Zero Shot Learning for Code Education: Rubric Sampling with Deep Learning Inference

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.Comment: To appear at AAAI 2019; 9 page

Treebank-based acquisition of a Chinese lexical-functional grammar

Scaling wide-coverage, constraint-based grammars such as Lexical-Functional Grammars (LFG) (Kaplan and Bresnan, 1982; Bresnan, 2001) or Head-Driven Phrase Structure Grammars (HPSG) (Pollard and Sag, 1994) from fragments to naturally occurring unrestricted text is knowledge-intensive, time-consuming and (often prohibitively) expensive. A number of researchers have recently presented methods to automatically acquire wide-coverage, probabilistic constraint-based grammatical resources from treebanks (Cahill et al., 2002, Cahill et al., 2003; Cahill et al., 2004; Miyao et al., 2003; Miyao et al., 2004; Hockenmaier and Steedman, 2002; Hockenmaier, 2003), addressing the knowledge acquisition bottleneck in constraint-based grammar development. Research to date has concentrated on English and German. In this paper we report on an experiment to induce wide-coverage, probabilistic LFG grammatical and lexical resources for Chinese from the Penn Chinese Treebank (CTB) (Xue et al., 2002) based on an automatic f-structure annotation algorithm. Currently 96.751% of the CTB trees receive a single, covering and connected f-structure, 0.112% do not receive an f-structure due to feature clashes, while 3.137% are associated with multiple f-structure fragments. From the f-structure-annotated CTB we extract a total of 12975 lexical entries with 20 distinct subcategorisation frame types. Of these 3436 are verbal entries with a total of 11 different frame types. We extract a number of PCFG-based LFG approximations. Currently our best automatically induced grammars achieve an f-score of 81.57% against the trees in unseen articles 301-325; 86.06% f-score (all grammatical functions) and 73.98% (preds-only) against the dependencies derived from the f-structures automatically generated for the original trees in 301-325 and 82.79% (all grammatical functions) and 67.74% (preds-only) against the dependencies derived from the manually annotated gold-standard f-structures for 50 trees randomly selected from articles 301-325

LFG without C-structures

We explore the use of two dependency parsers, Malt and MST, in a Lexical Functional Grammar parsing pipeline. We compare this to the traditional LFG parsing pipeline which uses constituency parsers. We train the dependency parsers not on classical LFG f-structures but rather on modified dependency-tree versions of these in which all words in the input sentence are represented and multiple heads are removed. For the purposes of comparison, we also modify the existing CFG-based LFG parsing pipeline so that these "LFG-inspired" dependency trees are produced. We find that the differences in parsing accuracy over the various parsing architectures is small

Arabic parsing using grammar transforms

We investigate Arabic Context Free Grammar parsing with dependency annotation comparing lexicalised and unlexicalised parsers. We study how morphosyntactic as well as function tag information percolation in the form of grammar transforms (Johnson, 1998, Kulick et al., 2006) affects the performance of a parser and helps dependency assignment. We focus on the three most frequent functional tags in the Arabic Penn Treebank: subjects, direct objects and predicates . We merge these functional tags with their phrasal categories and (where appropriate) percolate case information to the non-terminal (POS) category to train the parsers. We then automatically enrich the output of these parsers with full dependency information in order to annotate trees with Lexical Functional Grammar (LFG) f-structure equations with produce f-structures, i.e. attribute-value matrices approximating to basic predicate-argument-adjunct structure representations. We present a series of experiments evaluating how well lexicalized, history-based, generative (Bikel) as well as latent variable PCFG (Berkeley) parsers cope with the enriched Arabic data. We measure quality and coverage of both the output trees and the generated LFG f-structures. We show that joint functional and morphological information percolation improves both the recovery of trees as well as dependency results in the form of LFG f-structures

Discovering latent structures in syntax trees and mixed-type data

Gibbs sampling is a widely applied algorithm to estimate parameters in statistical models. This thesis uses Gibbs sampling to resolve practical problems, especially on natural language processing and mixed type data. It includes three independent studies. The first study includes a Bayesian model for learning latent annotations. The technique is capable of parsing sentences in a wide variety of languages, producing results that are on-par with or surpass previous approaches in accuracy, and shows promising potential for parsing low-resource languages. The second study presents a method to automatically complete annotations from partially-annotated sentence data, with the help of Gibbs sampling. The algorithm significantly reduces the time required to annotate sentences for natural language processing, without a significant drop in annotation accuracy. The last study proposes a novel factor model for uncovering latent factors and exploring covariation among multiple outcomes of mixed types, including binary, count, and continuous data. Gibbs sampling is used to estimate model parameters. The algorithm successfully discovers correlation structures of mixed-type data in both simulated and real-word data.Operations Research and Industrial Engineerin

Conversation Trees: A Grammar Model for Topic Structure in Forums

Online forum discussions proceed differently from face-to-face conversations and any single thread on an online forum contains posts on different subtopics. This work aims to characterize the content of a forum thread as a conversation tree of topics. We present models that jointly per- form two tasks: segment a thread into sub- parts, and assign a topic to each part. Our core idea is a definition of topic structure using probabilistic grammars. By leveraging the flexibility of two grammar formalisms, Context-Free Grammars and Linear Context-Free Rewriting Systems, our models create desirable structures for forum threads: our topic segmentation is hierarchical, links non-adjacent segments on the same topic, and jointly labels the topic during segmentation. We show that our models outperform a number of tree generation baselines

A Formal View on Training of Weighted Tree Automata by Likelihood-Driven State Splitting and Merging

The use of computers and algorithms to deal with human language, in both spoken and written form, is summarized by the term natural language processing (nlp). Modeling language in a way that is suitable for computers plays an important role in nlp. One idea is to use formalisms from theoretical computer science for that purpose. For example, one can try to find an automaton to capture the valid written sentences of a language. Finding such an automaton by way of examples is called training. In this work, we also consider the structure of sentences by making use of trees. We use weighted tree automata (wta) in order to deal with such tree structures. Those devices assign weights to trees in order to, for example, distinguish between good and bad structures. The well-known expectation-maximization algorithm can be used to train the weights for a wta while the state behavior stays fixed. As a way to adapt the state behavior of a wta, state splitting, i.e. dividing a state into several new states, and state merging, i.e. replacing several states by a single new state, can be used. State splitting, state merging, and the expectation maximization algorithm already were combined into the state splitting and merging algorithm, which was successfully applied in practice. In our work, we formalized this approach in order to show properties of the algorithm. We also examined a new approach – the count-based state merging algorithm – which exclusively relies on state merging. When dealing with trees, another important tool is binarization. A binarization is a strategy to code arbitrary trees by binary trees. For each of three different binarizations we showed that wta together with the binarization are as powerful as weighted unranked tree automata (wuta). We also showed that this is still true if only probabilistic wta and probabilistic wuta are considered.:How to Read This Thesis 1. Introduction 1.1. The Contributions and the Structure of This Work 2. Preliminaries 2.1. Sets, Relations, Functions, Families, and Extrema 2.2. Algebraic Structures 2.3. Formal Languages 3. Language Formalisms 3.1. Context-Free Grammars (CFGs) 3.2. Context-Free Grammars with Latent Annotations (CFG-LAs) 3.3. Weighted Tree Automata (WTAs) 3.4. Equivalences of WCFG-LAs and WTAs 4. Training of WTAs 4.1. Probability Distributions 4.2. Maximum Likelihood Estimation 4.3. Probabilities and WTAs 4.4. The EM Algorithm for WTAs 4.5. Inside and Outside Weights 4.6. Adaption of the Estimation of Corazza and Satta [CS07] to WTAs 5. State Splitting and Merging 5.1. State Splitting and Merging for Weighted Tree Automata 5.1.1. Splitting Weights and Probabilities 5.1.2. Merging Probabilities 5.2. The State Splitting and Merging Algorithm 5.2.1. Finding a Good π-Distributor 5.2.2. Notes About the Berkeley Parser 5.3. Conclusion and Further Research 6. Count-Based State Merging 6.1. Preliminaries 6.2. The Likelihood of the Maximum Likelihood Estimate and Its Behavior While Merging 6.3. The Count-Based State Merging Algorithm 6.3.1. Further Adjustments for Practical Implementations 6.4. Implementation of Count-Based State Merging 6.5. Experiments with Artificial Automata and Corpora 6.5.1. The Artificial Automata 6.5.2. Results 6.6. Experiments with the Penn Treebank 6.7. Comparison to the Approach of Carrasco, Oncina, and Calera-Rubio [COC01] 6.8. Conclusion and Further Research 7. Binarization 7.1. Preliminaries 7.2. Relating WSTAs and WUTAs via Binarizations 7.2.1. Left-Branching Binarization 7.2.2. Right-Branching Binarization 7.2.3. Mixed Binarization 7.3. The Probabilistic Case 7.3.1. Additional Preliminaries About WSAs 7.3.2. Constructing an Out-Probabilistic WSA from a Converging WSA 7.3.3. Binarization and Probabilistic Tree Automata 7.4. Connection to the Training Methods in Previous Chapters 7.5. Conclusion and Further Research A. Proofs for Preliminaries B. Proofs for Training of WTAs C. Proofs for State Splitting and Merging D. Proofs for Count-Based State Merging Bibliography List of Algorithms List of Figures List of Tables Index Table of Variable Name