Intro I need an input file of 5 letter English words to train my Bayesian model to infer the stochastic dependency between each position. For instance, is the probability of a letter at the position 5 dependent on the probability of a letter at position 1 etc. At the end of the day, I want to train this Bayesian network in order to be able to solve the Wordle game. What is Wordle? It’s a game where you guess 5 …
I'm recently reading a paper about Scoring Mechanisms for Bayesian Networks. For the BDeu score, it appears that the maximum possible score of BDeu for Bayesian Network structure learning is zero. Does it mean that the best network is always the empty network?
I am trying to understand how you marginalise a joint distribution. In my case I have a fair coin, $P(C) = \frac12$ and a fair dice $P(D) = \frac16$. I am told I win a prize if I flip the coin and it lands on Tails and if the outcome of the dice $= 1$. I am told at least one of them is correct. $$Q = (\text{Coin = Tails or Dice} = 1)$$ $$W = (\text{Coin = Tails and …
I am a newbie with python and I am have facing an issue regarding the application of a Bayesian neural network to fit some data (x,y). I was able to realize a simple Bayesian fully connected neural network with TensorFlow probability def normal_exp(params): return tfd.Normal(loc=params[:,0:1], scale=tf.math.exp(params[:,1:2])) def NLL(y, distr): return -distr.log_prob(y) inputs = Input(shape=(1,)) hidden = Dense(200,activation="relu")(inputs) hidden = Dropout(0.1)(hidden, training=True) hidden = Dense(500,activation="relu")(hidden) hidden = Dropout(0.1)(hidden, training=True) hidden = Dense(500,activation="relu")(hidden) hidden = Dropout(0.1)(hidden, training=True) hidden = Dense(200,activation="relu")(hidden) hidden = …
I am currently reading the paper "Importance Weighted Autoencoders" and am having a hard time understanding something regarding the original Variational Autoencoder (VAE) as described here In the first paragraph of the third subsection the author wrote this: The VAE objective of Eqn. 3 heavily penalizes approximate posterior samples which fail to explain the observations. This places a strong constraint on the model, since the variational assumptions must be approximately satisfied in order to achieve a good lower bound. In …
Given a directed cyclic graph where vertex A is 'infected', and there are different infection probabilities between each node, what is the best approach towards computing the conditional probability $p(F|A)$? Do I have to transform it into asyclic graph and use bayesian net-methods? How would I proceed in order to design an algorithm for computing probabilities like this one, and are there approaches to this that are computationally feasible for very large networks?
(You might think that this is more a more appropriate question for MathEd, but they tell me that it's more appropriate here, so go figure...) I'm trying to use linked Bayes Boxes in a spreadsheet to model sequential Bayes. Take the following problem (apologies to those of you who actually know Minecraft! :-) p(night|creeper) = p(night)*p(creeper|night)/p(creeper) p(zombie|night) = p(zombie)*p(night|zombie)/p(night) Separately these are very easy to model. But I want to combine them to get p(zombie|creeper). I could, of course, just …
For a project, I need to create synthetic categorical data containing specific dependencies between the attributes. This can be done by sampling from a pre-defined Bayesian Network. After some exploration on the internet, I found that Pomegranate is a good package for Bayesian Networks, however - as far as I'm concerned - it seems unpossible to sample from such a pre-defined Bayesian Network. As an example, model.sample() raises a NotImplementedError (despite this solution says so). Does anyone know if there …
Are there any approaches to model prior information in sequential models? Such as in Sequence classification. For example, I have an input sequence [[Z, 0, 1], [Y, 1, 1]]. I need to classfy this into one of A, B,C, D, E. But from prior knowledge I know that if the input is Y, the outputs would most likely be one of A, B, or C. Hence, I can initialize the model such that there is 25% prob its A and …
I am trying to understand and use Bayesian Networks. I see that there are many references to Bayes in scikit-learn API, such as Naive Bayes, Bayesian regression, BayesianGaussianMixture etc. On searching for python packages for Bayesian network I find bayespy and pgmpy. Is it possible to work on Bayesian networks in scikit-learn?
I learned how to use libpgm in general for Bayesian inference and learning, but I do not understand if I can use it for learning with hidden variable. More precisely, I am trying to implement approach for Social Network Analysing from this paper: Modeling Relationship Strength in Online Social Networks. They suggest to use following architecture Here S(ij) represents vector of similarity between user i and j - Observed z(ij) is a hidden variable - relationship strength (Normal distribution regularised …
I'm attempting a BSTS model on a multivariate time series. I have a csv file with a bunch of columns and I want to predict one column while using a subset of the remaining columns as regressors. I've been pretty confused on how to do this and I'd appreciate any help. One thing I tried is to define a variable and assign it to the column I'm trying to predict. I only pick about three fourths of the values in …
Is there a comprehensive open source package (preferably in python or R) that can be used for anomaly detection in time series? There is a one class SVM package in scikit-learn but it is not for the time series data. I’m looking for more sophisticated packages that, for example, use Bayesian networks for anomaly detection.
I am learning about Markov Chain and Bayesian Nets. However at this point I am a bit confused about what types of problems are modelled with the two different models presented to us. From what I understand (mostly from the examples I have read) Markov Chains are being used to represent the change in a single type of variable over time. So for example a random variable X representing the weather. Let X = {sun, rain}. Then for a markov …
I have a regression GAM (General Additive Model) and I want to learn its epistemic uncertainty( the variance of my residuals or predictions as a function of my input). I have already used a bayesian approach to turn my GAM into a gaussian process so I can construct a covariance matrix but this approach is not scalable due to the high dimension of my problem. I am trying to use an approach that uses the current model as a black-box …
I am training a variational autoencoder and I am getting a loss-plot as follows: Rigt after epoch 224, val-loss overtakes train-loss and sort of getting bigger but at an extremely slow pace as you can notice. I trained for 300 epochs. Any opinion about the training. I don't think it is overfitting the data. But I want to be sure and hence seeking opinion from the data science community. Thanks.
I'm working my way through the Bayesian world. So far I've understood that the MLE or the MPA are point estimates, therefore using such models just outputs one specific value and not a distribution. Moreover, vanilla neural networks do in fact something like MLE, because minimizing the squared-loss or the cross-entropy is similar to finding parameters that maximize the likelihood. Furthermore, using neural networks with regularization is comparable to the MAP estimates, as the prior works like the penalty term …
I have the following Bayesian network: I'm having trouble understanding how to calculate some of the conditional probabilities between nodes, in particular when they are independent. For instance, how would you calculate P(C=true, G=true|H=false)? I'm aware that I have to use the Bayes rule and the conditional probability formula. How do you go about setting up the equations for each of these and do you use variable elimination for any of these?
On Bayesian Networks, Ghahramani (2001) says: A node is independent of its non-descendants given its parents. This point is fundamental enough that Ghahramani calls it the “semantics” of a Bayesian network. It is certainly useful, and it is simple enough to prove using d-separation. But his characterization suggests that the property should be even more primitive than something provable by d-separation. Overall, I feel that I am missing something. Is there a more primitive way to verify the statement than …