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It is widely believed that the prediction accuracy of decision tree models is invariant under any strictly monotone transformation of the individual predictor variables. However, this statement may be false when predicting new observations…
We would like to congratulate Lee, Nadler and Wasserman on their contribution to clustering and data reduction methods for high $p$ and low $n$ situations. A composite of clustering and traditional principal components analysis, treelets is…
We consider predictive inference using a class of temporally dependent Dirichlet processes driven by Fleming--Viot diffusions, which have a natural bearing in Bayesian nonparametrics and lend the resulting family of random probability…
We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
The analysis of single-cell RNA sequencing (scRNA-seq) data often involves fitting a latent variable model to learn a low-dimensional representation for the cells. Validating such a model poses a major challenge. If we could sequence the…
Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…
Studying the human microbiome has gained substantial interest in recent years, and a common task in the analysis of these data is to cluster microbiome compositions into subtypes. This subdivision of samples into subgroups serves as an…
We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…
Real-life machine learning problems exhibit distributional shifts in the data from one time to another or from one place to another. This behavior is beyond the scope of the traditional empirical risk minimization paradigm, which assumes…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
We propose a new class of discrete generalized linear models based on the class of Poisson-Tweedie factorial dispersion models with variance of the form $\mu + \phi\mu^p$, where $\mu$ is the mean, $\phi$ and $p$ are the dispersion and…