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Session-based Recommender Systems (SRSs) have been actively developed to recommend the next item of an anonymous short item sequence (i.e., session). Unlike sequence-aware recommender systems where the whole interaction sequence of each user can be used to model both the short-term interest and the general interest of the user, the absence of user-dependent information in SRSs makes it difficult to directly derive the user's general interest from data. Therefore, existing SRSs have focused on how to effectively model the information about short-term interest within the sessions, but they are insufficient to capture the general interest of users. To this end, we propose a novel framework to overcome the limitation of SRSs, named ProxySR, which imitates the missing information in SRSs (i.e., general interest of users) by modeling proxies of sessions. ProxySR selects a proxy for the input session in an unsupervised manner, and combines it with the encoded short-term interest of the session. As a proxy is jointly learned with the short-term interest and selected by multiple sessions, a proxy learns to play the role of the general interest of a user and ProxySR learns how to select a suitable proxy for an input session. Moreover, we propose another real-world situation of SRSs where a few users are logged-in and leave their identifiers in sessions, and a revision of ProxySR for the situation. Our experiments on real-world datasets show that ProxySR considerably outperforms the state-of-the-art competitors, and the proxies successfully imitate the general interest of the users without any user-dependent information.