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Twitter, as a social media platform, has become an increasingly useful data source for health surveillance studies, and personal health experiences shared on Twitter provide valuable information to the surveillance. Twitter data are known for their irregular usages of languages and informal short texts due to the 140 character limit, and for their noisiness such that majority of the posts are irrelevant to any particular health surveillance. These factors pose challenges in identifying personal health experience tweets from the Twitter data. In this study, we designed deep neural networks with 3 different architectural configurations, and after training them with a corpus of 8,770 annotated tweets, we used them to predict personal experience tweets from a set of 821 annotate tweets. Our results demonstrated a significant amount of improvement in predicting personal health experience tweets by deep neural networks over that by conventional classifiers: 37.5% in accuracy, 31.1% in precision, and 53.6% in recall. We believe that our method can be utilized in various health surveillance studies using Twitter as a data source.