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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6 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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15 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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3 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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4 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
53 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 ...
3
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0answers
339 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
39 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
12 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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46 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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12 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
45 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
4 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
11 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
13 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
52 views
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21 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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7 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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44 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
8 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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0answers
52 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
30 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
16 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
30 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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72 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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61 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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54 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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25 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
15 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
80 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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0answers
28 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 ...
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33 views

Why is the posterior the stationary distribution of a Gibbs chain?

I'm having trouble understanding the setup here. I'm follow Probabilistic Graphical Models by Koller and Friedman. They say that we wish to generate samples from the posterior distribution ...
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27 views

Incorporating letter transition model into linear-chain CRF

Suppose I have a linear-chain CRF for e.g. handwriting recognition, $$ p(\mathbf{y}\mid\mathbf{X}) = \frac{1}{Z_\mathbf{X}}\exp\left(\sum_{j=1}^m\mathbf{w}_{y_j}^T\mathbf{x}_j + ...
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15 views

Odds Ratios and Seasonal Pattern

I want to interpret Odds ratios with weather temperature through a line or any kind of a graphic. Do I need to re-scale Odds and temperature? What do you recommend?
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1answer
66 views

Multinomial Naive Bayes is not Multinomial in text classification

According to Wiki, the Multinomial Naive Bayes's conditional distribution is: $$p(\mathbf{x} \vert C=k) = \text{Multinomial}(n,\mathbf p_k) = \frac{(\sum_d x_d)!}{\prod_d x_d !} \prod_d ...
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49 views

How to combine posterior probabilities from different classifiers?

I have four different images $(X_1, X_2, X_3, X_4)$ which I classify with four different discriminate probabilistic models (discriminative classifiers) to obtain posterior probabilities of a pixel ...
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3answers
59 views

How to show that stability is improved when using bagging in an unsupervised context?

I have a data set of 200 observations and around 10 continuous variables. I would like to build a graphical model to study dependencies between variables. Unfortunately, my data is not very stable. ...
3
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1answer
126 views

What is the point of graphical models?

I spent the day learning about the bnlearn package in R only to discover that Bayesian models do not work with undirected graphs. I'm trying to learn about the Markov Random Field Network, and so far ...
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0answers
10 views

automatic graph/network from data

This is meant to be a followup to this question: Approach and example of graph clustering in "R" This is my personal study, but not part of a class. I do not know where to start looking for ...
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3answers
703 views

Where's the graph theory in graphical models?

Introductions to graphical models describe them as "... a marriage between graph theory and probability theory." I get the probability theory part but I have trouble understanding where exactly graph ...
4
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1answer
101 views

What's the difference between a Markov Random Field and a Conditional Random Field?

If I fix the values of the observed nodes of an MRF, does it become a CRF?
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12 views

How to compute Potentials in Junction Tree from Set Chain using LS also?

I was going through the original LS algorithm paper. I was not able to compute the potentials from the set chains shown on the page 171 (Table 3). Apart from that, I was able to compute all the ...
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36 views

Latent SVM / Struct (output) SVM / Graphical Models(Markov random fields) relation?

What is the difference between Latent SVM and Struct (output) SVM? these terms often occure related to Deformable Part Model. For example in this implementation https://github.com/rbgirshick/voc-dpm ...
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22 views

Material on plate notation of bayesian hidden markov model

Does any one know some materials on plate notation of Bayesian Hidden Markov Model? Say, given multiple observed sequences, how to infer the posterior distribution of the parameters, and the ...
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0answers
23 views

Forming relational graph for a noun by mining web

I want to find a relational/relevance graph for any noun, by mining the web. For example the graph of sushi may be like : sushi -> fish(seafood),rice-> Japanese -> Food. PS : I may be missing some ...
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0answers
59 views

How can I infer the value of multiple dependent continuous random variables in conjunction with discriminative learners?

I have 2 continuous random variables V1, V2 which are dependent. I want to infer each of their values based on: The value of ...
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15 views

How generic are junction tree distributions?

A junction tree probability distribution takes the following form: $P(X) = \frac{\prod_{c\in C}P(X_c)}{\prod_{s \in S}P(X_s)^{\nu_s - 1}}$ where $C$ is the set of clusters, $S$ is the set of ...
2
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0answers
72 views

Regularization parameter to generate inverse covariance matrix

My data consists of approx. 5 Million binary strings (n) and every string is 2788 characters long. My goal is to find out if position i is correlated with position j. I approximated a covariance ...