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Sorry if this has been answered before but could someone help me with solving the following problem:

Each symbol in a dataset has a set of labels. Given a set of labels how can we predict more labels for that set?

Or to attempt a more formal wording: let a set of sets $S = \{ s_1, s_2, s_3, ... \} $ where $ s_i \subseteq L $ and $ L = \{ l_1, l_2, l_3,...,l_m\} $ where $L$ is the finite set of labels. Given a set of labels $Y = \{ y_1 ,..., y_n \} $ where $Y \subseteq X $ what is the probability $ P(r = l_i) \forall l_i \in L$ so that $Y \cup \{r\} \in S $.

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Maybe you could use some algorithm that solves "Market Basket Analysis". The problem is explained here:

Market Basket Analysis is a modelling technique based upon the theory that if you buy a certain group of items, you are more (or less) likely to buy another group of items. For example, if you are in an English pub and you buy a pint of beer and don't buy a bar meal, you are more likely to buy crisps (US. chips) at the same time than somebody who didn't buy beer.

http://albionresearch.com/data_mining/market_basket.php

One example of such an algorithm is: https://en.wikipedia.org/wiki/Association_rule_learning

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