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In this paper, we introduce a new concept of generalized convexity for E-differentiable vector optimization problems. Namely, the notion of exponentially E-invexity is defined. Further, some properties and results of exponentially E-invex…
We consider optimal designs for general multinomial logistic models, which cover baseline-category, cumulative, adjacent-categories, and continuation-ratio logit models, with proportional odds, non-proportional odds, or partial proportional…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…
We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
A new approach to adaptive design of clinical trials is proposed in a general multiparameter exponential family setting, based on generalized likelihood ratio statistics and optimal sequential testing theory. These designs are easy to…
A general theory for Gaussian mean estimation that automatically adapts to unknown sparsity under arbitrary norms is proposed. The theory is applied to produce adaptively minimax rate-optimal estimators in high dimensional regression and…
In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…
We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…
We consider the problem of designing experiments for investigating particle in-flight properties in thermal spraying. Observations are available on an extensive design for an initial day and thereafter in limited number for any particular…
The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
Generalized planning studies the construction of solution strategies that generalize across families of planning problems sharing a common domain model, formally defined by a transition function $\gamma : S \times A \rightarrow S$.…
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…
Generalized linear models are widely used in many areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in generalized linear models using residuals that are approximately standard…