30 Adham Beykikhoshk, Ognjen Arandjelovi´c, Dinh Phung, Svetha Venkatesh, and Terry Caelli as classifying tweets as being ASD related ( +1 ) or not ( − 1 ). Since all ASD tweets are medi- cal condition related, the probability of the classifier output being +1 given an ASD tweet is also p$_{m}$ . On the other hand, the control corpus contains both tweets not related to a medical condition as well as those which are related to medical conditions other than ASD. Hence, the probability of the classifier output being − 1 given a tweet from our control corpus is: where ρ$_{m}$ is the proportion of control tweets which are medical condition-related. The first term, p$_{n}$ (1 − ρ$_{m}$ ) , is the probability of a control tweet not related to a medical condition being selected as input to the classifier (probability 1 − ρ$_{m}$ ) and correctly classified (prob- ability p$_{n}$ ). The second term, (1 − p$_{m}$ ) ρ , is the probability of a medical condition related control tweet being selected as input (probability ρ$_{m}$ ) and incorrectly classified (probability 1 − p$_{m}$ ), as the classifier output of interest is − 1 . The expression in (8) can be rearranged to give: Since the proportion ρ$_{m}$ of medical condition related tweets is likely to be small, it can be seen that a good classifier which differentiates between medical condition related and other tweets can appear to be a good classifier of ASD vs. non-ASD-related tweets. Thus the question is if the results of our experiments described in the previous section really demonstrate good ASD vs. non-ASD discrimination, or is it simply the case that our methods learnt to distinguish between medical condition-related and non-medical condition-related tweets. We set out to investigate this next. For this experiment we followed the methodology described in the previous set of ex- periments with the sole difference being that learning was done using a different control corpus. Specifically, we collected a data set related to another pervasive medical condition – Alzheimer’s disease. In a similar manner as in Section 4.1 we collected tweets which con- tain the word “alzheimer” (or any of the words derived from it by suffixation), balancing p$_{n}$ (1 − ρ$_{m}$ ) + (1 − p$_{m}$ ) ρ$_{m}$ (8) p$_{n}$ + (1 − p$_{m}$ − p$_{n}$ ) ρ$_{m}$ (9)