2 added 4 characters in body edited Jun 4 '12 at 20:29 emrea 81644 silver badges1212 bronze badges I can see that this problem can be modeled with Bayesian networks. First, you need to decide which dependencies are there in your problem. As you said, (1) v depends on a,b,c,d,e (2) x depends on a,b,c,d,e,v (3) y depends on a,b,c,d,e,x and finally, (4) z depends on a,b,c,d,e,v,x,y Second, you need to implement these distributions. For example, for (1), you need to model P(v|a,b,c,d,e) how you do this is upto you. You can train a classifier, learn a regressor, etc. You will also need to model the prior probabilities of a,b,c,d,e. At this point, you can write the full joint distribution of all your variables using the conditional probabilities you have. Finally, you can answer any inference query with what you have. For example, let's say you're interested in answering P(z>q), the probability of revenue being higher than q. $$P(Z>q) = \int_q^\infty P(z)dz$$. $$P(z) = \sum_q \sum_b \sum_c \sum_d \sum_e \sum_v \sum_x \sum_y P(z,a,b,c,d,e,v,x,y)$$ where the joint factors into your conditional densitiesprobabilities: $$P(z,a,b,c,d,e,v,x,y) = P(z|a,b,c,d,e,v,y,x) P(v|a,b,c,d,e) \dots$$ Hope this helps. I can see that this problem can be modeled with Bayesian networks. First, you need to decide which dependencies are there in your problem. As you said, (1) v depends on a,b,c,d,e (2) x depends on a,b,c,d,e,v (3) y depends on a,b,c,d,e,x and finally, (4) z depends on a,b,c,d,e,v,x,y Second, you need to implement these distributions. For example, for (1), you need to model P(v|a,b,c,d,e) how you do this is upto you. You can train a classifier, learn a regressor, etc. You will also need to model the prior probabilities of a,b,c,d,e. At this point, you can write the full joint distribution of all your variables using the conditional probabilities you have. Finally, you can answer any inference query with what you have. For example, let's say you're interested in answering P(z>q), the probability of revenue being higher than q. $$P(Z>q) = \int_q^\infty P(z)dz$$. $$P(z) = \sum_q \sum_b \sum_c \sum_d \sum_e \sum_v \sum_x \sum_y P(z,a,b,c,d,e,v,x,y)$$ where the joint factors into your conditional densities: $$P(z,a,b,c,d,e,v,x,y) = P(z|a,b,c,d,e,v,y,x) P(v|a,b,c,d,e) \dots$$ Hope this helps. I can see that this problem can be modeled with Bayesian networks. First, you need to decide which dependencies are there in your problem. As you said, (1) v depends on a,b,c,d,e (2) x depends on a,b,c,d,e,v (3) y depends on a,b,c,d,e,x and finally, (4) z depends on a,b,c,d,e,v,x,y Second, you need to implement these distributions. For example, for (1), you need to model P(v|a,b,c,d,e) how you do this is upto you. You can train a classifier, learn a regressor, etc. You will also need to model the prior probabilities of a,b,c,d,e. At this point, you can write the full joint distribution of all your variables using the conditional probabilities you have. Finally, you can answer any inference query with what you have. For example, let's say you're interested in answering P(z>q), the probability of revenue being higher than q. $$P(Z>q) = \int_q^\infty P(z)dz$$. $$P(z) = \sum_q \sum_b \sum_c \sum_d \sum_e \sum_v \sum_x \sum_y P(z,a,b,c,d,e,v,x,y)$$ where the joint factors into your conditional probabilities: $$P(z,a,b,c,d,e,v,x,y) = P(z|a,b,c,d,e,v,y,x) P(v|a,b,c,d,e) \dots$$ Hope this helps. 1 answered Jun 4 '12 at 19:14 emrea 81644 silver badges1212 bronze badges I can see that this problem can be modeled with Bayesian networks. First, you need to decide which dependencies are there in your problem. As you said, (1) v depends on a,b,c,d,e (2) x depends on a,b,c,d,e,v (3) y depends on a,b,c,d,e,x and finally, (4) z depends on a,b,c,d,e,v,x,y Second, you need to implement these distributions. For example, for (1), you need to model P(v|a,b,c,d,e) how you do this is upto you. You can train a classifier, learn a regressor, etc. You will also need to model the prior probabilities of a,b,c,d,e. At this point, you can write the full joint distribution of all your variables using the conditional probabilities you have. Finally, you can answer any inference query with what you have. For example, let's say you're interested in answering P(z>q), the probability of revenue being higher than q. $$P(Z>q) = \int_q^\infty P(z)dz$$. $$P(z) = \sum_q \sum_b \sum_c \sum_d \sum_e \sum_v \sum_x \sum_y P(z,a,b,c,d,e,v,x,y)$$ where the joint factors into your conditional densities: $$P(z,a,b,c,d,e,v,x,y) = P(z|a,b,c,d,e,v,y,x) P(v|a,b,c,d,e) \dots$$ Hope this helps.