Two of the best books for teaching Bayesian networks are
- Michael Jordan, “Introduction to Graphical Models”, in preparation
- Daphne Koller and Nir Friedman, “Bayesian Networks and Beyond”, in preparation.
In preparation !@#. For eons now, these books have been “in preparation”. Civilizations have come and gone. Many courses in many universities have used these books in preliminary form as their primary text. Why are these authors so laid back! Do they live in Frank Capra’s Shangrila, where people live thousands of years, and don’t need to hurry much. Hmm, Jordan at Berkeley, Koller at Stanford. California…Shangrila. It seems that, for the time being, these gem books will be available only to surfer dudes, not to us hard working Yankees on the other coast.
Update (Sept 9, 2009)
Wow, 1200 pages! I take back all I said about Californian’s being laid back. Check out
Probabilistic Graphical Models
Principles and Techniques
Daphne Koller and Nir Friedman
(Aug 2009, MIT Press)
of an “energy” function 
. They have found that quantum computers can do this quadratically faster than classical computers.
points that is distributed according to a probability distribution 
, where 
is the stationary distribution of a Markov Chain. But in MH, 
. So simple and beautiful, and yet so useful.
Nope. None. Not yet. The field is a secret garden at present. A secret garden, having one is great solace from those aspects of life that make us inconsolably sad. For many years now, quantum bayesian networks has been one of my secret gardens. Which reminds me of the ![|0\rangle= \left[\begin{array}{c}1\\ 0 \end{array}\right]\;\;,\;\;|1\rangle = \left[\begin{array}{c}0\\ 1\end{array}\right]\;.](http://l.wordpress.com/latex.php?latex=%7C0%5Crangle%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C+0+%5Cend%7Barray%7D%5Cright%5D%5C%3B%5C%3B%2C%5C%3B%5C%3B%7C1%5Crangle+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%5C+1%5Cend%7Barray%7D%5Cright%5D%5C%3B.&bg=ffffff&fg=000000&s=0 "|0\rangle= \left[\begin{array}{c}1\\ 0 \end{array}\right]\;\;,\;\;|1\rangle = \left[\begin{array}{c}0\\ 1\end{array}\right]\;.")
![\overline{n} = P_0 = |0\rangle\langle 0|=\left[\begin{array}{c}1\;\;0\\ 0\;\;0\end{array}\right]\;\;,\;\; n = P_1 = |1\rangle\langle 1| =\left[\begin{array}{c}0\;\;0\\ 0\;\;1\end{array}\right]\;.](http://l.wordpress.com/latex.php?latex=%5Coverline%7Bn%7D+%3D+P_0+%3D+%7C0%5Crangle%5Clangle+0%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%3B%5C%3B0%5C%5C+0%5C%3B%5C%3B0%5Cend%7Barray%7D%5Cright%5D%5C%3B%5C%3B%2C%5C%3B%5C%3B++n+%3D+P_1+%3D+%7C1%5Crangle%5Clangle+1%7C+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%3B%5C%3B0%5C%5C+0%5C%3B%5C%3B1%5Cend%7Barray%7D%5Cright%5D%5C%3B.&bg=ffffff&fg=000000&s=0 "\overline{n} = P_0 = |0\rangle\langle 0|=\left[\begin{array}{c}1\;\;0\\ 0\;\;0\end{array}\right]\;\;,\;\; n = P_1 = |1\rangle\langle 1| =\left[\begin{array}{c}0\;\;0\\ 0\;\;1\end{array}\right]\;.")
is called the number operator because 
for 
. Note 
.![\sigma_X = \left[\begin{array}{c}0\;\;1\\1\;\;0\end{array}\right]\;\;,\;\;\sigma_Y =\left[\begin{array}{c}0\;-i\\i\;\;0\end{array}\right]\;\;,\;\;\sigma_Z = \left[\begin{array}{c}1\;\;0\\ 0\;-1\end{array}\right]\;.](http://l.wordpress.com/latex.php?latex=%5Csigma_X+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%3B%5C%3B1%5C%5C1%5C%3B%5C%3B0%5Cend%7Barray%7D%5Cright%5D%5C%3B%5C%3B%2C%5C%3B%5C%3B%5Csigma_Y+%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%5C%3B-i%5C%5Ci%5C%3B%5C%3B0%5Cend%7Barray%7D%5Cright%5D%5C%3B%5C%3B%2C%5C%3B%5C%3B%5Csigma_Z+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%3B%5C%3B0%5C%5C+0%5C%3B-1%5Cend%7Barray%7D%5Cright%5D%5C%3B.&bg=ffffff&fg=000000&s=0 "\sigma_X = \left[\begin{array}{c}0\;\;1\\1\;\;0\end{array}\right]\;\;,\;\;\sigma_Y =\left[\begin{array}{c}0\;-i\\i\;\;0\end{array}\right]\;\;,\;\;\sigma_Z = \left[\begin{array}{c}1\;\;0\\ 0\;-1\end{array}\right]\;.")
.
be the number of bits and 
the number of states. The operators in Fig.1 are a “universal” set: any matrix in 
can be constructed in terms of them. The operators in Figs. 2 and 3 can be expressed in terms of those in Fig.1.