Knowledge Tracing (KT), which aims to model student knowledge level and predict their performance, is one of the most important applications of user modeling. Modern KT approaches model and maintain an up-to-date state of student knowledge over a set of course concepts according to students' historical performance in attempting the problems. However, KT approaches were designed to model knowledge by observing relatively small problem-solving steps in Intelligent Tutoring Systems. While these approaches were applied successfully to model student knowledge by observing student solutions for simple problems, they do not perform well for modeling complex problem solving in students.M ost importantly, current models assume that all problem attempts are equally valuable in quantifying current student knowledge.However, for complex problems that involve many concepts at the same time, this assumption is deficient. In this paper, we argue that not all attempts are equivalently important in discovering students' knowledge state, and some attempts can be summarized together to better represent student performance. We propose a novel student knowledge tracing approach, Granular RAnk based TEnsor factorization (GRATE), that dynamically selects student attempts that can be aggregated while predicting students' performance in problems and discovering the concepts presented in them. Our experiments on three real-world datasets demonstrate the improved performance of GRATE, compared to the state-of-the-art baselines, in the task of student performance prediction. Our further analysis shows that attempt aggregation eliminates the unnecessary fluctuations from students' discovered knowledge states and helps in discovering complex latent concepts in the problems.

Although virtue ethics has repeatedly been proposed as a suitable framework for the development of artificial moral agents (AMAs), it has been proven difficult to approach from a computational perspective. In this work, we present the first technical implementation of artificial virtuous agents (AVAs) in moral simulations. First, we review previous conceptual and technical work in artificial virtue ethics and describe a functionalistic path to AVAs based on dispositional virtues, bottom-up learning, and top-down eudaimonic reward. We then provide the details of a technical implementation in a moral simulation based on a tragedy of the commons scenario. The experimental results show how the AVAs learn to tackle cooperation problems while exhibiting core features of their theoretical counterpart, including moral character, dispositional virtues, learning from experience, and the pursuit of eudaimonia. Ultimately, we argue that virtue ethics provides a compelling path toward morally excellent machines and that our work provides an important starting point for such endeavors.

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.

The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, where the weights correspond to the utility being chosen. By choosing the utility function for expected improvement (EI), LFBO outperforms various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also effectively leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.

You wake up one morning feeling a bit unwell and you decide to pay a visit to the physician. The physician after basic examinations runs some tests for a rare disease which happens to only 1 in a thousand people.

A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and play a vital role in many industrial modeling areas. LVM can be generally divided into statistical learning-based classic LVM and neural networks-based deep LVM (DLVM). We first discuss the definitions, theories and applications of classic LVMs in detail, which serves as both a comprehensive tutorial and a brief application survey on classic LVMs. Then we present a thorough introduction to current mainstream DLVMs with emphasis on their theories and model architectures, soon afterwards provide a detailed survey on industrial applications of DLVMs. The aforementioned two types of LVM have obvious advantages and disadvantages. Specifically, classic LVMs have concise principles and good interpretability, but their model capacity cannot address complicated tasks. Neural networks-based DLVMs have sufficient model capacity to achieve satisfactory performance in complex scenarios, but it comes at sacrifices in model interpretability and efficiency. Aiming at combining the virtues and mitigating the drawbacks of these two types of LVMs, as well as exploring non-neural-network manners to build deep models, we propose a novel concept called lightweight deep LVM (LDLVM). After proposing this new idea, the article first elaborates the motivation and connotation of LDLVM, then provides two novel LDLVMs, along with thorough descriptions on their principles, architectures and merits. Finally, outlooks and opportunities are discussed, including important open questions and possible research directions.

In this thesis, we research learning algorithms for optimal decision making in two different contexts, Reinforcement Learning in Part I and Auction Design in Part II. Reinforcement learning (RL) is an area of machine learning that is concerned with how an agent should act in an environment in order to maximize its cumulative reward over time. In Chapter 2, inspired by statistical physics, we develop a novel approach to Reinforcement Learning (RL) that not only learns optimal policies with enhanced desirable properties but also sheds new light on maximum entropy RL. In Chapter 3, we tackle the generalization problem in RL using a Bayesian perspective. We show that imperfect knowledge of the environments dynamics effectively turn a fully-observed Markov Decision Process (MDP) into a Partially Observed MDP (POMDP) that we call the Epistemic POMDP. Informed by this observation, we develop a new policy learning algorithm LEEP which has improved generalization properties. Designing an incentive compatible, individually rational auction that maximizes revenue is a challenging and intractable problem. Recently, deep learning based approaches have been proposed to learn optimal auctions from data. While successful, this approach suffers from a few limitations, including sample inefficiency, lack of generalization to new auctions, and training difficulties. In Chapter 4, we construct a symmetry preserving neural network architecture, EquivariantNet, suitable for anonymous auctions. EquivariantNet is not only more sample efficient but is also able to learn auction rules that generalize well to other settings. In Chapter 5, we propose a novel formulation of the auction learning problem as a two player game. The resulting learning algorithm, ALGNet, is easier to train, more reliable and better suited for non stationary settings.

Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the dynamics are affected by extremely slow time dependencies. This situation becomes critical when dealing with low-dimensional clustered datasets, where the time required to sample ergodically the trained models becomes computationally prohibitive. In this work, we show that this divergence of Monte Carlo mixing times is related to a phenomenon of phase coexistence, similar to that which occurs in physics near a first-order phase transition. We show that sampling the equilibrium distribution using the Markov chain Monte Carlo method can be dramatically accelerated when using biased sampling techniques, in particular the Tethered Monte Carlo (TMC) method. This sampling technique efficiently solves the problem of evaluating the quality of a given trained model and generating new samples in a reasonable amount of time. Moreover, we show that this sampling technique can also be used to improve the computation of the log-likelihood gradient during training, leading to dramatic improvements in training RBMs with artificial clustered datasets. On real low-dimensional datasets, this new training method fits RBM models with significantly faster relaxation dynamics than those obtained with standard PCD recipes. We also show that TMC sampling can be used to recover the free-energy profile of the RBM. This proves to be extremely useful to compute the probability distribution of a given model and to improve the generation of new decorrelated samples in slow PCD-trained models.

Reinforcement learning (RL) in partially observable syste ms is a challenging problem. While partially observable Markov decision process (POMDP) is a versatile fra mework, POMDPs are generally hard to learn, primarily because the optimal policy depends on the entire h istory of the process [ 40, 28 ]. Due to its fundamental hardness, it is important to consider sub-classes of POMDPs that allow tractable solutions for a variety of applications. We are interested in a special and p revalent sub-class of POMDPs where the latent (unobservable) parts of the system remain static in each epi sode. Specifically, we consider the framework of Latent MDPs (LMDP s), which has been studied in a few several works ( e.g., [ 8, 5, 22, 41, 30 ]). In LMDPs, one MDP is randomly chosen from M possible candidate models at the beginning of every episode, and an agent intera cts with the chosen MDP for H time steps of an episode. However, the identity of the chosen MDP is unknown t o the agent, which we call the latent contexts . To learn near-optimal policies with latent contexts, exist ing POMDP solutions would require strong assumptions on reachability of the system ( e.g., [ 2, 21 ]) or certain separability assumptions ( e.g., see conditions Most work is done while the author is at The University of Texa s at Austin.

Data streams are often defined as large amounts of data flowing continuously at high speed. Moreover, these data are likely subject to changes in data distribution, known as concept drift. Given all the reasons mentioned above, learning from streams is often online and under restrictions of memory consumption and run-time. Although many classification algorithms exist, most of the works published in the area use Naive Bayes (NB) and Hoeffding Trees (HT) as base learners in their experiments. This article proposes an in-depth evaluation of k-Nearest Neighbors (k-NN) as a candidate for classifying data streams subjected to concept drift. It also analyses the complexity in time and the two main parameters of k-NN, i.e., the number of nearest neighbors used for predictions (k), and window size (w). We compare different parameter values for k-NN and contrast it to NB and HT both with and without a drift detector (RDDM) in many datasets. We formulated and answered 10 research questions which led to the conclusion that k-NN is a worthy candidate for data stream classification, especially when the run-time constraint is not too restrictive.