Used for statistical models expressed via graphs, causal or not. ("graph" here as in graph theory). See https://en.wikipedia.org/wiki/Graphical_model

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21 views

what's the period for state in Markov chain?

I have two questions: 1.What's the period for state A or does A have a period? Is there a specified name for those states like state A who gives all to other state and won't be returned back? Are B ...
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13 views

Directed graph algorithm

Say I have the following graph: ...
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1answer
303 views

Looking for proof of conditional dependence, when the conditioning variables are linearly related

Suppose we have three random variables, $X$, $Y_1$, and $e$ (for error). Variable $e$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture ...
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4 views

Analysis to show averages for more each year of exposure to a treatment does not shift the averages toward an expected average

I apologize if there is appropriate terminology I should be using in my description that I do not know. Hopefully the way I've made my question generic for the sake of preserving the integrity of my ...
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1answer
24 views

Prediction of vertex scores in a bipartite graphs

I have a bipartite graph with two sets, A and M, of nodes. Every vertex in M has a score associated with it. I have two tasks: To every vertex a in A, I have to assign a score based on the scores of ...
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6 views

How does loop belief propagation differ from variational message passing?

I'm reading Yedidia et al.'s paper and Winn et al.'s paper. The two approaches (LBP and VMP) are pretty similar to each other: Eq (5,7) in Yedidia are similar to Eq (19,20) in Winn. They both update ...
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78 views

Can (loopy) belief propagation be used to learn from a data set?

I'm trying to expand my experience with restricted Boltzmann machines to a more general class of graphical models and currently learning about belief propagation using message passing algorithms. One ...
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6 views

About the evaluation of covariance of linear Gaussian model in PRML

Section 8.1.4 of Pattern Recognition and Machine Learning introduces the linear Gaussian model where each node has distribution $$ p(x_i \big|pa_i) = \mathcal{N}\left ( x_i \Bigg| \sum_{j\in pa_i}w_{...
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55 views

Probabilistic Graphical Model - Modelling a Bayesian Network on Real Life Data

Recently, I have started studying about Probabilistic Graphical Models (PGMs). While the examples provided in the textbook essentially convey the message of what and how things are happening, I am ...
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21 views

Specifying conditional probability tables for nodes with large number of Parents in a Bayesian Belief Network

What is the ideal way to specify the conditional probability tables for belief propagation in a Bayesian Network, for nodes with large number of parents? I am currently using gRain package in R. But ...
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25 views

Data structure for general MRF

I want to implement the junction tree algorithm for a general MRF. What data structure should one use to represent an arbitrary MRF? Storing the underlying undirected graph is simple but what is the ...
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0answers
32 views

General approach to learning a graphical model

Lately I've been reading a lot about inference and learning in probabilistic graphical models. I mostly understand specific methods (e.g. junction tree, message passing, MCMC; gradient descent, ...
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22 views

Best approach for calculating confidence score (p-value) - for Bayes models

This is a generic question on the best approach for giving a p-value to a "most likely" solution given by a graphical Bayes model. I am building a graphical model in Stan, for finding the most likely ...
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6 views

What graphical model formalism should I use to model state-space model?

I have a state-space model of a greenhouse control model that I'd like to transform into a probabilistic graphical model (to make it easier for non-technical managers to understand relationships among ...
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1answer
49 views

Bayesian inference when observed variable contains uncertainty

I have a very simple graphical model to describe the relationship between two categorical variables $c \in \{0,1\}$ and $l \in \{A,B,C\}$: $$c \rightarrow l$$ I know all the conditional ...
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1answer
35 views

Confusion regarding terminology related to the junction tree algorithm

As far as I understand, the "junction tree algorithm" is a general inference framework which roughly consists of the four steps 1) triangulate, 2) construct junction tree, 3) propagate probabilities/...
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2answers
46 views

Book recommendation for probabilistic networks

I'm a student interested in learning about probabilistic networks — Bayesian Networks Markov models etc. I have a good background in probability, statistics and Markov chains. Some good ...
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30 views

Regular weighted average vs. Kernel Weighted average

I am somewhat familiar with using kernels for density estimation (i.e. KDE), but not so much with using them as weights to calculate weighted averages. I am looking for some intuition on the latter. ...
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1answer
37 views

Conditional Independence in Graph

I have a factor graph like following: How can I check if Q1 and Q2 are independent given the value of g1? More specifically can someone explain following in easy way? It would be great if you can ...
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0answers
8 views

How to deal with the factors when moralize a directed network?

Consider we have a simple V-Structure Bayesian network which we use it for model some random variables. in other words we have a distribution $P(C|A,B)$ where A and B are the parents of C in the ...
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97 views

Graphical LASSO Interpretation

I have a conceptual question about graphical LASSO interpretation. I have been using the huge package in R to estimate an association network for a matrix of node ...
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1answer
71 views

glasso- Assumptions of Meinhausen-Buhlmann approximation?

First off, This is not an R question - it is a conceptual question, so there is no need to perform any code. Problem: I'm trying to invert a large dimensional covariance matrix of p features. For ...
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1answer
15 views

What is the type of precision in the prior distribution over user's and item's latent factors in PMF?

I am trying to implement the pmf model in stan. paper In this model, there are two prior normal distribution over the latent factors of users and items: $U_i$ ~ $normal(0,\sigma^2I$) And it is said ...
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26 views

Which machine learning approach/algorithm do I choose for path validation?

I apologize for lack of terminology, I'm no computer scientist. I have a problem of validating paths in a directed graph with complex nodes. The full description is the following: I have a decent ...
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0answers
9 views

Is there any reason to use MRFs instead of CRFs for image segmentation?

Markov Random Fields (MRFs) are probabilistic, graphical, undirected models. As far as I understood it, image segmentation with MRFs works by making one random variable per feature (typically pixel) ...
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13 views

Looking for algorithm that is a discounted min-cost-maximum-flow calculation

In terms of graph theory I am very familiar with minimum-cost maximum flow, connectivity and ...
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1answer
69 views

With complete data and a factored prior, the posterior also factors

In the second paragraph of Section 11.3 in Machine Learning A Probabilistic Perspective, the author concisely summarizes Section 10.4.2 by saying that for the standard bayesian model $$P({\boldsymbol\...
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3 views

Is linearity an issue for structural learners?

I have a matrix of z-scores. Let's say these z-scores are trustworthy and that the assumption that the data fits a normal distribution has been tested for our data. I have a large feature space (>...
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0answers
1k views

Dealing with auxiliary random variables for Mean-Field Variational Inference in Bayesian Poisson factorization

I am studying as a part of a class assignment a recent paper on Poisson factorization. Some points of the paper regarding the usage of some auxiliary variables are not clear to me. I would like to ...
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2answers
117 views

R - glasso very slow for high feature space

all, I'm doing a graphical lasso in order to approximate the inverse of the covariance matrix of a 1200 (p-features) by 100 or so (n observations) data matrix. Basically, I'm inverting a 1200 x 1200 ...
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1answer
17 views

Using Clustering Coefficient to Improve Naive Bayesian Classifier

I am new at statistics and ML. Due to my lack of theoretical background I was wandering if does it make sense to combine NBC and CC. I am participating to the kaggle competition https://www.kaggle.com/...
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8 views

Visualization for discrete integers on a non-fixed domain

So I am wondering if someone can give some input on how I might go creating some good visualization for this data set I have. Lets say that I am allocating buffers in some code that I have and that ...
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47 views

How to predict with the known information in an undirected graph

Protein-protein interaction networks are known. It is an undirected graph. Each row of the networks is like this (Protein 2 - Protein 6), and It represents the interaction between Protein 2 and ...
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13 views

What are the values of output g_i in Bengio's paper “Taking on the Curse of Dimensionality in Joint Distributions Using Neural Networks”

Figure 2 of Bengio's paper "Taking on the Curse of Dimensionality in Joint Distributions Using Neural Networks" http://www.iro.umontreal.ca/~lisa/pointeurs/jdm.pdf describes a neural network ...
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1answer
101 views

Markov Cluster Algorithm transition matrix

I am reading the notes on Markov Cluster Algorithm by Kathy Macropol (http://www.cs.ucsb.edu/~xyan/classes/CS595D-2009winter/MCL_Presentation2.pdf) On slide 14/46 the author talks about inflation and ...
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6 views

Sequence tagging with additional structure

I am looking for pointers (papers, algorithms etc) for learning models for sequence tagging but which allow for additional structure. Consider Part of Speech Tagging, I could train a CRF which would ...
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0answers
69 views

Create a precision matrix and get desired covariance matrix

I am trying to build a Gaussian graphical model for a simulation. I want to achieve the following: Simulate an undirected graph structure (Markov network). Take nodes as variables and edges as ...
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0answers
15 views

Is it possible that maximal probabilities in hidden markov model are same for all sates?

I developed forward/backward algorithm for calculating probabilities for each state in hidden markov model and I got that maximal probabilities are the same in final probability matrix. This is data ...
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1answer
193 views
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40 views

Probabilistic models for sales forecasting on irregular intervals

I'm working on a very similar problem to the one presented here by @Ivan Dimitrov. The task is to predict how many products will be sold in a given time interval, knowning the past sales (which are ...
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11 views

Can two configurations (values) of sets of variables be independent, as opposed to two sets of variables?

I've been having a discussion about the validity of this idea, which seems to have originated from the definition of conditional independence found in the book "Probabilistic Graphical Models" by ...
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0answers
53 views

EdgeRank for eCommerce product feed

I am running my eCommerce store with around 1000 products with 10 categories. I want to show these products in feeds. But there are lots of products so its very complex to define priority list for ...
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0answers
12 views

Representing the joint distribution of a cyclic directed graph with an undirected model

Are there any directed cyclic graphs whose joint distributions cannot be represented by an undirected graph (assuming no limits on connectivity)?
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60 views

How to get a probability distribution by combining multiple individual distributions

I want to classify some data, but I can only observe some of that data at any one time. Unfortunately, there is no trivial way of combining multiple observations into one single form. For each of ...
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41 views

Modeling a Classification Problem with an Undirected Graphical Model

I have an undirected graphical model problem which I'm looking for some help on. So, the goal is to perform multivariate classification: based on a set of observations, I want to predict the correct ...
1
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1answer
37 views

How can I solve this graphical model?

I have a classification problem, with the following structure. There is a fully-connected graph, and each node needs be assigned a class label. Every pair of nodes in the graph has a probability ...
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0answers
19 views

How to do inference in (undirected) triangular graphical network?

I have dataset of sequences where every element of a sequence is a vector. The goal is to classify entire sequences into $K$ classes. The important part is that the sequence, not the elements, get the ...
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1answer
50 views

Counting non-reduntant parameters in probabilistic graphical models

Let's say we have the following problem from this book: Consider a very simple medical diagnosis setting, where we focus on two diseases — flu and hayfever; these are not mutually exclusive, as ...
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93 views

Model for supervised learning on graphs with varying structure

Colorization problem is considered. I have a training set of unordered graphs (images) with varying number of vertices and edges (color regions and adjacency between them, resp.). A fixed number ...
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144 views

Graphical lasso numerical problem (not SPD matrix result)

I am trying to apply glasso on a very simple as well as sparse dataset made by 60+ features and 30k+ observations. Here you can find it in a csv format, if you are ...