In modern computer science education, massive open online courses (MOOCs) log thousands of hours of data about how students solve coding challenges. Being so rich in data, these platforms have garnered the interest of the machine learning community, with many new algorithms attempting to autonomously provide feedback to help future students learn. But what about those first hundred thousand students? In most educational contexts (i.e. classrooms), assignments do not have enough historical data for supervised learning. In this paper, we introduce a human-in-the-loop "rubric sampling" approach to tackle the "zero shot" feedback challenge. We are able to provide autonomous feedback for the first students working on an introductory programming assignment with accuracy that substantially outperforms data-hungry algorithms and approaches human level fidelity. Rubric sampling requires minimal teacher effort, can associate feedback with specific parts of a student's solution and can articulate a student's misconceptions in the language of the instructor. Deep learning inference enables rubric sampling to further improve as more assignment specific student data is acquired. We demonstrate our results on a novel dataset from Code.org, the world's largest programming education platform.
Theoretical inspiration for our expert-based generative rubric sampling derives from Brown's Repair Theory" which argues that the best way to help students is to understand the generative origins of their mistakes @cite_7 . Simulating student cognition has been applied to simple arithmetic problems @cite_8 and recent hard coded models have been very successful in inferring why students make subtraction mistakes @cite_13 . Researchers have argued that such expert models are infeasible for assignments as complex as coding @cite_21 . However, the automated hierarchical decomposition achieved by @cite_4 inspired us to develop rubric sampling, a simple expert model that works for programming assignments.
@cite_4 @cite_7 @cite_8 @cite_21 @cite_13
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We consider the problem of using a large unlabeled sample to boost performance of a learning algorit,hrn when only a small set of labeled examples is available. In particular, we consider a problem setting motivated by the task of learning to classify web pages, in which the description of each example can be partitioned into two distinct views. For example, the description of a web page can be partitioned into the words occurring on that page, and the words occurring in hyperlinks t,hat point to that page. We assume that either view of the example would be sufficient for learning if we had enough labeled data, but our goal is to use both views together to allow inexpensive unlabeled data to augment, a much smaller set of labeled examples. Specifically, the presence of two distinct views of each example suggests strategies in which two learning algorithms are trained separately on each view, and then each algorithm’s predictions on new unlabeled examples are used to enlarge the training set of the other. Our goal in this paper is to provide a PAC-style analysis for this setting, and, more broadly, a PAC-style framework for the general problem of learning from both labeled and unlabeled data. We also provide empirical results on real web-page data indicating that this use of unlabeled examples can lead to significant improvement of hypotheses in practice. *This research was supported in part by the DARPA HPKB program under contract F30602-97-1-0215 and by NSF National Young investigator grant CCR-9357793. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. TO copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or a fee. COLT 98 Madison WI USA Copyright ACM 1998 l-58113-057--0 98 7... 5.00 92 Tom Mitchell School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213-3891 mitchell+@cs.cmu.edu Traditional sampling theories consider the problem of reconstructing an unknown signal x from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that x lies in a known subspace. Recently, there has been growing interest in nonlinear but structured signal models, in which x lies in a union of subspaces. In this paper, we develop a general framework for robust and efficient recovery of such signals from a given set of samples. More specifically, we treat the case in which x lies in a sum of k subspaces, chosen from a larger set of m possibilities. The samples are modeled as inner products with an arbitrary set of sampling functions. To derive an efficient and robust recovery algorithm, we show that our problem can be formulated as that of recovering a block-sparse vector whose nonzero elements appear in fixed blocks. We then propose a mixed lscr2 lscr1 program for block sparse recovery. Our main result is an equivalence condition under which the proposed convex algorithm is guaranteed to recover the original signal. This result relies on the notion of block restricted isometry property (RIP), which is a generalization of the standard RIP used extensively in the context of compressed sensing. Based on RIP, we also prove stability of our approach in the presence of noise and modeling errors. A special case of our framework is that of recovering multiple measurement vectors (MMV) that share a joint sparsity pattern. Adapting our results to this context leads to new MMV recovery methods as well as equivalence conditions under which the entire set can be determined efficiently. From a computational perspective, there is a close connection between various probabilistic reasoning tasks and the problem of counting or sampling satisfying assignments of a propositional theory. We consider the question of whether state-of-the-art satisfiability procedures, based on random walk strategies, can be used to sample uniformly or nearuniformly from the space of satisfying assignments. We first show that random walk SAT procedures often do reach the full set of solutions of complex logical theories. Moreover, by interleaving random walk steps with Metropolis transitions, we also show how the sampling becomes near-uniform. We empirically characterize the performance of discriminative and generative LSTM models for text classification. We find that although RNN-based generative models are more powerful than their bag-of-words ancestors (e.g., they account for conditional dependencies across words in a document), they have higher asymptotic error rates than discriminatively trained RNN models. However we also find that generative models approach their asymptotic error rate more rapidly than their discriminative counterparts---the same pattern that Ng & Jordan (2001) proved holds for linear classification models that make more naive conditional independence assumptions. Building on this finding, we hypothesize that RNN-based generative classification models will be more robust to shifts in the data distribution. This hypothesis is confirmed in a series of experiments in zero-shot and continual learning settings that show that generative models substantially outperform discriminative models.