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The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
Random forest is a classification algorithm well suited for microarray data: it shows excellent performance even when most predictive variables are noise, can be used when the number of variables is much larger than the number of…
It is becoming increasingly important for machine learning methods to make predictions that are interpretable as well as accurate. In many practical applications, it is of interest which features and feature interactions are relevant to the…
Interpretable machine learning has emerged as central in leveraging artificial intelligence within high-stakes domains such as healthcare, where understanding the rationale behind model predictions is as critical as achieving high…
This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which…
Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…
In this paper, error estimates of classification Random Forests are quantitatively assessed. Based on the initial theoretical framework built by Bates et al. (2023), the true error rate and expected error rate are theoretically and…
Random forests are widely used in regression. However, the decision trees used as base learners are poor approximators of linear relationships. To address this limitation we propose RaFFLE (Random Forest Featuring Linear Extensions), a…
It has been postulated and observed in practice that for prediction problems in which covariate data can be naturally partitioned into clusters, ensembling algorithms based on suitably aggregating models trained on individual clusters often…
We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many…
This paper promotes the use of random forests as versatile tools for estimating spatially disaggregated indicators in the presence of small area-specific sample sizes. Small area estimators are predominantly conceptualized within the…
Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…
We establish the consistency of an algorithm of Mondrian Forests, a randomized classification algorithm that can be implemented online. First, we amend the original Mondrian Forest algorithm, that considers a fixed lifetime parameter.…
Random forests have proven to be reliable predictive algorithms in many application areas. Not much is known, however, about the statistical properties of random forests. Several authors have established conditions under which their…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…
Random forests have become popular for clinical risk prediction modelling. In a case study on predicting ovarian malignancy, we observed training c-statistics close to 1. Although this suggests overfitting, performance was competitive on…
Survival analysis of right censored data arises often in many areas of research including medical research. Effect of covariates (and their interactions) on survival distribution can be studied through existing methods which requires to…