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<h2>Viral Marketing</h2>
<p>
A firm is interested in marketing a new product to its 
customers. These are connected in a social network that is known to the firm: the network represents
the trust relationships between customers.
The firm has decided to adopt a marketing strategy that involves giving the product for free to a
number of its customers, in the hope that these influence the other customers and entice them to
buy the product. The firm wants to choose the customers to which marketing is applied so that 
its return is maximized. This involves computing the probability that the non-marketed customers
will acquire the product given the action to the marketed customers. 
</p>
<p>
This viral marketing scenario is inspired by [1].
</p>
<p>
We can model this domain with an LPAD where the predicate <code>trust/2</code> encodes the links
between customers in the social network and predicate <code>has/1</code> is true of customers that possess
the product, either received as a gift or bought. Predicate <code>trust/2</code> is defined by a 
number of certain facts, while predicate <code>has/1</code> is defined by two rules, one expressing the
prior probability of a customer to buy the product and one expressing the fact that if a trusted customer has the product, then there is a certain probability that the trusting customer buys the
product. 
</p>
<p>
In the example code below the social network is:
</p>
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graph(G).
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<p>We want to compute the probability that customer 2 buys the product if
we perform the action of giving the product to customer 3. We need to 
use causal reasoning so we use the action <code>do(has(3))</code> as evidence:
</p>
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prob(has(2),do(has(3)),P).
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<p>If instead we compute the effect of the action using regular probabilistic
inference, we get:
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prob(has(2),has(3),P).
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<p>So not distinguishing seeing from doing leads to an overly optimistic estimate.
</p>
<h3>Code</h3>
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:- use_module(library(pita)).

:- if(current_predicate(use_rendering/1)).
:- use_rendering(graphviz).
:- endif.
graph(digraph([rankdir="LR"|G])):-
    findall(edge(A -&gt; B,[]),
      clause(trusts(A,B,_,_),_),
      G).

:- pita.

:- begin_lpad.

:- action has/1.

has(_):0.1.

has(P) :0.4 :- trusts(P, Q), has(Q).

trusts(2,1).
trusts(3,1).
trusts(3,2).
trusts(4,1).
trusts(4,3).
:-end_lpad.
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<h3>References</h3>
[1] 
G. V. den Broeck, I. Thon, M. van Otterlo, L. D. Raedt, Dtproblog: A decision-theoretic probabilistic prolog, in: M. Fox, D. Poole (Eds.), 24th AAAI Conference on Artificial Intelligence, AAAI’10, Atlanta, Georgia, USA, July 11-15, 2010, AAAI Press, 2010, pp. 1217–1222.
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