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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16 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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26 views

Using BUGS/JAGS for Gibbs sampling for inference in a (discrete) Bayesian Network for estimating conditional probability tables

My goal is to use BUGS (more accurately, JAGS) to perform Gibbs sampling as a process for parameter estimation in Bayesian networks that only have discrete random variables. I am using the following ...
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16 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
33 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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22 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
47 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. ...
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1answer
49 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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7 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
604 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 ...
3
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46 views
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8 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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16 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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11 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
22 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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55 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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13 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
43 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 ...
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1answer
32 views

normalization constant for categorical distribution as exponential family

Let r.v. $X$ has categorical distribution. We can represent its pmf as $f(x\mid\vec{p})=\Pi_{i=1}^{K}p_i^{I[x=i]}=\exp[\sum_{i=1}^{K}I[x=i]\ln p_i]$, there is no explicit normalization constant ...
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22 views

A question on notation in variational message passing

This paper introduces variational message passing. Formula (8) is based on Fig 1. Formula (a) is $\ln Q^*_j(H_j)=\langle\ln P(H_j\mid\vec{pa_j})\rangle_{\sim Q(H_j)}+\sum_{k\in ch_j}\langle\ln ...
0
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0answers
30 views

How to model the relation between two variables based on other common relations?

I am trying to model an inference problem, but it doesn't seem to readily fit with the algorithms we usually hear about. I am hoping that I have missed something, and someone hear can point out that ...
3
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1answer
53 views

Predict user behaviour with constantly changing input variables

How to work on building an engine for a website wherein we want to score/recommend stuff based on her different activities, like the music she rated or the article she read, or whether email ...
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0answers
19 views

What is meant by “weakly dependent” on p. 64 of Bayesian Reasoning and Machine Learning?

I'm reading Bayesian Reasoning and Machine Learning (here is a free online copy). On page 64, beginning with equation (4.2.20), Barber says Our aim is to show that a distribution of the form ...
2
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1answer
77 views

How to represent distribution dependencies in Bayesian graphical models?

In a Bayesian graphical model, suppose that we have a random variable $B$ whose parent is the random variable $A$. So there is an arrow from $A$ to $B$, and this means that the joint distribution is ...
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1answer
30 views

What is the predictive distribution of Bayesian supervised Learning? (rigorous argument)

I was trying to understand the posterior predictive distribution for any supervised predictor (by that I mean any classifier or regression predictor $f$). The exact equation I am unsure of is: $$ ...
2
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1answer
43 views

What is the relationship between graphical models (such as in the Koller book) and the type of analysis you can do with pyMC?

I'm somewhat familiar with the contents of the Koller Probabilistic Graphical Models book (followed some of the Coursera course but didn't have time to do all the homework). I'd recently had the ...
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19 views

Finding conditional distribution in graphical model (undirected graph)

Given that I have a graph $G=(V,E)$ and a set of random variables $X:=(X_v: v\in V)$. I also have the joint distribution of $X\sim p(x)$. What are the ways to find out the conditional distribution of ...
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0answers
23 views

What data generating process can't be expressed as a probabilistic graphical model?

I've been reading a bit on probabilistic programming, and one of the main claims is that it is more expressive than graphical models. As the representational capacity of PPLs is anything that can be ...
0
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0answers
21 views

Unsupervised Learning in Markov Random Fields

Is there any algorithm to estimate the parameters of a Markov Random Field (MRF) model, by observing unlabeled data (Unsupervised Learning)? By "unlabeled data", I mean the state of each node in MRF ...
0
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0answers
22 views

Dealing with constraints in probabilistic graphical models

Suppose I have a graphical model with i.i.d. $\Lambda_i \sim exp(\lambda),\ \ i = 1,...,n$, and $\bf{\Lambda} = \sum_{i=1}^{n}\Lambda_i$. Imagine that that these $n$ lambda and this capital ...
2
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0answers
103 views

Deep learning: representation learning or classification?

For classification, I have often heard about deep learning / deep neural networks as a form of representation learning. I am confused as to what "representation learning" means in this context. Which ...
1
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1answer
52 views

D-separation in a Bayesian Network [closed]

The above question asks to see if Radio is D-Separated from Petrol given certain evidence. For evidence (i), why would this mean D-Separation? If Battery is true, we have a inactive triple. If ...
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16 views

Discretizing Conditional Probability Density Function of varying dimensions

I hope I can explain this well without too big a wall of text. I have a conditional probability density (CPD) function of arbitrary shape that varies in the number of dimensions depending on the ...
0
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46 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 ...
3
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2answers
46 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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10 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
25 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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15 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 ...
4
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1answer
91 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
67 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) ...
0
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0answers
12 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 ...
0
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0answers
25 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, $P(X_1,X_2,...,X_n) = \prod_{i=1}^n P(X_i|Cond(X_i))$ ...
0
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0answers
30 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
21 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 ...
4
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2answers
352 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
133 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 ...
1
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1answer
66 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 ...
3
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1answer
51 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 $z_{t}$, ...
1
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0answers
48 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 ...
0
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0answers
18 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 ...