# Tag Info

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*AI, A Modern Approach," was given that title to break from previously narrow approaches to duplicating desirable qualities of human thinking. Although Bayesian networks require somewhat resource intensive computational elements, the importance of Bayesian inference and probability are still of paramount importance in that some of the highest scientific ...

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we start with $\frac{\partial}{\partial \theta} \mathbb E_{q(\mathbf w\mid\theta)}[f(\mathbf w, \theta)]$ using definition of expectation for continuous case: $\mathbb E[X] = \int xp(x) dx$ for the first equation we get: $\frac{\partial}{\partial \theta} \int f(\mathbf w, \theta)q(\mathbf w \mid \theta) d\mathbf w$ we swap $q(\mathbf w \mid \... 3 By far the most common form of heuristic evaluation functions for Chess-playing (or, really, any game-playing) agents are simple linear functions. At least when we're talking about handcrafted features that's the case, of course all the hype with Deep Neural Networks in more recent years is different. So, when it's not specified in a paper like this exactly ... 2 Heuristics can be understood aas rules. Typically heuristics are thought of as problem-specific strategies. Expert systems were an early form of AI that utilized rules-based decisions. In a game-playing context, heuristics can be pure strategies. A heuristic function would be one that includes a some predefined decision rules. Russell and Norvig have a ... 1 I am not an expert on this, but I'll try to explain my understnding of this. A Bayesian Network is a Directed Graphical Model (DGM) with the ordered Markov property i.e the relationship of a node (random variable) depends only on its immediate parents and not its predecessors (generalized from first order Markov process). A Markov chain on the other hand ... 1 The main difference between a Bayesian network and a Markov chain is not that a Markov Chain is not directional, it is that the graph of the Bayesian network is not trivial whereas the graph of a Markov chain would be somewhat trivial, as all the previous$k$nodes would just point to the current node. To illustrate further why this would be trivial, we let ... 1 This is one of the main skills that separates someone with a deep understanding of, and experience in, machine learning learning, from a neophyte. There are several approaches: Try several methods, perhaps with automated hyperparameter optimization, and see if there's a big difference in typical model quality. This is pretty common if you don't have a lot ... 1 This is a bit of a puzzle but you can compute a reasonable narrow limit even without knowing whether or not$P(S,A) = P(S) P(A)$. Start with the contingency table relating$P(S, A)$,$P(S,\neg A)$,$P(\neg S, A)$,$P(\neg S,\neg A)$to$P(S)$and$P(A)$:$\$\begin{array}{cc|c} P( S,A)& P(\neg S,A) & P(A) \\ P(S,\neg A)& P(\neg S,\neg A) & P(...

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It's not completely clear from your question, but it looks like you want to prove that exact inference in a Bayesian Network is both NP-Hard and P-Hard. It appears that you have proven that it is NP-Hard, but are unsure how to show that it is also P-Hard. This is more of a TCS question than an AI question, but shouldn't be too difficult. You just need to ...

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The chapters for Bayesian Networks are: Quantifying Uncertainty Probabilistic Reasoning Dynamic Bayesian don't forget: Naive Bayes, hidden variables, Markov Maybe helpful: . Are We Going in the Right Direction? ... p.1049 If you find them interesting then invest more time to it. You might improve them and break new scientific ground. Recent trend goes ...

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