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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13
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2answers
373 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 ...
2
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0answers
34 views
0
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0answers
6 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 ...
0
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0answers
8 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 ...
0
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0answers
6 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 ...
0
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0answers
21 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 ...
0
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0answers
50 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 ...
0
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0answers
11 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
37 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 ...
0
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1answer
24 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 ...
1
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0answers
18 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
28 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
votes
1answer
50 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 ...
0
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0answers
18 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
votes
1answer
67 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 ...
1
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1answer
27 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
votes
1answer
38 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 ...
0
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0answers
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 ...
1
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0answers
21 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
16 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
19 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
votes
0answers
79 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
vote
1answer
48 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 ...
0
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0answers
15 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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0answers
40 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 ...
2
votes
2answers
37 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 ...
0
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0answers
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 ...
0
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0answers
22 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 ...
1
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0answers
11 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 ...
3
votes
1answer
82 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
votes
0answers
66 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
11 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
22 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
29 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 ...
0
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0answers
20 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
votes
2answers
281 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
votes
1answer
125 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
vote
1answer
61 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
votes
0answers
33 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
vote
0answers
45 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
votes
0answers
17 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 ...
0
votes
1answer
69 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 ...
3
votes
1answer
160 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 ...
0
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0answers
127 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: $$ ...
1
vote
0answers
26 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
votes
1answer
115 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 $G$ ...
2
votes
0answers
16 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 ...
1
vote
1answer
75 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 ...
1
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0answers
29 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
votes
1answer
59 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 ...