Related papers: Generalized Arithmetic and Geometric Mean Divergen…
We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…
The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
We introduce a type of measurements that generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the…
Extending the concept of level measure $\mu(\{f\ge a\})$ we introduce a generalized level measure based on a~family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the…
We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…
Given a black-box classification model and an unlabeled evaluation dataset from some application domain, efficient strategies need to be developed to evaluate the model. Random sampling allows a user to estimate metrics like accuracy,…
Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…
Flag measures are descriptors of convex bodies $K$ in $d$-dimensional Euclidean space generalizing the classical area measures. They have been used to provide general integral formulas for mixed volumes (see Hug, Rataj and Weil (2017)).…
We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the examples published recently in this journal, like unit steps and…
This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating $P\ast\mathcal{N}_\sigma$, for $\mathcal{N}_\sigma\triangleq\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$, by…
In the first part we study deviation of a polynomial from its mathematical expectation. This deviation can be estimated from above by Carbery--Wright inequality, so we investigate estimates of the deviation from below. We obtain such…
We give a simpler proof of a result of Holland concerning a mixed arithmetic-geometric mean inequality. We also prove a result of mixed mean inequality involving the symmetric means.
Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum…
We are interested in the estimation of the distance in total variation $$ \Delta := \|P_{f(X)} - P_{g(X)}\|_{\mathrm var} $$ between distributions of random variables $f(X)$ and $g(X)$ in terms of proximity of $f$ and $g.$ We propose a…
A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are…
Understanding the generalization behaviour of deep neural networks is a topic of recent interest that has driven the production of many studies, notably the development and evaluation of generalization "explainability" measures that…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…