structure in networks? I have a data set with a couple dozen variables, such as age, level of education, self-assessed (via a Likert scale) ...
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0answers
8 views

Number of parameters for Directed Graphical Models (with Latent variables)

I was looking through "Machine Learning :a probabilistic perspective" by Kevin Murphy and was confused about parameters in Directed Graphical Models(DGM), discrete probability distributions in ...
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0answers
17 views

Factorization of probability distribution and its Bayesian Network

My question is if we have a distribution $P$ that can be factorized into cond. distributions, can we model it with Bayesian Networks? I mean, $P(X_1,X_2,...,X_n) = \prod_{i=1}^n P(X_i|Cond(X_i))$ ...
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0answers
20 views

BN2O Network Question

Hi I was trying to solve Exercise. 5.13 from Probabilistic Graphical Models by Koller and Friedman but not able to fathom how to proceed with the solution. Here is the question as mentioned in the ...
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0answers
12 views

Bayesian Graphical Network with Time Series

I am not so strong with Time Series so I thought I'd ask here. I am working on a Bayesian Graphical Model where I have observations recorded once a day. So obviously, there is some influence of time ...
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2answers
106 views

Data Visualization: Alternatives to Choropleth maps for spatial data and statistical graphics

This question is about data visualization and statistical graphics. I have been trying to present statistical data in map. The data is at county level in the US and also at time state level. My data ...
3
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1answer
100 views

Distinguish an ARMA and an ARIMA model graphically

I'm currently analyzing some time series data and I need to know how to distinguish an ARMA model from an ARIMA model just by looking at the auto-correlation function and partial auto-correlation ...
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1answer
56 views

Specify conditional probability of a continuous node given a continuous node as its parent

This question is essentially same as this one. The question is: How do you calculate conditional probability of a node in Bayesian network when it has a continuous node as a parent? However, I cannot ...
2
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0answers
25 views

Kalman filter with input control noise?

assume we have a standard Kalman filter with input controls, following wikipedia notation (http://en.wikipedia.org/wiki/Kalman_filter) where the latent state is $x_{t}$ and the observation is $z_{t}$, ...
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0answers
38 views

Learn the bayes net structure with latent variables while testing (but observed while training)

I want to use Bayesian network for data which has 5 types of variables which are inter-dependent on each other. Out of that, 1 variable is observed only while training but it is unavailable during ...
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0answers
10 views

Number of parameters in multinomial logistic regression

In Chapter 10 (Directed graphical models) of Murphy's Machine Learning text, the author claims that multinomial logistic regression has $O(K^2 V^2)$ parameters, where $K$ is the number of discrete ...
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1answer
55 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...
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1answer
84 views

Examples of marginal independence, conditional dependence

I am interested in finding "real-world" examples of when variables might exhibit marginal independence but are conditionally dependent given some other variable. It seems to me that the converse ...
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0answers
119 views

What distribution is the expectation taken over in the total expected pay-off in reinforcement learning? Is it consistent with Bellman's Equation?

I was following the reinforcement learning lecture notes on CS229: http://cs229.stanford.edu/notes/cs229-notes12.pdf on page 3 they have the equation for the expectation of the total pay-off: $$ ...
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0answers
23 views

Flow of influence in a v-structure for Probabilistic Graphical Models

I'm not very sure I understand why an observed v-structure have different flow of influence behaviour for a directed and an undirected graph. What is the intuition behind the actual definition for ...
2
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0answers
94 views

Minimizing KL divergence from a given distribution, according to a graph

Given $n$ discrete random variables $X_1,...,X_n$, a distribution $p$ on $X=(X_1,...,X_d)$ and a DAG (Directed Acyclic Graph) $G$ on $\{1,...,d\}$, which is the distribution $q$ factorizing with $G$ ...
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0answers
15 views

Using Bayesian Graphical Models to reconstruct duplicated damaged data

I am a computer science student specialised in machine learning. Recently I fell in love with Probabilistic Graphical Models (and probabilistic programming) because of the flexibility to focus on ...
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1answer
49 views

Mean field variational inference

In Chris Bishop PRML book p.465 equation 10.6, the derivation doesn't explain why exactly the term $\int q_j ln(q_j) dz_j $ was generated, is not that term supposed to be multiplied by constant, did ...
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0answers
15 views

How to Mine Tree Structures?

To learn similarities/differences between different instances (that are in the form of tree), what are the suitable methods/approaches? I know kernel methods and particularly tree kernels, but would ...
3
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1answer
56 views

How do you find mathematical expressions for the posterior marginals i.e. $P(x_n|y_0, … , y_n)$ in an HMM?

My goal is to find closed form equations for posterior marginals $P(x_n|y_0, ... , y_n)$ in a general HMM. I was told that we can calculate it exactly via BP (belief propagation, thought not sure how ...
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0answers
48 views

Comparing Factorie and Figaro languages for Statistical Relational Learning

I am looking to implement statistical relational learning, preferably in a modern programming language, and came across Factorie and Figaro for Scala. But most resources online that compare these are ...
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1answer
31 views

Message passing (belief propagation) in practice - observed variables

In a graphical model with variables with continuous distriubtions, and some observed variables, how can I compute the messages to be passed? I know the messages but I don't know how to implement it? ...
1
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1answer
54 views

Probabilistic Logical Graphical models like Markov Logic networks etc

I can't quite get a grasp of how and where these Probabilistic Logical Graphical Models (or PLGM or Statistical Relational Learning Models) score better than ordinary Probabilistic Graphical ...
1
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1answer
49 views

Does a Bayesian network include the CPTs?

I'm preparing slides for a lecture, and I require some guidance. I'm only talking about discrete variables. How would you formally define the concepts surrounding Bayesian networks? A Bayesian ...
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0answers
22 views

Best way to graph probabilities of feature vectors

I have a lot of feature vectors in the form of: v1=[x0, x1, x2, x3, x4] where x0, x1, and x2 can take binary values. either 0 or 1 x3 and x4 can take values from 0 up to 9 I have a lot of vectors ...
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0answers
51 views

stochastic network optimization

I'd like to optimize the flow of materials through a network. There are vertices (i.e. physical locations) and edges (i.e. links between the physical locations). Inputs: locations transactional ...
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0answers
11 views

Why do chordal graphs not lose conditional independences when its transformed from undirected to directed to factor graphs and around?

When chordal graphs are used to model probability distributions, why is it that they do not lose conditional independences when its transformed from a undirected to a directed to a factor graph and ...
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0answers
15 views

Why are chordal graphs special for inference in the context of Probabilistic graphical model?

I was trying to make a list of the reasons of why chordal graphs are important or interesting in the context of inference and probabilistic graphical models. Some of the reasons I have so far are: ...
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0answers
37 views

Efficient algorithm to enumerate all member DAGs of a Markov equivalence class

I'm working on a research project involving Bayesian networks. BNs are directed acyclic graphs (DAGs) used to compactly represent joint distributions of variables. In many cases, multiple DAGs can ...
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0answers
22 views

When would Probabilistic Graphical Model be more useful compared to other commonly used models?

When would PGMs be better compared to other classification algos like DT, or LR? I see that it will be better if there are relationships / dependencies between the features. Are there any other ...
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2answers
35 views

Factor graph vs Factor graphical model

In inference we use the terms undirected graphical models and directed graphical models. Why do we say factor graph instead of factor graphical models?
2
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1answer
60 views

How to perform Cross-Validation for glasso to select lambda in R

I am using glasso for variable selection. To get the best possible value of lambda cross validation is recommended. However, I am not able to find how to perform cross validation for glasso in R. ...
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2answers
71 views

What is the name of this type of tree / graph / representation?

I have come across a tree like way to organize variables and I wonder if anybody knows the name. A colleague thinks it has a "Japanese sounding name" (sorry by no mean I wish to be derogatory). So ...
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1answer
46 views

An example of r.v.s such that their distribution has more (conditional) independencies than their directed graphical model

I was trying to form an example where I had 3 r.v.s such that the distribution describing them had more conditional independencies or independencies than the directed graphical model corresponding to ...
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1answer
58 views

How does explaining away cause problems for learning?

In one of his lectures Geoff Hinton explains that a big problem of sigmoid belief nets is the explaining away phenomenon. I didn't fully understand this. I see that the induced width of the graph ...
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0answers
155 views

How to interpret residual vs fitted values plot with clustered points

I am performing a multiple linear regression and I have a plot of the my first two explanatory variables vs the residuals and also a plot with the residuals vs the fitted values. I am not quite sure ...
0
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1answer
48 views

Question of unary term (data term) of the graph cut method

I am trying to apply graph cut method for my segmentation task. I found some example codes at Graph_Cut_Demo. Part of the codes are showing below ...
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1answer
48 views

In Probabilistic Graphical Models, what does it mean that r.v. X influences r.v Y?

I wanted to pin down what the intuitive phrase: r.v. X influences r.v. Y as precisely and as rigorously as I could, and wanted to check if my interpretation was correct and complete with the ...
0
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1answer
60 views

Why do we need undirected (Markov) graphical models?

I understand the modular nature of directed models, and that each node captures a conditional probability. But why do we need undirected models? As far as I can see they lack intuition in that the ...
1
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1answer
26 views

Gaussian MRF/Markov Network: the zero precision = no connection?

Gaussian MRF in Gaussian information form: edge potential: $exp(\frac{-1}{2} y_s\Lambda_{st} y_t)$ node potential: $exp(\frac{-1}{2} y_t\Lambda_{t} y_t+\eta_ty_t)$ Why: precision parameter ...
2
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1answer
62 views

What is the role/purpose of hidden variables in graphical models?

Is there a formal treatment of the role/power of latent/hidden variables in graphical models and other machine learning models (e.g., structural equation models)? For example, the Restricted Boltzman ...
0
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1answer
123 views

about the definition of bayesian network

In this PDF http://people.csail.mit.edu/yks/documents/classes/mlbook/pdf/chapter2.pdf page 5 says: Given a set of functions $f(x_i,pa(x_i))$ non-negative and sum to 1, we define a joint ...
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1answer
33 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 ...
0
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1answer
47 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 $P(A,B,C)=P(A|C)P(B|C)P(C)$ ...