Bayesian Networks

How Bayesian Networks Are Superior in Understanding Effects of Variables


Bayes Nets (or Bayesian Networks) give remarkable results in determining the effects of many variables on an outcome. They typically perform strongly even in cases when other methods falter or fail. These networks have had relatively little use with business-related problems, although they have worked successfully for years in fields such as scientific research, public safety, aircraft guidance systems and national defense. Importantly, they often outperform regression, particularly in determining variables' effects. Regression is one of the most august multivariate methods, and among the most studied and applied.



This repository contains the Tensorflow implementation of the Bayesian GAN by Yunus Saatchi and Andrew Gordon Wilson. This paper will be appearing at NIPS 2017. In the Bayesian GAN we propose conditional posteriors for the generator and discriminator weights, and marginalize these posteriors through stochastic gradient Hamiltonian Monte Carlo. Key properties of the Bayesian approach to GANs include (1) accurate predictions on semi-supervised learning problems; (2) minimal intervention for good performance; (3) a probabilistic formulation for inference in response to adversarial feedback; (4) avoidance of mode collapse; and (5) a representation of multiple complementary generative and discriminative models for data, forming a probabilistic ensemble. We illustrate a multimodal posterior over the parameters of the generator.

Naive Bayes in Machine Learning – Towards Data Science


Bayes' theorem finds many uses in the probability theory and statistics. There's a micro chance that you have never heard about this theorem in your life. Turns out that this theorem has found its way into the world of machine learning, to form one of the highly decorated algorithms. In this article, we will learn all about the Naive Bayes Algorithm, along with its variations for different purposes in machine learning. As you might have guessed, this requires us to view things from a probabilistic point of view.

Algorithms Identify People with Suicidal Thoughts

IEEE Spectrum Robotics Channel

Mention strong words such as "death" or "praise" to someone who has suicidal thoughts and chances are the neurons in their brains activate in a totally different pattern than those of a non-suicidal person. That's what researchers at University of Pittsburgh and Carnegie Mellon University discovered, and trained algorithms to distinguish, using data from fMRI brain scans. The scientists published the findings of their small-scale study Monday in the journal Nature Human Behaviour. They hope to study a larger group of people and use the data to develop simple tests that doctors can use to more readily identify people at risk of suicide. Suicide is the second-leading cause of death among young adults, according to the U.S. Centers for Disease Control and Prevention.

AI - The present in the making


For many people, the concept of Artificial Intelligence (AI) is a thing of the future. It is the technology that has yet to be introduced. But Professor Jon Oberlander disagrees. He was quick to point out that AI is not in the future, it is now in the making. He began by mentioning Alexa, Amazon's star product.

Bayesian Decision Theory Made Ridiculously Simple · Statistics @ Home


The formal object that we use to do this goes by many names depending on the field: I will refer to it as a Loss function (\(\mathcal{L}\)) but the same general concept may be alternatively called a cost function, a utility function, an acquisition function, or any number of different things. The crucial idea is that this is a function that allows us to quantify how bad/good a given decision (\(a\)) is given some information (\(\theta\)). By convention I mean a real number (between \(-\infty\) and \( \infty\)). The crucial idea is that the loss function ties together our decision space (\(\mathcal{A}\)) and our information space (\(\Theta\)).

Chapter 1 : Supervised Learning and Naive Bayes Classification -- Part 1 (Theory)


Now, can you guess who is the sender for the content: "Wonderful Love." P(Fire Smoke) means how often there is fire when we see smoke. Naive Bayes classifier calculates the probabilities for every factor ( here in case of email example would be Alice and Bob for given input feature). In next part we shall use sklearn in Python and implement Naive Bayes classifier for labelling email to either as Spam or Ham.

Bayesian Estimation of Signal Detection Models, Part 1


First, we'll compute for each trial whether the participant's response was a hit, false alarm, correct rejection, or a miss. For a single subject, d' can be calculated as the difference of the standardized hit and false alarm rates (Stanislaw and Todorov 1999): Its inverse, \(\Phi {-1}\), converts a proportion (such as a hit rate or false alarm rate) into a z score. We can use R's proportion to z-score function (\(\Phi {-1}\)), qnorm(), to calculate each participant's d' and c from the counts of hits, false alarms, misses and correct rejections: This data frame now has point estimates of every participant's d' and c. The implied EVSDT model for participant 53 is shown in Figure 1. Figure 1: The equal variance Gaussian signal detection model for the first participant in the data, based on manual calculation of the parameter's point estimates.

Should we worry about rigged priors? A long discussion.


Due to publication bias, researcher biases, etc., effects found in prior studies may be highly inflated, right? Picking a prior distribution based on biased point estimates from the published literature, that's not a good justification. In particular, the leap from "statistical significance" to "the treatment works" is only valid when type M and type S errors are low--and any statement about these errors requires assumptions about effect size. So my point is that the classical inferences–the conclusion that the treatment works and the point estimate of the effect–are strongly based on assumptions which, in conventional reporting, are completely hidden.

Bayesian Learning for Statistical Classification – Stats and Bots


What is the probability that the next card drawn is worth ten points (is a ten or a face card) given that the previous card was also worth ten points? With prior, joint, and conditional probabilities defined, we are set to write down Bayes' theorem. It could have been modelled: perhaps we have an algorithm that we trust that returns modelled radiances depending on different parameters describing the land surface. The element of the confusion matrix in the ith row and jth column tells us: for all of the test data, how many test samples had the ith class but the classifier returned the jth class?