Researchers find a new way to describe maximal surfaces using a specific method.
problem Finding representations for maximal surfaces in Lorentz-Minkowski space.
method Weierstrass-Enneper representation and Barbishov-Chernikov method applied to hodographic coordinates.
result Established a connection between maximal surface equation and Born-Infeld equation via Wick rotation.
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.
Paper introduces stochastic mesh methods for efficient CVA computation.
problem Efficient computation of CVA for large systems using Monte Carlo methods.
method Introduces two stochastic mesh methods for CVA computation.
result Demonstrates the rate of convergence of the methods to real CVA values.
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.
A new method speeds up optimization for sums, simpler than others.
problem Optimizing finite sums, especially in non-smooth cases.
method A novel accelerated method based on SAGA, with one parameter.
result Achieves accelerated convergence on strongly convex smooth problems.
Unified analysis of momentum methods for deep learning.
problem Convergence analysis of stochastic momentum methods for convex and non-convex optimization.
method Developed a convergence analysis for two stochastic momentum methods.
result Unified framework revealing similarities and differences between methods.
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.
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.
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.
The paper introduces admissible hierarchical clustering methods for asymmetric networks.
problem Characterizing and implementing hierarchical clustering methods for asymmetric networks.
method The paper characterizes admissible hierarchical clustering methods and proposes algorithms for their implementation.
result The paper describes three families of intermediate methods for admissible hierarchical clustering of asymmetric networks.
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.
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…
This paper provides mathematical foundations for regression methods used in forward initial margin approximation.
problem Developing robust methods for approximating forward initial margin.
method Introduces mathematical rigor to show that regression methods are variations of approximating the conditional expectation function.
result Each regression method is a numerical estimation of the conditional expectation with a different functional form.
We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods - one …
The article derives a formula for predicting claims uncertainty using the GCC method.
problem Claims reserving uncertainty in non-life insurance modeling.
method Generalized Cape Cod (GCC) method, derived an analytical formula for MSEP.
result Derives an analytical formula for the mean squared error of prediction (MSEP) of the GCC method.
Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and clustering. In this paper, we present an ensemble method to improve community detection by…
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…
A new method selects the best feature selection technique for datasets.
problem Selecting the best feature selection method for unseen datasets.
method Data synthesis, meta features, fuzzy similarity, classification model training.
result Successfully recommended the best feature selection method for five out of eight datasets.
Novel prediction method using string invariants with evolutionary optimization.
problem Optimal prediction parameters for string invariants.
method Evolutionary algorithm for parameter optimization.
result Method performs well in single step prediction but needs improvement for multiple steps.
Two new methods reduce OCO problem complexity without projections.
problem Efficiently solving smooth Online Convex Optimization problems without projections.
method ORGFW and MORGFW methods using recursive gradient estimation.
result Achieve optimal regret bounds with low computational costs.
Bayesian methods improve kernel and mutual k-nearest neighbor regression.
problem Improving nonparametric regression methods for better accuracy and hyperparameter selection.
method Bayesian extensions of kernel and mutual k-nearest neighbor regression methods based on Gaussian process models.
result The proposed methods asymptotically converge to the original methods and perform better or equally well in simulations.
A lattice method simulates Ricci flow on 2D axisymmetric manifolds.
problem Simulating Ricci flow on specific 2D manifolds.
method Lattice-based numerical method applied to 2D axially symmetric initial data.
result The method accurately simulates Ricci flow and agrees with finite difference methods.