Previous papers have tested efficient risk sharing under the assumption of identical risk preferences. In this paper we show that, if in the data households have heterogeneous risk preferences, the tests proposed in the past reject efficiency even if households share risk efficiently. To address this issue we propose a method that enables one to test efficiency even when households have different preferences for risk. The method is composed of three tests. The first one can be used to determine whether in the data under investigation households have homogeneous risk preferences.The second and third tests can be used to evaluate efficient risk sharing when the hypothesis of homogeneous risk preferences is rejected. We use this method to test efficient risk sharing in rural India. Using the first test, we strongly reject the hypothesis of identical risk preferences. We then test efficiency with and without the assumption of preference homogeneity. In the first case we reject efficient risk sharing at the village and caste level. In the second case we still reject efficiency at the village level, but we cannot reject this hypothesis at the caste level. This finding suggests that the relevant risk-sharing unit in rural India is the caste and not the village.

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Interactive learning environments facilitate learning by providing hints to fill the gaps in the understanding of a concept. Studies suggest that hints are not used optimally by learners. Either they are used unnecessarily or not used at all. It has been shown that learning outcomes can be improved by providing hints when needed. An effective hinttaking prediction model can be used by a learning environment to make adaptive decisions on whether to withhold or provide hints. Past work on student behavior modeling has focused extensively on the task of modeling a learner's state of knowledge over time, referred to as knowledge tracing. The other aspects of a learner's behavior such as tendency to use hints has garnered limited attention. Past knowledge tracing models either ignore the questions where a hint was taken or label hints taken as an incorrect response. We propose a multi-task memory-augmented deep learning model to jointly predict the hint-taking and the knowledge tracing task. The model incorporates the effect of past responses as well as hints taken on both the tasks. We apply the model on two datasets -ASSISTments 2009-10 skill builder dataset and Junyi Academy Math Practicing Log. The results show that deep learning models efficiently leverage the sequential information present in a learner's responses. The proposed model significantly out-performs the past work on hint prediction by at least 12% points. Moreover, we demonstrate that jointly modeling the two tasks improves performance consistently across the tasks and the datasets, albeit by a small amount.

A major difficulty in debugging distributed systems lies in manually determining which of the many available debugging tools to use and how to query its logs. Our own study of a production debugging workflow confirms the magnitude of this burden. This paper explores whether a machine-learning model can assist developers in distributed systems debugging. We present Revelio, a debugging assistant which takes user reports and system logs as input, and outputs debugging queries that developers can use to find a bug's root cause.The key challenges lie in (1) combining inputs of different types (e.g., natural language reports and quantitative logs) and (2) generalizing to unseen faults. Revelio addresses these by employing deep neural networks to uniformly embed diverse input sources and potential queries into a high-dimensional vector space. In addition, it exploits observations from production systems to factorize query generation into two computationally and statistically simpler learning tasks. To evaluate Revelio, we built a testbed with multiple distributed applications and debugging tools. By injecting faults and training on logs and reports from 800 Mechanical Turkers, we show that Revelio includes the most helpful query in its predicted list of top-3 relevant queries 96% of the time. Our developer study confirms the utility of Revelio.