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The task of ultra-fine entity typing (UFET) seeks to predict diverse and free-form words or phrases that describe the appropriate types of entities mentioned in sentences. A key challenge for this task lies in the large amount of types and the scarcity of annotated data per type. Existing systems formulate the task as a multi-way classification problem and train directly or distantly supervised classifiers. This causes two issues: (i) the classifiers do not capture the type semantics since types are often converted into indices; (ii) systems developed in this way are limited to predicting within a pre-defined type set, and often fall short of generalizing to types that are rarely seen or unseen in training. This work presents LITE, a new approach that formulates entity typing as a natural language inference (NLI) problem, making use of (i) the indirect supervision from NLI to infer type information meaningfully represented as textual hypotheses and alleviate the data scarcity issue, as well as (ii) a learning-to-rank objective to avoid the pre-defining of a type set. Experiments show that, with limited training data, LITE obtains state-of-the-art performance on the UFET task. In addition, LITE demonstrates its strong generalizability, by not only yielding best results on other fine-grained entity typing benchmarks, more importantly, a pre-trained LITE system works well on new data containing unseen types.