Probabilistic Graphical Models (PGMs) are:
Connectionist: RBMs are PGMs and neural networks (source)
Bayesian: Bayes Networks are bayesian (Wikipedia article)
Symbolist: Markov Logic Networks (source)
Analogizers and Evolutionaries: According to Domingos, they are also in Markov Logic Networks.
So the answer is that you can't simply categorize such a ...
OK, here are my attempts with R & ggplot2
1 Simple stacked histogram
2 Dodged stacked histogram ~ bacteria
3 Dodged histogram ~ Culture
4 Dodged histogram ~ change
5 Grouped by number of unique 'patterns' Change~Bacteria
6 Grouped by number of unique 'patterns' Change~Bacteria, jittered
7 Grouped by number of unique 'patterns' Change~Bacteria, ...
Super comprehensive question. You are basically asking for tones of directions! I'd suggest to start with link prediction problem. So assume you have a directed/signed/weighted graph and you want to find the most probable next interaction (link/edge). I'd suggest to have a look at Jerome Kunegis papers and you may see it as a starting point and go on from ...
You are making one mistake which cascades on towards other mistakes. The multiple inputs are different features of the same sample. Let's say we want to regress house prices based on some features of a house. These three nodes could represent the rating of the neighborhood, the surface area and the number of bedrooms for example. Then you take a weighted sum ...
Based on this paper (Qi, Szummer, and Minka. 2005. Bayesian Conditional Random Fields):
In this paper, we propose Bayesian Conditional Random Fields (BCRF), a novel Bayesian approach to training and inference for conditional random fields
We can see that the original CRF model is presumably not Bayesian, since this paper's contribution is a novel ...
Only Domingos knows for sure, since he invented this taxonomy, but I'd guess it would fall under "connectionists" (which he associates with neural networks), since graphs are all about connections (between random variables). Bayesians would be my second choice. CRFs are not natively Bayesian (you don't use priors or posteriors of the model parameters), but ...
First, a note: don't let the graph structure make you think that this can be addressed with neural networks; this structure only suggests that this is a hierarchical model.
Second, let's take into account the following:
In your first figure, you don't connect A, B or C to the output. I assume that there is a relationship from A,B,C to output.
You mention ...
Apparently, I misunderstood your question.
There are several methods for finding the k-best paths with extending versions of the Viterbi algorithm.
My first advice would be to look at this question on SO that is similar to yours and has a good illustrated answer.
Then, I would refer you to two articles/thesis that are publicly available and from where one ...
Not a library, but a interactive GUI based tool is "samiam" (Sensitivity Analysis Modeling Inference and More) from a research group at UCLA.
I am not sure about your "continuous PDFs" requirement, whether it's possible to define them inside the samiam GUI.
samiam is free to download, but registration is required.
The size of the software is small, but ...
I'd represent actual repeated values differently from missing data. The latter is straightforward; the former I'd interpolate with Gaussian process regression. This way you'll be able to get error bars like so:
Note how the sample functions (and thus error bars) expand and contract as you depart and approach the measurements, as you would intuitively expect....