# Tag Info

Accepted

### Strong ignorability: confusion on the relationship between outcomes and treatment

I'll try to break it down a bit.. I think most of the confusion when studying potential outcomes (ie $Y_0,Y_1$) is to realize that $Y_0,Y_1$ are different than $Y$ without bringing in the covariate $X$...
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### Strong ignorability: confusion on the relationship between outcomes and treatment

Doubled has a fantastic answer, but I wanted to follow up with some intuitions that have helped me. First, think of potential outcomes as pre-treatment covariates. I know this seems like a strange ...
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### Explanation of I-map in a Markov/Bayesian network

From my understanding, if a DAG G is said to be the I-Map of probability distribution P, then every independence we can observe from G is encoded in P. Let's consider a simple example: Suppose ...
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Accepted

### What is probabilistic inference?

Probabilistic inference uses probabilistic models, i.e. models that describe the statistical problems in terms of probability theory and probability distributions. While statistics use probability ...
• 140k
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### Posterior distribution is impossible depending on which prior hyperparameters are used?

Let's work through the steps. To begin with we have $$p(\delta|\beta)\,p(\beta|\alpha)\,p(\alpha) ,$$ where \begin{align} p(\delta|\beta) &= \textsf{Bernoulli}(\delta|\...
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• 2,513

### Dynamic Bayesian Network library in Python

Try pgmpy. You can also create something on your own by using more generic tools for Graphical Probabilistic Models such as PyJaggs or Edward.
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### Why is computing the partition function expensive?

A probability distribution needs to integrate to one. 1 = \int_{x_1 \in \omega_1} \int_{x_2 \in \omega_2} \dots \int_{x_N \in \omega_N} \frac {1} {Z(\theta)} \underbrace{\prod_C \psi_C (\mathsf{x_C} ...
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### Inconsistencies between conditional probability calculations by hand and with pgmpy (Bayesian Graphical Models)

Seems as thought I figured this out. I'm posting it here just in case it helps someone. Well, it turns out that I wasn't making an error with my "by-hand" calculation, but it was indeed a problem ...
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### Given an adjacency matrix, how can we fit a covariance matrix based on that for a graph without running into a NON-positive definite matrix?

Here is an explanation which might provide some intuition about what is going on here. Suppose that in your graph you have three vertices where vertex 1 is adjacent to both vertices 2 and 3, but ...
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### What is the benefit of latent variables?

There are some elements to answer your question in Section 16.5 of the Deep Learning book by Ian Goodfellow and al.: A good generative model needs to accurately capture the distribution over the ...
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### Are all statistical models also causal models?

But is $Y = aX + cZ + e$ (as a regression model, not a math equation) also a causal model (albeit a "wrong" causal model)? If I manipulate $X$ it tells me what happens to $Y$. Doesn't it ...
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### Converse of pairwise Markov property

Who says we don't impose the converse? Pasting a block quote from these CMU 10-702 course notes as taught by Singh and Wasserman. The notes also comment on the complete graph. Pairwise Markov ...
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### List of graph layout algorithms

Spring-Electric Force Directed Placement algorithm as explained in Efficient and High Quality Force-Directed Graph Drawing by Yifan Hu. Buchheim Tree Drawing Spring/Repulsion Model Stress Majorization ...

### What is the difference between denoising autoencoder and contractive autoencoder?

No. The CAE tries to make the encoder (i.e. mapping from input to hidden layer) have the property of locality, i.e. small changes in input lead to small changes at hidden layer. This is a nice ...
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### Why do we interpret neural networks as graphical models?

As a compilation of my comments on the question: The definition of a graphical model is: "a probabilistic model for which a graph expresses the conditional dependence structure between random ...
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### How are graphical models "a subset of log-linear models"?

EDIT 1: The following, seemingly contradictory, quotes, are both found in the preface of Joe Whittaker's book Graphical Models in Applied Multivariate Statistics. ... the development of log-linear ...
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### Support vector machines (SVMs) are the zero temperature limit of logistic regression?

In the case of hard-margin SVM and linearly separable data, this is true. An intuitive sketch: The loss for each datapoint in logistic regression dies out almost as an exponential decay curve as you ...
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### What is the benefit of latent variables?

In many cases the data we observe depends on some hidden variables, that were not observed, or could not be observed. Knowing those variables would simplify our model, and in many cases we can get ...
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### Causality: Models, Reasoning, and Inference: Diagram Question

If you allow for bidirected edges, you can draw:
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### Isn't strong ignorability an incorrect assumption in complex causal structures?

I guess the answer to 1. is yes. As for 2., at least in social sciences, the idea behind this condition is that conditional on covariates -- i.e. observable pre-treatment characteristics -- the ...
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### Combination of variational methods and empirical Bayes

Generally, in empirical Bayes, you maximise the marginal likelihood (also called model evidence, or the normalising constant of the posterior) with respect to the hyperparameters and plug this ...
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### What's the difference between a Markov Random Field and a Conditional Random Field?

Let's contrast conditional inference under MRFs with modeling using a CRF, settling on definitions along the way, and then address the original question. MRF A Markov Random Field (MRF) with respect ...
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I disagree, there is nothing invalid about the so-called multinomial naive bayes model in this case. I think the confusion you are facing is because you are thinking $n$ is a parameter of the model ...