# Predicting a combination

## Question

Suppose we have a training set of families. Where each family is defined as such…

Family: A list of integers. Each integer is the age of one of the family members. (e.g. with a 45 year old mother and father, and a 10 year old child you’d have {45, 45, 10}.)

Given a list of n integers, how might one predict the breakdown of families into subsets from that set?

For example: Suppose we have three families

1. {45, 45, 10}
2. {25, 24}
3. {30, 35, 1, 4, 7}

I want a model that would take the union of these families:

{45, 45, 10, 25, 24, 30, 35, 1, 4, 7}

and return the correct family breakdown:

1. {45, 45, 10}
2. {25, 24}
3. {30, 35, 1, 4, 7}

## Current Thoughts

Search randomly (intelligently'd be nice) through the space of all possible combinations of subsets for a maximally probable combination. The probability of each combination could be estimated by multiplying the empirical probabilities of each combination in the data set.

Problem here is that each set would be very rare, so maybe I’d have to create some features (size of family, distance btwn 2 oldest ages, etc...) for a family.

Additionally, I could add to the empirical probability of a family if I the training data has similar families.

• You would need some empirical data for ages in families (and family sizes). Then maybe simulated annealing (would be better than random search). – kjetil b halvorsen Sep 27 '18 at 21:05
• The "training set of families" is the empirical data. Thank you, a meta-heuristic approach definitely seems a good way to go for intelligently searching. – timwiz Sep 27 '18 at 21:14
• Could you please tell us what a "breakdown of families into subsets" might refer to? I can think of many possible interpretations. – whuber Sep 27 '18 at 21:44
• Sure. I added an example of how I am thinking about the inputs and outputs. – timwiz Sep 27 '18 at 22:04