This  content of this roadmap follows Prof. Jordan's lectures/textbook. I'll update it as I/we work through the material. Send me an email if you'd like to contribute (colorado _AT_ berkeley _DOT_ edu)
  ## Conditional Independence and Factorization
  *   Much of our early discussion focused on [[conditional independence]] in the context of [directed graphical models (Bayes nets)](Bayesian networks) and [undirected graphical models (Markov random fields - MRFs)](Markov random fields)
  * We can use the [[Bayes Ball]] algorithm to determine conditional independencies in  Bayes nets.
  * We can use simple [reachability algorithms]( to determine conditional independencies in MRFs
  *  We briefly discussed [[factor graphs]], which provide a more fine-grained representation of the independencies in a MRF
  ## Exact Inference
  *  The [[variable elimination]] algorithm  is based on interchanging sums and products in the definitions of marginals or partition functions.
  *  The [sum product algorithm](sum_product_on_trees)  is a belief propagation algorithm based on dynamic programming. It has the advantage over naive variable elimination in that it reuses computations to compute marginals for all nodes in the graph
  *  [[junction trees]] generalize the sum product algorithm to arbitrary graphs by  grouping variables together into cliques such that the cliques form a tree.
  ## Sampling-based inference
  *  [[rejection sampling]]  is a Monte Carlo method for sampling from a potentially complex distribution p(x) given a simpler distribution q(x)
  *  [[importance sampling]]  is a way of estimating expectations under an intractable distribution p by sampling from a tractable distribution q and reweighting the samples according to the ratio of the probabilities
  * We discussed some standard [[Markov chain Monte Carlo]] methods:
      * [[Metropolis-Hastings algorithm]] is a very general method for approximately sampling from a distribution p by defining a Markov chain which has p as a stationary distribution 
      * [[Gibbs sampling]] is an MCMC algorithm where each random variable is iteratively resampled from its conditional distribution given the remaining variables -- it can be viewed [as a special case of Metropolis-Hastings](gibbs_as_mh)
      * we also touched on determining [[MCMC convergence]]
      * we can use [simulated annealing](simmulated_annealing) to determine a [MAP estimates](map_parameter_estimation)
   * Some fancier MCMC algorithms we touched on include:
       * [hybrid Monte Carlo](Hamiltonian Monte Carlo )
       * [slice sampling](slice_sampling)
       * [[reversible jump MCMC]]
       * [[sequential Monte Carlo]]
  ## Statistical Concepts
  We  discussed Bayesian vs frequentist inference; some topics we touched on include:
  * [[maximum likelihood]] and [[asymptotics of maximum likelihood]] and the various prerequisites for these concepts
  *  [[bias_variance_decomposition]]
  * [[Bayesian model averaging]]
  ## Linear Regression and the Least Mean Squares algorithm
  * We discussed [[linear regression]] and its [closed form solution](linear_regression_closed_form) and their various prerequisites