arXiv subjects

Hildo Bijl

Publications and source records attributed to Hildo Bijl.

7 recordsLinked to original sources

arXiv2026

Exploring Student Expectations and Confidence in Learning Analytics

Learning Analytics (LA) is nowadays ubiquitous in many educational systems, providing the ability to collect and analyze student data in order to understand and optimize learning and the environments in which it occurs. On the other hand, the collection of data requires to comply with the growing demand regarding privacy legislation. In this paper, we use the Student Expectation of Learning Analytics Questionnaire (SELAQ) to analyze the expectations and confidence of students from different faculties regarding the processing of their data for Learning Analytics purposes. This allows us to identify four clusters of students through clustering algorithms: Enthusiasts, Realists, Cautious and Indifferents. This structured analysis provides valuable insights into the acceptance and criticism of Learning Analytics among students.

cs.LG↗

arXiv2025

Structuring Competency-Based Courses Through Skill Trees

Computer science education has seen two important trends. One has been a shift from raw theory towards skills: competency-based teaching. Another has been increasing student numbers, with as a result more automation in teaching. When automating education, it is crucial to properly structure courses, both to manage digitalized educational resources and to facilitate automated coaching algorithms. Currently existing structuring methodologies are focused around theory and not around skills, and are incapable of modeling the dependency links between skills. Because of this, a new didactic framework is needed. This paper presents a new method of structuring educational contents around skills: something that a student is expected to be able to do. It defines Skill Trees that show dependencies between skills, and subsequently couples these to Concept Trees that contain intuitive ideas/notional machines. Due to the algorithmic nature of computer science, this step-wise approach is especially well-suited to this field of education. Next to formal definitions on Skill Trees and Concept Trees, guidelines are given on how to design them and how to plan a course using them. The Skill Trees framework has been applied to improve the structure of a university database course. Student interviews indicated reduced confusion/stress and less study time required for students to meet their desired skill level.

cs.CY↗

arXiv2025

Tracking student skills real-time through a continuous-variable dynamic Bayesian network

The field of Knowledge Tracing is focused on predicting the success rate of a student for a given skill. Modern methods like Deep Knowledge Tracing provide accurate estimates given enough data, but being based on neural networks they struggle to explain how these estimates are formed. More classical methods like Dynamic Bayesian Networks can do this, but they cannot give data on the accuracy of their estimates and often struggle to incorporate new observations in real-time due to their high computational load. This paper presents a novel method, Performance Distribution Tracing (PDT), in which the distribution of the success rate is traced live. It uses a Dynamic Bayesian Network with continuous random variables as nodes. By tracing the success rate distribution, there is always data available on the accuracy of any success rate estimation. In addition, it makes it possible to combine data from similar/related skills to come up with a more informed estimate of success rates. This makes it possible to predict exercise success rates, providing both explainability and an accuracy indication, even when an exercise requires a combination of different skills to solve. And through the use of the beta distribution functions as conjugate priors, all distributions are available in analytical form, allowing efficient online updates upon new observations. Experiments have shown that the resulting estimates generally feel sufficiently accurate to end-users such that they accept recommendations based on them.

stat.ML↗

arXiv2018

Optimal controller/observer gains of discounted-cost LQG systems

The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds on from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.

eess.SY↗

arXiv2017

System Identification through Online Sparse Gaussian Process Regression with Input Noise

There has been a growing interest in using non-parametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally intensive, (2) it cannot efficiently implement newly obtained measurements online, and (3) it cannot deal with stochastic (noisy) input points. In this paper we present an algorithm tackling all these three issues simultaneously. The resulting Sparse Online Noisy Input GP (SONIG) regression algorithm can incorporate new noisy measurements in constant runtime. A comparison has shown that it is more accurate than similar existing regression algorithms. When applied to non-linear black-box system modeling, its performance is competitive with existing non-linear ARX models.

stat.ML↗

arXiv2017

A sequential Monte Carlo approach to Thompson sampling for Bayesian optimization

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point to try out. This recommendation is usually selected by optimizing a given acquisition function. After a sufficient number of measurements, a recommendation about the maximum is made. However, a key realization is that the maximum of a Gaussian process is not a deterministic point, but a random variable with a distribution of its own. This distribution cannot be calculated analytically. Our main contribution is an algorithm, inspired by sequential Monte Carlo samplers, that approximates this maximum distribution. Subsequently, by taking samples from this distribution, we enable Thompson sampling to be applied to (armed-bandit) optimization problems with a continuous input space. All this is done without requiring the optimization of a nonlinear acquisition function. Experiments have shown that the resulting optimization method has a competitive performance at keeping the cumulative regret limited.

stat.ML↗

arXiv2016

Mean and variance of the LQG cost function

Linear Quadratic Gaussian (LQG) systems are well-understood and methods to minimize the expected cost are readily available. Less is known about the statistical properties of the resulting cost function. The contribution of this paper is a set of analytic expressions for the mean and variance of the LQG cost function. These expressions are derived using two different methods, one using solutions to Lyapunov equations and the other using only matrix exponentials. Both the discounted and the non-discounted cost function are considered, as well as the finite-time and the infinite-time cost function. The derived expressions are successfully applied to an example system to reduce the probability of the cost exceeding a given threshold.

eess.SY↗