We introduce Locally Interpretable Tree Boosting (LitBoost), a tree boosting model tailored to applications where the data comes from several heterogeneous yet known groups with a limited number of observations per group. LitBoost constraints the complexity of a Gradient Boosted Trees model in a way that allows us to express the final model as a set of local Generalized Additive Models, yielding significant interpretability benefits while still maintaining some of the predictive power of a Gradient Boosted Trees model. We use house price prediction as a motivating example and demonstrate the performance of LitBoost on a data set of N=14382 observations from 15 different city districts in Oslo (Norway). We also test the robustness of LitBoost in an extensive simulation study on a synthetic data set.

New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets and enables fitting of both proportional and non-proportional extensions of the Cox model. Through simulation studies, the proposed loss function is verified to be a good approximation for the Cox partial log-likelihood. The proposed methodology is compared to existing methodologies on real-world data sets and is found to be highly competitive, typically yielding the best performance in terms of Brier score and binomial log-likelihood. A python package for the proposed methods is available at https://github.com/havakv/pycox.

Clicking data, which exists in abundance and contains objective user preference information, is widely used to produce personalized recommendations in web-based applications. Current popular recommendation algorithms, typically based on matrix factorizations, often focus on achieving high accuracy. While achieving good clickthrough rates, diversity of the recommended items is often overlooked. Moreover, most algorithms do not produce interpretable uncertainty quantifications of the recommendations. In this work, we propose the Bayesian Mallows for Clicking Data (BMCD) method, which simultaneously considers accuracy and diversity. BMCD augments clicking data into compatible full ranking vectors by enforcing all the clicked items clicked by a user to be top-ranked regardless of their rarity. User preferences are learned using a Mallows ranking model. Bayesian inference leads to interpretable uncertainties of each individual recommendation, and we also propose a method to make personalized recommendations based on such uncertainties. With a simulation study and a real life data example, we demonstrate that compared to state-of-the-art matrix factorization, BMCD makes personalized recommendations with similar accuracy, while achieving much higher level of diversity, and producing interpretable and actionable uncertainty estimation.

MOTIVATION: Missing values are problematic for the analysis of microarray data. Imputation methods have been compared in terms of the similarity between imputed and true values in simulation experiments and not of their influence on the final analysis. The focus has been on missing at random, while entries are missing also not at random. RESULTS: We investigate the influence of imputation on the detection of differentially expressed genes from cDNA microarray data. We apply ANOVA for microarrays and SAM and look to the differentially expressed genes that are lost because of imputation. We show that this new measure provides useful information that the traditional root mean squared error cannot capture. We also show that the type of missingness matters: imputing 5% missing not at random has the same effect as imputing 10-30% missing at random. We propose a new method for imputation (LinImp), fitting a simple linear model for each channel separately, and compare it with the widely used KNNimpute method. For 10% missing at random, KNNimpute leads to twice as many lost differentially expressed genes as LinImp. AVAILABILITY: The R package for LinImp is available at http://folk.uio.no/idasch/imp.