Mark de Rooij

Wouter van Loon, Marjolein Fokkema, Frank de Vos et al.

Data for which a set of objects is described by multiple distinct feature sets (called views) is known as multi-view data. When missing values occur in multi-view data, all features in a view are likely to be missing simultaneously. This may lead to very large quantities of missing data which, especially when combined with high-dimensionality, can make the application of conditional imputation methods computationally infeasible. However, the multi-view structure could be leveraged to reduce the complexity and computational load of imputation. We introduce a new imputation method based on the existing stacked penalized logistic regression (StaPLR) algorithm for multi-view learning. It performs imputation in a dimension-reduced space to address computational challenges inherent to the multi-view context. We compare the performance of the new imputation method with several existing imputation algorithms in simulated data sets and a real data application. The results show that the new imputation method leads to competitive results at a much lower computational cost, and makes the use of advanced imputation algorithms such as missForest and predictive mean matching possible in settings where they would otherwise be computationally infeasible.

Kevin Kloos, Julian D. Karch, Quinten A. Meertens et al.

A quantifier is a supervised machine learning algorithm, focused on estimating the class prevalence in a dataset rather than labeling its individual observations. We introduce Continuous Sweep, a new parametric binary quantifier inspired by the well-performing Median Sweep, which is an ensemble method based on Adjusted Count estimators. We modified two aspects of Median Sweep: 1) using parametric class distributions instead of empirical distributions for the true and false positive rate; 2) using the mean instead of the median of a set of Adjusted Count estimates. These two modifications allow for a theoretical analysis of the bias and variance of Continuous Sweep. Furthermore, the expressions of bias and variance can be used to define optimal decision boundaries of the set of Adjusted count estimates to be used in the ensemble. We show in three simulation studies that Continuous Sweep outperforms the quantifiers in the group Classify, Count, and Correct, including Median Sweep, and is competitive with the two best quantifiers from the group Distribution Matchers. Also an empirical data set is analysed with these quantifiers showing similar performances.

Wouter van Loon, Frank de Vos, Marjolein Fokkema et al.

Multi-view data refers to a setting where features are divided into feature sets, for example because they correspond to different sources. Stacked penalized logistic regression (StaPLR) is a recently introduced method that can be used for classification and automatically selecting the views that are most important for prediction. We introduce an extension of this method to a setting where the data has a hierarchical multi-view structure. We also introduce a new view importance measure for StaPLR, which allows us to compare the importance of views at any level of the hierarchy. We apply our extended StaPLR algorithm to Alzheimer's disease classification where different MRI measures have been calculated from three scan types: structural MRI, diffusion-weighted MRI, and resting-state fMRI. StaPLR can identify which scan types and which derived MRI measures are most important for classification, and it outperforms elastic net regression in classification performance.

Mark de Rooij, Patrick J. F. Groenen

Logistic regression is a commonly used method for binary classification. Researchers often have more than a single binary response variable and simultaneous analysis is beneficial because it provides insight into the dependencies among response variables as well as between the predictor variables and the responses. Moreover, in such a simultaneous analysis the equations can lend each other strength, which might increase predictive accuracy. In this paper, we propose the MELODIC family for simultaneous binary logistic regression modeling. In this family, the regression models are defined in a Euclidean space of reduced dimension, based on a distance rule. The model may be interpreted in terms of logistic regression coefficients or in terms of a biplot. We discuss a fast iterative majorization (or MM) algorithm for parameter estimation. Two applications are shown in detail: one relating personality characteristics to drug consumption profiles and one relating personality characteristics to depressive and anxiety disorders. We present a thorough comparison of our MELODIC family with alternative approaches for multivariate binary data.

Wouter van Loon, Marjolein Fokkema, Botond Szabo et al.

Multi-view stacking is a framework for combining information from different views (i.e. different feature sets) describing the same set of objects. In this framework, a base-learner algorithm is trained on each view separately, and their predictions are then combined by a meta-learner algorithm. In a previous study, stacked penalized logistic regression, a special case of multi-view stacking, has been shown to be useful in identifying which views are most important for prediction. In this article we expand this research by considering seven different algorithms to use as the meta-learner, and evaluating their view selection and classification performance in simulations and two applications on real gene-expression data sets. Our results suggest that if both view selection and classification accuracy are important to the research at hand, then the nonnegative lasso, nonnegative adaptive lasso and nonnegative elastic net are suitable meta-learners. Exactly which among these three is to be preferred depends on the research context. The remaining four meta-learners, namely nonnegative ridge regression, nonnegative forward selection, stability selection and the interpolating predictor, show little advantages in order to be preferred over the other three.

Wouter van Loon, Marjolein Fokkema, Botond Szabo et al.

In biomedical research, many different types of patient data can be collected, such as various types of omics data and medical imaging modalities. Applying multi-view learning to these different sources of information can increase the accuracy of medical classification models compared with single-view procedures. However, collecting biomedical data can be expensive and/or burdening for patients, so that it is important to reduce the amount of required data collection. It is therefore necessary to develop multi-view learning methods which can accurately identify those views that are most important for prediction. In recent years, several biomedical studies have used an approach known as multi-view stacking (MVS), where a model is trained on each view separately and the resulting predictions are combined through stacking. In these studies, MVS has been shown to increase classification accuracy. However, the MVS framework can also be used for selecting a subset of important views. To study the view selection potential of MVS, we develop a special case called stacked penalized logistic regression (StaPLR). Compared with existing view-selection methods, StaPLR can make use of faster optimization algorithms and is easily parallelized. We show that nonnegativity constraints on the parameters of the function which combines the views play an important role in preventing unimportant views from entering the model. We investigate the performance of StaPLR through simulations, and consider two real data examples. We compare the performance of StaPLR with an existing view selection method called the group lasso and observe that, in terms of view selection, StaPLR is often more conservative and has a consistently lower false positive rate.