Investigates conditional Chisini means and their application to risk measures.
problem Existence of conditional nonlinear means for bounded random variables.
method Defines a mean as a solution to a functional equation induced by T, and provides conditions for the existence of a unique solution.
result Characterizes the scalarization of conditional Risk Measures.
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…
New recursive algorithm estimates conditional kernel mean embeddings in Hilbert space.
problem Estimating conditional distributions in RKHS for supervised learning.
method Recursive algorithm in L2 space for conditional kernel mean map. result Strong L2 consistency of recursive estimator proved. Proposes a new method to analyze the distributional effects of treatments.
problem Analyzing the full distributional impact of treatments beyond just the mean.
method Uses kernel conditional mean embeddings and U-statistic regression to investigate the CoDiTE.
result Demonstrates the effectiveness of the proposed method through experiments.
The paper proves uniqueness of evolving graphs by mean curvature flow under specific conditions.
problem Proving uniqueness of entire graphs evolving by mean curvature flow.
method Analyzes graphs of locally Lipschitz functions and rotationally symmetric solutions, proving uniqueness under uniform lower bounds and proper graphs.
result Uniqueness of entire graphs evolving by mean curvature flow under specified conditions.
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
Special Liouville metrics with Ricci-like conditions are determined by elliptic functions.
problem Characterizing Liouville metrics with Ricci-like conditions in complex space forms.
method Analyzing necessary conditions for induced metrics of parallel mean curvature surfaces and proving the existence of specific Liouville metrics.
result Explicit determination of special Liouville metrics with Ricci-like conditions by elliptic functions.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
GAAVI offers anytime-valid tests for CMF global null and contrasts.
problem Inference on the conditional mean function for high confidence decisions.
method Asymptotic anytime-valid tests for CMF global null and contrasts.
result Achieves asymptotic type-I error guarantees, power one, and optimal sample complexity.
Two spheres found with specific curvature constraints.
problem Existence of spheres with prescribed mean curvature.
method Proved existence of at least two embedded spheres with curvature h satisfying pinching condition. result Existence of at least two embedded spheres with prescribed mean curvature h. The study examines continuous mean curvature functions on manifolds without conjugate points.
problem Understanding properties of manifolds with specific curvature functions.
method Analyzing simply connected Riemannian manifolds with continuous horospherical mean curvature functions.
result Compact rank one manifolds without conjugate points are locally symmetric spaces of negative curvature.
A novel k-NN method estimates conditional mean and variance efficiently.
problem Joint estimation of conditional mean and variance.
method Integrates k-NN with automated variance selection.
result Achieves fast convergence rates and improved precision.
New existence results for curvature problem on balls with specific conditions.
problem Existence of solutions for a prescribed mean curvature problem on a ball.
method Combining critical points at infinity approach with Morse theory.
result New existence results for higher dimensional case n≥5 under pinching conditions. Probit Monotone BART estimates binary outcomes using monotonic functions.
problem Estimating conditional mean functions for binary outcomes with monotonicity constraints.
method Proposes a new BART variant that incorporates monotonicity constraints for binary outcomes.
result Allows for more precise estimation of monotonic functions in binary outcome models.
In this note we study a large class of mean curvature type flows of graphs in product manifold N×R where N is a closed Riemann- ian manifold. Their speeds are the mean curvature of graphs plus a prescribed function. We establish long time existence and uniformly convergence of those flows with a barrier conditi…
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
The paper explores rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.
problem Rigidity of hypersurfaces with constant shifted curvature functions in hyperbolic space.
method Characterizations and rigidity investigations for hypersurfaces with constant weighted shifted mean curvatures or ratios.
result Rigidity results for hypersurfaces with constant linear combinations of weighted shifted mean curvatures and radially symmetric shifted mean curvatures.
New method optimizes portfolio weights as functions, outperforming traditional approaches.
problem Optimizing portfolio weights in mean-variance models.
method Functional optimization approach, treating weights as functions of past values.
result Gradient-ascent algorithms can solve functional optimization problems for mean-variance portfolio management.
New insights into correntropy-based regression reveal robustness and unified approaches.
problem Learning robust regression functions under additive noise.
method Minimum distance estimation and conditional mean, mode, median functions.
result Unified approach to conditional mean, mode, and median functions.
We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime N under the necessary and sufficent assumptions that N satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter t can be used to d…
Solves a problem in Riemannian geometry for scalar-flat metrics with boundary conditions.
problem Finding a conformal metric with zero scalar curvature and prescribed boundary mean curvature.
method Construction of local test functions to resolve open cases and establish new solvability conditions.
result Established new solvability conditions for the problem.
We obtain the explicit representation of Legendre surfaces in the unit 5-sphere with harmonic mean curvature vector field, under the condition that the mean curvature function is constant along a certain special direction.
We study the line bundle mean curvature flow on Kähler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of Kähler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian-Yang-Mil…
Graphs with bounded anisotropic mean curvature are regular almost everywhere.
problem Understanding the regularity of graphs with anisotropic mean curvature.
method Proving regularity for m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in Lp. result Graphs with bounded anisotropic mean curvature are regular almost everywhere.
This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated b…
This paper develops q-learning methods for mean-field control problems.
problem Continuous-time mean-field control problems with interaction between agents.
method Introduces two q-functions and devises model-free learning algorithms.
result Developed algorithms can learn optimal value functions and q-functions.
We show that under suitable non-degeneracy conditions, complete gradient flow lines of the scalar curvature functional of a riemannian manifold perturb into eternal forced mean curvature flows with large forcing term.
A new ML-based filter improves data assimilation for nonlinear systems.
problem Improving data assimilation for nonlinear systems using ensemble methods.
method Developed a machine learning-based conditional mean filter (ML-EnCMF) integrating ANN and linear functions.
result ML-EnCMF outperforms EnKF and likelihood-based EnCMF in nonlinear systems.
The study improves VaR forecast accuracy by modeling conditional quantile dynamics.
problem Improving the accuracy of Value-at-Risk (VaR) forecasts for time-varying quantiles.
method Time-varying modeling of VaR, evaluation via simulation, asymmetric Mean Absolute Deviation loss function.
result Substantial improvements in forecasting conditional quantiles by maintaining predicted quantile unchanged.
Gradient estimate for harmonic functions with boundary condition proved.
problem Proving gradient estimates for harmonic functions with boundary conditions.
method Using weighted f-harmonic functions and infinite dimensional Bakry-Emery Ricci tensor. result Gradient estimates for positive f-harmonic functions with Dirichlet boundary condition. The bias of the sample means of the arms in multi-armed bandits is an important issue in adaptive data analysis that has recently received considerable attention in the literature. Existing results relate in precise ways the sign and magnitude of the bias to various sources of data adaptivity, but do not apply to the c…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from Pontryagin's stochastic maximum principle. Although the same cost functions as well…
New principles for collapsing law-invariant functionals to means, extending beyond convexity.
problem Conditions for law-invariant functionals to reduce to means.
method Establishing collapse to the mean principles for non-convex functionals.
result General principles apply beyond convexity, including quasiconvex and Choquet integrals.
The paper proves functions related to mean field equations on surfaces are Morse functions under certain conditions.
problem Analyzing the Morse property of functions related to mean field equations on surfaces.
method Examining functions of the form \( f_g(x) \) on a smooth compact surface \( \Sigma \) with boundary, proving the existence of a metric \( \widetilde{g} \) close to \( g \) making \( f_{\widetilde{g}} \) a Morse function.
result For any Riemannian metric \( g \), there exists a metric \( \widetilde{g} \) arbitrarily close to \( g \) and in the conformal class of \( g \) such that \( f_{\widetilde{g}} \) is a Morse function.
This paper considers the prescribed zero scalar curvature and mean curvature problem on the n-dimensional Euclidean ball for n≥3. Given a rotationally symmetric function H:∂Bn→R, in this work, we will prove that if H′(r) changes signs where H>0 and H(r) also satisfies a flatness con…
Study shows price bubbles can exist even with heterogeneous beliefs.
problem Equilibrium price formation in markets with different belief groups.
method Analyzes continuous time asset trading with heterogeneous investors and mean reverting asset.
result Price bubbles may not form even with heterogeneous beliefs, contrary to initial expectations.
To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their result is pivotal for deriving interesting properties of consensus clustering beyond…
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
Proposes a new framework for deep learning conditional mean estimation with confidence regions.
problem Lack of asymptotic properties in deep nonparametric regression models.
method Transforms deep estimation into conditional diffusion model for conditional mean estimation.
result Developed end-to-end convergence rate and asymptotic normality for conditional diffusion model.
In this paper, we investigate the problem of finding minimal graphs in Mn×R with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a functional adapted from the area functional. We construct barriers to show that f…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are intro…
We consider a multi-armed bandit problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditi…
The purpose of this paper is to study immersed surfaces in the product spaces M2(κ)×R, whose mean curvature is given as a C1 function depending on their angle function. This class of surfaces extends widely, among others, the well-known theory of surfaces with constant mean curvature. In th…
New entropy functionals for curved spaces help predict shape behavior.
problem Understanding entropy behavior in curved spaces.
method Introduced new entropy functionals for submanifolds of Cartan-Hadamard manifolds.
result Obtained sharp lower bounds on these entropies for certain closed hypersurfaces and observed a novel rigidity phenomenon.
Boosting trees can test necessary conditions for regression model calibration.
problem Testing calibration and auto-calibration in regression models.
method Using boosting trees to test calibration and auto-calibration.
result Boosting trees prove to be very powerful in testing calibration and auto-calibration in large insurance datasets.
Unified q-learning for mean-field jump-diffusion models with unobservable population distribution.
problem Continuous-time q-learning in mean-field jump-diffusion models with unobservable population distribution.
method Proposed decoupled Iq-function for unified policy evaluation in MFG and MFC problems; unified q-learning algorithm based on test policies and averaged martingale orthogonality condition.
result Unified policy evaluation rule for MFG and MFC problems based on decoupled Iq-function.
Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional distributions which cannot be meaningfully summarized using expectation only (due to e…
New method tests CMI using deep neural networks for high-dimensional data.
problem Testing conditional mean independence in high-dimensional settings.
method Population CMI measure and bootstrap-based testing with deep generative neural networks.
result Strong empirical performance and versatility in various scenarios.