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Although social anxiety and depression are common, they are often under diagnosed and under treated, in part due to difficulties identifying and accessing individuals in need of services. Current assessments rely on client self-report and clinician judgment, which are vulnerable to social desirability and other subjective biases. Identifying objective, non-burdensome markers of these mental health problems, such as features of speech, could help advance assessment, prevention, and treatment approaches. Prior research examining speech detection methods has focused on fully supervised learning approaches employing strongly labeled data. However, strong labeling of individuals high in symptoms or state affect in speech audio data is impractical, in part because it is not possible to identify with high confidence which regions of a long speech indicate the person’s symptoms or affective state. We propose a weakly supervised learning framework for detecting social anxiety and depression from long audio clips. Specifically, we present a novel feature modeling technique named NN2Vec that identies and exploits the inherent relationship between speakers’ vocal states and symptoms/affective states. Detecting speakers high in social anxiety or depression symptoms using NN2Vec features achieves F-1 scores 17% and 13% higher than those of the best available baselines. In addition, we present a new multiple instance learning adaptation of a BLSTM classifier, named BLSTM-MIL. Our novel framework of using NN2Vec features with the BLSTM-MIL classifier achieves F-1 scores of 90.1% and 85.44% in detecting speakers high in social anxiety and depression symptoms.