Study on a Bahri-Brezis problem on hyperbolic manifolds.
problem Existence of solutions on asymptotically hyperbolic manifolds.
method Algebraic Topological argument of Bahri-Coron.
result Existence of at least one solution under specific conditions.
The study finds solutions for CR spheres with a curvature condition.
problem Prescribing scalar curvature on Cauchy-Riemann spheres.
method Bahri methods and critical points at infinity theory.
result Lower bound for the number of solutions found.
Paper simplifies and proves Bahri-Xu conjecture for various cases.
problem Universal inequality for p points in R^m
method Simplified conjecture, inductive conditions, reduction to basic case m=1
result Proved conjecture for m=1 with arbitrary p, and for p=4,5 and m≥2
We consider the fractional Nirenberg problem on the standard sphere Sn with n≥4. Using the theory of critical points at infinity, we establish an Euler-Hopf type formula and obtain some existence results for curvature satisfying assumptions of Bahri-Coron type.
We solve the remaining cases of the Riemann mapping problem of Escobar. Indeed, performing a suitable scheme of the barycenter technique of Bahri-Coron via the Chen's bubbles, we solve the cases left open after the work of Chen. Thus, combining our work with the ones of Almaraz, Chen, Escobar and Marques we have that e…
Method shows existence of conformal metrics with constant Q-curvature on manifolds.
problem Existence of conformal metrics with constant Q-curvature on manifolds. method Bahri-Coron barycenter method applied to GJMS operator.
result Existence of positive solutions for the 2k-th order Q-curvature equation. In this paper, we solve the remaining cases of the boundary Yamabe problem introduced by Escobar in 1992. Indeed, using the bubbles of Brendle-Chen, which are an adaptation to manifolds with boundary of the original ones introduced by Brendle for the study of the Yamabe flow on closed Riemannian manifolds of dimension …
Study solves a mathematical problem related to elliptic Schroedinger-to-Neumann maps.
problem Solving a Cherrier-Escobar problem for elliptic Schroedinger-to-Neumann maps.
method Using algebraic topological argument of Bahri-Coron, assuming positive eigenvalue and Green function.
result Solvability of the extended problem under specified conditions.
In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact 4−dimensional manifold (M4,g0) with positive scalar curvature. We prove new exitence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri-Coron and…
Study on 4D Riemannian manifolds solves curvature problem.
problem Resonant prescribed T-curvature problem on compact manifolds.
method Variational theory, energy and gradient estimates, Morse lemma, Liouville technique.
result New existence results for critical points at infinity.
We study in this paper the fractional Yamabe problem first considered by Gonzalez-Qing on the conformal infinity (Mn,[h]) of a Poincaré-Einstein manifold (Xn+1,g+) with either n=2 or n≥3 and (Mn,[h]) is locally flat - namely (M,h) is locally conformally flat. However, as for the classic…
Given a compact four-dimensional Riemannian manifold (M,g) with boundary, we study the problem of existence of Riemannian metrics on M conformal to g with prescribed Q-curvature in the interior M˚ of M, and zero T-curvature and mean curvature on the boundary ∂M of M. This geometric …
The topology of the intersection of two real homogeneous coaxial quadrics was studied by the second author who showed that its intersection with the unit sphere is in most cases diffeomorphic to a connected sum of sphere products. Combining that approach with a recent one (due to Antony Bahri, Martin Bendersky, Fred Co…
Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Unified framework for model explanation methods based on feature removal.
problem Unclear relationships and preferences among various model explanation methods.
method Characterizes removal-based explanations along three dimensions.
result Unified 26 existing methods, including widely used approaches.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
problem Calibration of prediction intervals in regression problems.
method Four classes of methods: Bayesian, ensemble, direct interval estimation, and conformal prediction.
result Conformal prediction can be used as a general calibration procedure.
Derives kernel PCA with Nyström method for scalability.
problem Scalability of kernel PCA.
method Nyström method for kernel PCA.
result Provides scalable alternative to full kernel PCA.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
Two RBF methods solve complex financial derivatives pricing problems.
problem Pricing derivatives in models with multiple stochastic factors.
method Radial Basis Function Partition of Unity and Radial Basis Function generated Finite Differences methods.
result Both methods achieve high accuracy and are efficient for solving multi-dimensional PDEs.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
VAN method optimizes learning tasks with unified methods.
problem Optimizing learning tasks in active and reinforcement learning.
method Variational Adaptive-Newton method that unifies optimization, inference, and evolution strategies.
result VAN performs well on various learning tasks.
A comprehensive benchmark of 15 scRNA-seq imputation methods across various datasets and analyses.
problem Imputation of single-cell RNA sequencing data to recover latent transcriptional signals.
method Evaluation of 15 imputation methods across 30 datasets and 6 downstream analyses.
result Traditional methods generally outperform DL-based methods in scRNA-seq data analysis.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Improved A2C method with lower variance.
problem Reducing variance in deep policy gradient methods.
method Using control variate theory, derived a new A2C formulation with lower variance.
result New A2C method has lower variance and improved performance.
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
A new method speeds up deep neural network training.
problem Nonconvex optimization in deep neural networks.
method Scaled conjugate gradient method for nonconvex optimization.
result The method converges faster and achieves lower scores in practical applications.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch…
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Proposes UTC method for stock price prediction with uncertainty quantification.
problem Lack of uncertainty estimates in stock prediction methods.
method Combines TC method with probabilistic modeling for point and uncertainty predictions.
result UTC method achieves higher returns and lower risks than baselines.
Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a p…
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Geometric methods study 3-manifold splittings.
problem Studying Heegaard splittings of 3-manifolds.
method Geometric approaches.
result Recent advances in geometric methods.
A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.
problem Improving feature selection accuracy and stability in machine learning models.
method Combination of four feature selection methods using fuzzy sets and bootstrap.
result Our method achieved significantly higher stability than individual methods.
New method improves accuracy in computing implied volatility.
problem Computing implied volatility from the Black-Scholes model.
method Adaptive gradient descent optimizers for numerical computation.
result More accurate results compared to close form approximation and Newton-Raphson method.
The paper examines Wiener process for LID estimation methods.
problem Estimating local intrinsic dimension in high-dimensional datasets.
method Investigates recent LID estimation methods from a Wiener process perspective.
result Explains how methods behave under non-ideal conditions.
Discuss ML methods for economists, highlighting better performance in econometrics.
problem Applying ML methods to econometrics problems.
method Supervised and unsupervised learning methods, matrix completion, causal inference, optimal policy estimation.
result ML methods often outperform traditional econometric methods in specific econometrics problems.
New method detects business-relevant outliers in e-commerce conversion rates.
problem Identifying outliers in e-commerce conversion rate data.
method A novel unsupervised fluid IQR method that adjusts sensitivity based on platform activity.
result Fluid IQR method outperforms existing methods in business-relevance and robustness.
Saliency methods often misattribute predictions due to input transformations.
problem Saliency methods lack reliability when explanations are sensitive to non-contributing factors.
method Used a simple pre-processing step to demonstrate that transformations with no effect on the model can cause misleading attributions.
result Saliency methods that do not satisfy input invariance (mirror model sensitivity to input transformations) result in misleading attributions.
Medical image reconstruction advances from sparse models to machine learning.
problem Improving image quality and reducing noise in medical imaging.
method Iterative reconstruction, modified data acquisition methods, and machine learning models.
result Machine learning methods show promise in improving image quality.
We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex prob…
R package for counterfactual explanation methods.
problem Lack of unified interfaces for counterfactual explanation methods.
method Developed a modular R6-based interface for three existing counterfactual methods and proposed extensions.
result Comparison of implemented methods' quality and runtime behavior.
A new method for faster optimization in high dimensions.
problem Slow convergence in high-dimensional optimization problems.
method Subspace cubic regularized Newton method within Krylov subspace.
result Achieves a dimension-independent convergence rate of O(1/mk + 1/k^2).
Derives new optimization methods using variational integrators.
problem Optimization methods in machine learning.
method Variational integrators and principles of Hamilton and Lagrange-d'Alembert.
result Derives two families of optimization methods, including Nesterov's accelerated gradient method.