# Is this a really a belief propagation problem?

BACKGROUND

This is basically a reputation problem that involves a set of interacting entities $e_i$. Each entity has, in principle, a reputation vector $\vec{b}_i$. That reputation depends on what the entity is intrinsically, i.e., on the features $\vec{\delta}_i$ describing $e_i$, but also on the reputations $\vec{b}_j$ of the entities $e_{j \neq i}$ interacting with $e_i$.

An anthropomorphic example would be as follows:

$$$\vec{\delta}_{\scriptsize \mbox{Joe}} = \big[\mbox{pays taxes, clean criminal record, gives to charity}\big]$$$ ,

therefore one would conclude a priori that

$$$\vec{b}_{\scriptsize \mbox{Joe}} = \big[ \mbox{good guy} \big]$$$.

However, on a given day, Joe was seen exchanging a briefcase Bob, whose reputation vector

$$$\vec{b}_{\scriptsize \mbox{Bob}} = \big[ \mbox{shady criminal} \big]$$$.

Clearly, the reputation vector of Joe needs to be re-assessed to something else than good guy. In other words, the reputation of the interacting entity $\vec{b}_{\scriptsize \mbox{Bob}}$ should somehow enter as a feature along with $\vec{\delta}_{\scriptsize \mbox{Joe}}$. But is that the right way to model this?

GOAL

Given the data involved in any interaction between $e_i$ and $e_j$, how should one (re-)assess the reputation of $e_i$ given both its (intrinsic) attributes $\vec{\delta}_i$ and the reputations of the entities it interacts with? Does it suffice to concatenate $\vec{\delta}_i$ and $\vec{b}_j$ into a single, all-encompassing feature vector $\vec{d}_i$ and then update the mapping $\mathcal{F}: \vec{d}_i \equiv (\vec{\delta}_i, \vec{b}_j) \rightarrow \vec{b}_i$?

CLARIFICATION

I didn't specify on purpose whether this would be supervised learning or not. If the true reputation $\vec{b}_i$ is known, then this would be supervised learning. However, I'd also like to account for when that is not the case and then have reputation being propagated from $e_j$ to $e_i$.

• What does this have to do with belief propagation? – Neil G Feb 13 '18 at 9:08
• @NeilG If we believe that Bob is bad then badness will propagate from Bob to Joe... Isn't that what belief propagation is all about, namely the propagation of belief between the nodes in a graph of interactions? Here "reputation" is tantamount to belief. – Tfovid Feb 13 '18 at 9:12
• Yes. Why don't you start by telling us what kind of network you have? – Neil G Feb 13 '18 at 9:13
• @NeilG That's my problem. I don't really know how to model this more than what I described. I just know that there is some kind of an "edge" between Bob and Joe, but I'm not sure if I should pursue the whole route of modeling this as a graph. – Tfovid Feb 13 '18 at 9:14
• You don't even know your problem if you can't say if it's supervised learning or not. – Neil G Feb 13 '18 at 9:15