Word problems are an established technique for teaching mathematical modeling skills in K-12 education. However, many students find word problems unconnected to their lives, artificial, and uninteresting. Most students find them much more difficult than the corresponding symbolic representations. To account for this phenomenon, an ideal pedagogy might involve an individually crafted progression of unique word problems that form a personalized plot. We propose a novel technique for automatic generation of personalized word problems. In our system, word problems are generated from general specifications using answer-set programming (ASP). The specifications include tutor requirements (properties of a mathematical model), and student requirements (personalization, characters, setting). Our system takes a logical encoding of the specification, synthesizes a word problem narrative and its mathematical model as a labeled logical plot graph, and realizes the problem in natural language. Human judges found our problems as solvable as the textbook problems, with a slightly more artificial language.

When a transition probability matrix is represented as the product of two stochastic matrices, swapping the factors of the multiplication yields another transition matrix that retains some fundamental characteristics of the original. Since the new matrix can be much smaller than its precursor, replacing the former for the latter can lead to significant savings in terms of computational effort. This strategy, dubbed the "stochastic-factorization trick," can be used to compute the stationary distribution of a Markov chain, to determine the fundamental matrix of an absorbing chain, and to compute a decision policy via dynamic programming or reinforcement learning. In this paper we show that the stochastic-factorization trick can also provide benefits in terms of the number of samples needed to estimate a transition matrix. We introduce a probabilistic interpretation of a stochastic factorization and build on the resulting model to develop an algorithm to compute the factorization directly from data. If the transition matrix can be well approximated by a low-order stochastic factorization, estimating its factors instead of the original matrix reduces significantly the number of parameters to be estimated. Thus, when compared to estimating the transition matrix directly via maximum likelihood, the proposed method is able to compute approximations of roughly the same quality using less data. We illustrate the effectiveness of the proposed algorithm by using it to help a reinforcement learning agent learn how to play the game of blackjack.

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of non-crossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parametrization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit.

We present an approach to Intelligent Tutoring Systems which adaptively personalizes sequences of learning activities to maximize skills acquired by students, taking into account the limited time and motivational resources. At a given point in time, the system proposes to the students the activity which makes them progress faster. We introduce two algorithms that rely on the empirical estimation of the learning progress, RiARiT that uses information about the difficulty of each exercise and ZPDES that uses much less knowledge about the problem. The system is based on the combination of three approaches. First, it leverages recent models of intrinsically motivated learning by transposing them to active teaching, relying on empirical estimation of learning progress provided by specific activities to particular students. Second, it uses state-of-the-art Multi-Arm Bandit (MAB) techniques to efficiently manage the exploration/exploitation challenge of this optimization process. Third, it leverages expert knowledge to constrain and bootstrap initial exploration of the MAB, while requiring only coarse guidance information of the expert and allowing the system to deal with didactic gaps in its knowledge. The system is evaluated in a scenario where 7-8 year old schoolchildren learn how to decompose numbers while manipulating money. Systematic experiments are presented with simulated students, followed by results of a user study across a population of 400 school children.

With few exceptions, the field of Machine Learning (ML) research has largely ignored the browser as a computational engine. Beyond an educational resource for ML, the browser has vast potential to not only improve the state-of-the-art in ML research, but also, inexpensively and on a massive scale, to bring sophisticated ML learning and prediction to the public at large. This paper introduces MLitB, a prototype ML framework written entirely in JavaScript, capable of performing large-scale distributed computing with heterogeneous classes of devices. The development of MLitB has been driven by several underlying objectives whose aim is to make ML learning and usage ubiquitous (by using ubiquitous compute devices), cheap and effortlessly distributed, and collaborative. This is achieved by allowing every internet capable device to run training algorithms and predictive models with no software installation and by saving models in universally readable formats. Our prototype library is capable of training deep neural networks with synchronized, distributed stochastic gradient descent. MLitB offers several important opportunities for novel ML research, including: development of distributed learning algorithms, advancement of web GPU algorithms, novel field and mobile applications, privacy preserving computing, and green grid-computing. MLitB is available as open source software.

We introduce Bayesian optimization, a technique developed for optimizing time-consuming engineering simulations and for fitting machine learning models on large datasets. Bayesian optimization guides the choice of experiments during materials design and discovery to find good material designs in as few experiments as possible. We focus on the case when materials designs are parameterized by a low-dimensional vector. Bayesian optimization is built on a statistical technique called Gaussian process regression, which allows predicting the performance of a new design based on previously tested designs. After providing a detailed introduction to Gaussian process regression, we introduce two Bayesian optimization methods: expected improvement, for design problems with noise-free evaluations; and the knowledge-gradient method, which generalizes expected improvement and may be used in design problems with noisy evaluations. Both methods are derived using a value-of-information analysis, and enjoy one-step Bayes-optimality.

We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. As our two-sample test statistic, we use an unbiased estimate of the maximum mean discrepancy, which is the centerpiece of the nonparametric kernel two-sample test proposed by Gretton et al. (2012). We compare to the adversarial nets framework introduced by Goodfellow et al. (2014), in which learning is a two-player game between a generator network and an adversarial discriminator network, both trained to outwit the other. From this perspective, the MMD statistic plays the role of the discriminator. In addition to empirical comparisons, we prove bounds on the generalization error incurred by optimizing the empirical MMD.

Students in a Massive Open Online Course (MOOC) interact with each other and the course staff through online discussion forums. While discussion forums play a central role in MOOCs, they also pose a challenge for instructors. The large number of student posts makes it difficult for an instructor to know where to intervene to answer questions, resolve issues, and provide feedback. In this work, we focus on automatically predicting speech acts in MOOC forum posts. Our speech act categories describe the purpose or function of the post in the ongoing discussion. Specifically, we address three main research questions. First, we investigate whether crowdsourced workers can reliably label MOOC forum posts using our speech act definitions. Second, we investigate whether our speech acts can help predict instructor interventions and assignment completion and performance. Finally, we investigate which types of features (derived from the post content, author, and surrounding context) are most effective for predicting our different speech act categories.

Representing biology textbook knowledge involves handling numerous concepts that have multiple possible states, for example, developmental states such as embryo, juvenile and larva; system states such as homeostasis and equilibrium; states of chromosomes such as chromatin, nicked, etc. Though substantial research exists on formalisms for representing states, relatively less work exists on ontologically representing them in a complex domain. Our findings include: (a) the word state in natural language is used with both entities and events which requires that we generalize the traditional definition of state to distinguish between an entity state and an event state; (b) an abstract modeling pattern called the process flow diagram that provides a practically achievable target for the output of natural language processing programs, and enables knowledge authoring by domain experts that can be compiled into a well-known background theory based on action languages. The background theory, combined with reasoning methods from the action language, allows building tools that simulate processes and answer sophisticated questions about process interruptions.

I draw the reader's attention to machine teaching, the problem of finding an optimal training set given a machine learning algorithm and a target model. In addition to generating fascinating mathematical questions for computer scientists to ponder, machine teaching holds the promise of enhancing education and personnel training. The Socratic dialogue style aims to stimulate critical thinking.