Related papers: Maximal signed volume for (multivariate) supermodu…
The performance of known and new parametric estimators for Archimedean copulas is investigated, with special focus on large dimensions and numerical difficulties. In particular, method-of-moments-like estimators based on pairwise Kendall's…
The conditional value-at-risk (CVaR) is a useful risk measure in fields such as machine learning, finance, insurance, energy, etc. When measuring very extreme risk, the commonly used CVaR estimation method of sample averaging does not work…
We study the following basic machine learning task: Given a fixed set of $d$-dimensional input points for a linear regression problem, we wish to predict a hidden response value for each of the points. We can only afford to attain the…
We introduce the notion of \emph{mostly nonuniform sectional expanding} (MNUSE) for singular flows which encompasses the notions of sectional hyperbolicity, asymptotically sectional and multisingular hyperbolicity. We exhibit an example of…
Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar's theorem, "the fundamental theorem of copulas", makes a clear distinction between the continuous case…
Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
In this work, we examine Asymmetric Shapley Values (ASV), a variant of the popular SHAP additive local explanation method. ASV proposes a way to improve model explanations incorporating known causal relations between variables, and is also…
We perform Monte Carlo simulations to determine the average excluded volume <V_{ex}> of randomly oriented rectangular prisms, randomly oriented ellipsoids and randomly oriented capped cylinders in 3-D. There is agreement between the…
Let $(M^{n+1},g)$ be a closed Riemannian manifold of dimension $3\le n+1\le 5$. We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $M$ contains infinitely many geometrically distinct constant…
The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating…
In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…
A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes…
Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the…
We study conformal metrics on R^{2m} with constant Q-curvature and finite volume. When m=3 we show that there exists V* such that for any V\in [V*,\infty) there is a conformal metric g on R^{6} with Q_g = Q-curvature of S^6, and vol(g)=V.…
Finding upper and lower bounds to integrals with respect to copulas is a quite prominent problem in applied probability. In their 2014 paper, Hofer and Iaco showed how particular two dimensional copulas are related to optimal solutions of…
An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{AdS_5}$ black holes was previously proposed by the authors in ref. 1, in terms of transcendental equations involving the Painlev\'e VI (PVI)…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
Enumerative invariants in Algebraic Geometry 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=a$ in some geometric problem, using a virtual class $[{\cal M}_a^{\rm ss}(\tau)]_{\rm virt}$ in homology, for the…
We incorporate the conditional value-at-risk (CVaR) quantity into a generalized class of Pickands estimators. By introducing CVaR, the newly developed estimators not only retain the desirable properties of consistency, location, and scale…