相关论文: Generalized Fr\'{e}chet means with random minimizi…

We address the problem of testing hypotheses about a specific value of the Fr\'echet mean in metric spaces, extending classical mean testing from Euclidean spaces to more general settings. We extend an Euclidean testing procedure…

We consider generalizations of classical function spaces by requiring that a holomorphic in ${\Omega}$ function satisfies some property when we approach from ${\Omega}$, not the whole boundary, but only a part of it. These spaces endowed…

Fr\'echet regression extends the principles of linear regression to accommodate responses valued in generic metric spaces. While this approach has primarily focused on exploring relationships between Euclidean predictors and non-Euclidean…

Experimental studies are a cornerstone of Machine Learning (ML) research. A common and often implicit assumption is that the study's results will generalize beyond the study itself, e.g., to new data. That is, repeating the same study under…

As demonstrated in our previous work on ${\boldsymbol T}_{4}$, the space of phylogenetic trees with four leaves, the global, as well as the local, topological structure of the space plays an important role in the non-classical limiting…

We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…

In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,...,x_n):=(f_1+...+f_n)^{-1}(f_1(x_1)+...+f_n(x_n))$, where $f_1,...,f_n:I\to\mathbb{R}$ are strictly increasing and continuous functions.…

Traditional domain generalization methods often rely on domain alignment to reduce inter-domain distribution differences and learn domain-invariant representations. However, domain shifts are inherently difficult to eliminate, which limits…

For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…

We consider the lattice, $\mathcal{L}$, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, $n(\cdot)$, on $\mathcal{L}$. We derive from…

Training and deploying machine learning models that meet fairness criteria for protected groups are fundamental in modern artificial intelligence. While numerous constraints and regularization terms have been proposed in the literature to…

In the present work, we provide the general expression of the normalized centered moments of the Fr\'echet extreme-value distribution. In order to try to represent a set of data corresponding to rare events by a Fr\'echet distribution, it…

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In 2011, Mileyko and his collaborators made the first study of the properties of the…

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Fr\'echet mean. In this…

Advancements in data collection have led to increasingly common repeated observations with complex structures in biomedical studies. Treating these observations as random objects, rather than summarizing features as vectors, avoids feature…

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of…

Fr\'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such…

A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…