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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3 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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50 views
+50

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 ...
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27 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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12 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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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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17 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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5 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
41 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
34 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 ...
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2answers
43 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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24 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
34 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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87 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
61 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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24 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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7 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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11 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
65 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 ...
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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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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
89 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
16 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 ...
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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
77 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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0answers
5 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
46 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
162 views
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31 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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10 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
50 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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58 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 ...
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1answer
34 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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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 ...
0
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1answer
45 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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84 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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116 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 ...
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0answers
56 views

What is relation between RBM and DBN? [duplicate]

What is relation between Restricted Boltzmann Machine, Deep Belief Networks, Deep Boltzmann Machines? Are they related to deep learning or to graphical models(Probabilistic Graphical Models)? ...
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29 views

Belief propagation Message Passing

I'm reading Nowozin thesis, and i'm a bit confused on how the message passing in the belief propagation are defined in a factor graph such as the one below: The ...
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0answers
22 views

Compute all paths in graph that has multiple inputs and one output

I want to compute all the paths in directed acyclic graph from multiple inputs (x1, .., xn) to one output. The graph has the same depth which d and the inputs come to the graph at the same time (the ...
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1answer
94 views

Generative-Discriminative pairs: Naive Bayes and Logistic Regression

I'm trying to understand the something written in this paper. At the bottom of page 7: This means that if the naive Bayes model $$ p(y,\mathbf{x}) = p(y) \prod_k p(x_k|y) $$ is trained to ...
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40 views

Is every Conditional Random Field simply a Markov Random Field with restricted structure?

If I have a graph $H$ with nodes $\mathbf{X} \cup \mathbf{Y}$, and a set of factors $\phi_1(D_1), \ldots, \phi_k(D_k)$, where for each $i$, $D_i \not\subset X$, then doesn't this define both a MRF and ...