"Non-naive" bayesian classification algorithms Based on the problem description in this post:
Relating parameters to a measured variable

Based on a suggestion, I thought of studying the relationship between the parameters and a measured metric using Naive-Bayes classification. As, I was reading about it, I got to know that it assumes conditional independence i.e. P(x1 | A,x2) = P(x1 | A), where x1  and x2 are parameters.

This may not be true in my case. Are there similar classification algorithms that do not assume independence? I understand that I may require higher number of samples but I can get them because this data is obtained from simulations.
It would be nice if I do not have to code one for myself; so please let me know if R-packages may be available?
 A: For a classification problem with data $X$ and labels $Y \in \mathcal{Y}$, if you know the exact distributions, the classifier least likely to make a mistake (the Bayes classifier) is given by
\begin{align}
\hat{y}(x)
&= \arg\max_{y \in \mathcal{Y}} P(Y = y \mid X = x)
\\&= \arg\max_{y \in \mathcal{Y}} \frac{P(X = x \mid Y = y) P(Y = y)}{P(X = x)}
\\&= \arg\max_{y \in \mathcal{Y}} P(X = x \mid Y = y) P(Y = y)
.\end{align}
Since of course in practice we don't know those distributions, we can replace them by an estimate.
The Naive Bayes classifier follows from assuming the components of $X$ are independent, and using some density estimator or another on each dimension of $X$.
The $k$-nearest neighbor classifier is basically equivalent to using a $k$-NN density estimator for $P(X = x \mid Y = y)$ (the built-in knn function). Using kernel density estimation gives you a kernel-based classifier (the np package does this well, though I don't think it has a built-in classifier). These make no independence assumptions.
As @Jacques notes, you can do similar thing with so-called Bayesian networks, which assumes an independence structure according to a particular graph; you can attempt to learn that graph from the data.
Many other classifiers can also be cast in this framework.
A: The package bnlearn have different forms of "learning the Bayesian network" from the data. 
