Jan Pablo Burgard

Decision trees are one of the most popular methods for solving classification problems, mainly because of their good interpretability properties. Moreover, due to advances in recent years in mixed-integer optimization, several models have been proposed to formulate the problem of computing optimal classification trees. The goal is, given a set of labeled points, to split the feature space with hyperplanes and assign a class to each part of the resulting partition. In certain scenarios, however, labels are only available for a subset of the given points. Additionally, this subset may be non-representative, such as in the case of self-selection in a survey. Semi-supervised decision trees tackle the setting of labeled and unlabeled data and often contribute to enhancing the reliability of the results. Furthermore, undisclosed sources may provide extra information about the size of the classes. We propose a mixed-integer linear optimization model for computing semi-supervised optimal classification trees that cover the setting of labeled and unlabeled data points as well as the overall number of points in each class for a binary classification. Our numerical results show that our approach leads to a better accuracy and a better Matthews correlation coefficient for biased samples compared to other optimal classification trees, even if only few labeled points are available.

Cluster sampling is a widely used sampling design for survey data selection. The collected data provide information on both the individual units and the clusters. The parameter of interest is an unknown population total at the unit level. Due to the cluster sampling design, the model-assisted generalized regression estimator can be established either at the unit or at the cluster level. The unit-level estimator, however, ignores the cluster sampling design. The cluster-level estimator relies solely on the per-cluster aggregated information, which leads to the loss of individual patterns and the risk of ecological fallacy. As a remedy, in this paper we propose a hybrid generalized regression estimator as a new approach that balances between unit- and cluster-level modeling. It is implemented at the unit level like the study variable. However, in addition to the information of the units, it also takes into account the information of the other cluster members.

Agent-based models (ABMs) are powerful tools for simulating disease spread, relying on individual-level representations and interaction rules from which emergent dynamics arise. These rules need to be accurately specified as minor differences can lead to vastly different disease dynamics. An important component in ABMs is the contact behaviour. To decrease the computational complexity the contact behaviour is often assumed as random mixing within settings. Here, individuals randomly contact other individuals associated with the same settings, such as colleagues in their workplace, where the setting associations are based on empirical data such as census data. However, the validity of the random mixing assumption within settings remains unclear. We address this gap by comparing the contact structure in a large-scale ABM (GEMS) with empirical contact survey data (COVIMOD). We compare the age contact matrices for households, schools, workplaces, all remaining contact settings combined, and all contacts combined. This includes calculating the difference matrix and the sum of squared errors (SSE), i.e. the element-wise squared difference. Our results demonstrate that random mixing in settings generated based on known age-compositions like households (SSE:0.7(95%CI0.4–0.9)), schools (SSE:0.7(95%CI:0.3–1.1)) and workplaces (SSE:0.5(95%CI:0.2-0.7)), can capture the basic interaction patterns. However, it fails to account for age-related variations in contact numbers, leading to discrepancies between the simulated and observed contact behaviour. The largest differences arise for contacts outside of households, schools and workplaces (SSE:3.8(95%CI:1.2–6.5)), due to the model’s structure. These contacts are modelled as random regional contacts not capturing the age-structured behaviour observed in COVIMOD. We conclude that random mixing in accurately defined settings provides an approximation for contact structures in settings where the age-structure of associated individuals is similar to the observed contact structure. For settings where the age-structure deviates from the contact structure, advanced methods are required to represent real-world contact structures. Author Summary: Infectious disease modelling is a prominent tool for understanding disease spread and evaluating potential countermeasures. Agent-based models simulate the behaviour of individuals based on a set of simple rules and allow for a detailed representation of disease transmissions. One essential rule is the contact behaviour of individuals, which determines the potential transmission pathways of pathogens. Agent-based models often assume simple random-mixing of individuals in the locations they are associated with, such as their households or workplaces. We investigate if this assumption is appropriate by comparing the contact structure simulated in the agent-based model GEMS with the contact data gathered through the Germany-wide COVIMOD survey. We find that the random mixing can serve as an approximation for settings such as household, schools and workplaces where the contact structure is similar to the age structure of the individuals present in the setting. However, discrepancies arise as random mixing cannot account for the differing number of contacts by age or household size. We identified the most discrepancies for contacts outside of the household, school and workplace. Here, the highly age-structured contact behaviour observed in COVIMOD strongly deviates from the random mixing of all ages observed in GEMS.

Zusammenfassung: In dynamischen Mikrosimulationen wird die Entwicklung von Populationen auf der Ebene von Personen und Haushalten simuliert, wodurch die Populationsdynamik viel detaillierter abgebildet werden kann als mit herkömmlichen Prognosemodellen auf Makroebene. Diese feine Granularität führt jedoch dazu, dass die Einflüsse von Modellierungsentscheidungen und Modellunsicherheiten deutlich stärker hervortreten. Daher ist eine eingehende Auseinandersetzung mit den verschiedenen Arten von Unsicherheit im Simulationsmodell erforderlich. Wir schlagen vor, varianzbasierte Sensitivitätsanalysen zur Analyse von Unsicherheiten und Szenarien in Mikrosimulationen einzusetzen. Diese sind bereits ein etabliertes Instrument zur Untersuchung von Unsicherheiten, etwa bei der Messung zusammengesetzter Indikatoren. Im Kontext von Mikrosimulationen fehlt bisher eine klare Formulierung und anwendungsorientierte Anleitung. Anhand eines Praxisbeispiels wird exemplarisch gezeigt, wie Unsicherheiten mit Sensitivitätsanalysen bewertet werden können. Zudem wird aufgezeigt, dass Sensitivitätsanalysen auch zur Abwägung verschiedener politischer Maßnahmen genutzt werden können. Dies ist insbesondere dann unabdingbar, wenn verschiedene Maßnahmen mit intertemporalen oder interregionalen Wechselwirkungen untersucht werden.

In this paper, we propose , a package providing a framework for fair classification in machine learning. In this framework, the fair learning process is divided into three stages. Each stage aims to reduce unfairness, such as disparate impact and disparate mistreatment, in the final prediction. For the pre-processing stage, we present a resampling method that addresses unfairness coming from data imbalances. The in-processing phase consists of a classification method. This can be either one coming from the package, or a user-defined one. For this phase, we incorporate fair ML methods that can handle unfairness to a certain degree through their optimization process. In the post-processing, we discuss the choice of the cutoff value for fair prediction. With simulations, we show the performance of the single phases and their combinations.

Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify a new given point. In some scenarios, however, labels are only accessible for a proper subset of the given points. Moreover, this subset can be non-representative, e.g., due to collection bias. Semi-supervised learning considers the setting of labeled and unlabeled data and often improves the reliability of the results. In addition, it can be possible to obtain additional information about class sizes from undisclosed sources. We propose a mixed-integer linear optimization model for computing a semi-supervised random forest that covers the setting of labeled and unlabeled data points as well as the overall number of points in each class for a binary classification. Since the solution time rapidly grows as the number of variables increases, we present some problem-tailored preprocessing techniques and an intuitive branching rule. Our numerical results show that our approach leads to better accuracy and a better Matthews correlation coefficient for biased samples compared to random forests by majority vote, even if only a few labeled points are available.