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This was a somewhat hotly debated question in the 1980s. The debate was more-or-less ended with papers like Cheeseman's In Defense of Probability. The short answer is that Fuzzy Logic does not just assign a continuous value to sentences, what it does is assign degrees of membership in different fuzzy sets. These degrees of membership range between 0 and 1. ...


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Demster-Shafer Theory and Bayesian Networks were both techniques that rose to prominence within AI in the 1970's and 1980's, as AI started to seriously grapple with uncertainty in the world, and move beyond the sterilized environments that most early systems worked in. In the 1970's and perhaps even earlier, it became apparent that direct applications of ...


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Introduction: MAP finds a point estimate! As opposed to your apparently current belief, in maximum a posteriori (MAP) estimation, you are looking for a point estimate (a number or vector) rather than a full probability distribution. The MAP estimation can be seen as a Bayesian version of the maximum likelihood estimation (MLE). Therefore, I will first ...


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Using as a best reference accordingly my own google research, find the best post about best introductory Bayesian statistics book and summarize the answers. I find this post in stats.stackexchange about bayesian statistics books maybe this is the best recomendation for you. I read the post weeks ago and some books are stunning. This is my TOP 3 books from ...


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In expectation step, firstly we calculate the posterior of latent variable $Z$ and then the $Q(θ | θ^{(t)})$ is defined as the expected value of the log likelihood of $θ$, with respect to the current conditional contribution of $Z$ given $X$ and the current estimates of $θ^{(t)}$. In maximization step, we update $θ$ using the argmax on $Q$, with respect to $...


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Bernoulli naïve Bayes $P(x|c_k) = \prod^{n}_{i=1} p^{x_i}_{ki} (1-p_{ki})^{(1-x_i)}$ Let's examine the example of document classification. Let K different text classes and n different terms that our vocabulary contains. $x_i$ are boolean variables (0, 1) expressing if the $i^{th}$ term exists in document x. x is a vector of dimension n. $P(x|c_k)$ ...


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