Data from populations of systems are prevalent in many industrial applications. Machines and infrastructure are increasingly instrumented with sensing systems, emitting streams of telemetry data with complex interdependencies. In practice, data-centric monitoring procedures tend to consider these assets (and respective models) as distinct -- operating in isolation and associated with independent data. In contrast, this work captures the statistical correlations and interdependencies between models of a group of systems. Utilising a Bayesian multilevel approach, the value of data can be extended, since the population can be considered as a whole, rather than constituent parts. Most interestingly, domain expertise and knowledge of the underlying physics can be encoded in the model at the system, subgroup, or population level. We present an example of acoustic emission (time-of-arrival) mapping for source location, to illustrate how multilevel models naturally lend themselves to representing aggregate systems in engineering. In particular, we focus on constraining the combined models with domain knowledge to enhance transfer learning and enable further insights at the population level.

Abstract: Multilevel linear models allow flexible statistical modelling of complex data with different levels of stratification. Identifying the most appropriate model from the large set of possible candidates is a challenging problem. In the Bayesian setting, the standard approach is a comparison of models using the model evidence or the Bayes factor. However, in all but the simplest of cases, direct computation of these quantities is impossible. Markov Chain Monte Carlo approaches are widely used, such as sequential Monte Carlo, but it is not always clear how well such techniques perform in practice.

Procrastination, the irrational delay of tasks, is a common occurrence in online learning. Potential negative consequences include higher risk of drop-outs, increased stress, and reduced mood. Due to the rise of learning management systems and learning analytics, indicators of such behavior can be detected, enabling predictions of future procrastination and other dilatory behavior. However, research focusing on such predictions is scarce. Moreover, studies involving different types of predictors and comparisons between the predictive performance of various methods are virtually non-existent. In this study, we aim to fill these research gaps by analyzing the performance of multiple machine learning algorithms when predicting the delayed or timely submission of online assignments in a higher education setting with two categories of predictors: subjective, questionnaire-based variables and objective, log-data based indicators extracted from a learning management system. The results show that models with objective predictors consistently outperform models with subjective predictors, and a combination of both variable types perform slightly better. For each of these three options, a different approach prevailed (Gradient Boosting Machines for the subjective, Bayesian multilevel models for the objective, and Random Forest for the combined predictors). We conclude that careful attention should be paid to the selection of predictors and algorithms before implementing such models in learning management systems.

Multilevel modeling is a technique for dealing with data that has been clustered or grouped. Data with repeated measures can also be analyzed using multilevel modeling. For example, If we are testing the blood pressure of a group of patients on a weekly basis, we can think of the succeeding measurements as being grouped inside the individual subjects. It can handle data with different measurement periods from one subject to the next. A multilevel model in machine learning can be applied in such cases that models the parameters that vary at more than one level.

Many data sets contain an inherent multilevel structure, for example, because of repeated measurements of the same observational units. Taking this structure into account is critical for the accuracy and calibration of any statistical analysis performed on such data. However, the large number of possible model configurations hinders the use of multilevel models in practice. In this work, we propose a flexible framework for efficiently assessing differences between the levels of given grouping variables in the data. The assessed group heterogeneity is valuable in choosing the relevant group coefficients to consider in a multilevel model. Our empirical evaluations demonstrate that the framework can reliably identify relevant multilevel components in both simulated and real data sets.

I have learned many of curve fitting models in the past, including their technical and mathematical details. Now I have been working on real-world problems and I face a great shortcoming: which method to use. As an example, I have to predict the demand of a product. I have a time series collected over the last 8 years. I have this for 9 products.

In applications including chemoinformatics, bioinfor- matics, information retrieval, text classification, com- puter vision and others, a variety of common issues have been identified involving frequency of occurrence, variation and similarities of instances, and lack of pre- cise class labels. These issues continue to be important hurdles in machine intelligence and my doctoral thesis focuses on developing robust machine learning models that address the same.