R2T hybrid model improves robust regression for asymmetric noise.
problem Least-squares regression fails with asymmetric structured noise.
method Transformer encoder, compression NN, fixed symbolic equation.
result Median regression MSE of 6e-6 to 3.5e-5 on synthetic data.
Optimizes learning rates for kernel-based expectile regression.
problem Estimating conditional expectiles efficiently.
method Support vector machine type approach using Gaussian RBF kernels.
result Learning rates are minimax optimal with a logarithmic factor.
BAEN-SVM improves SVM robustness to noisy data.
problem Noise and geometric irrationalities in SVM.
method Bounded asymmetric elastic net loss combined with SVM.
result BAEN-SVM is robust to noise and geometrically well-defined.
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes it possible to estimate expectiles in a non-parametric framework by a support vec…
Improved robustness in kernel-based regression via novel loss function and IRLS.
problem Noise sensitivity in kernel-based regression methods.
method Proposed ℓs-loss function and iteratively reweighted least squares (IRLS) optimization. result Improved noise robustness in kernel-based regression methods.
A new convex loss function optimizes set predictions with balanced size and coverage.
problem Optimizing set predictions with balanced size and coverage.
method Proposes a convex loss function using Choquet integrals for nondecreasing subset-valued functions.
result Optimal trade-offs between conditional probabilistic coverage and set size.
The paper improves Kaczmarz algorithm with momentum for linear least squares.
problem Improving convergence of the Kaczmarz algorithm for linear least squares.
method Integrates geometrically smoothed momentum into the randomized Kaczmarz algorithm.
result Proves expected error reduction in singular vector directions.
New IRLS algorithms for SVM fitting via MM approach.
problem Fitting support vector machines (SVMs) via quadratic programming.
method Majorization--Minimization (MM) paradigm for iteratively-reweighted least-squares (IRLS) algorithms.
result IRLS algorithms for SVM risk minimization problems with various losses and penalties.
We find a convex model for traditional nonlinear regression under L2 loss.
problem Nonlinear regression under L2 loss with non-convex optimization.
method Showed a convex nonlinear regression model for least squares problem.
result Existence of a convex model simplifies training complex systems.
Paper develops a least-squares framework for learning discrete losses.
problem Learning strategies for discrete losses (e.g., multilabeling, ranking).
method Least-squares framework to systematically design learning algorithms for discrete losses.
result Improved results with explicit dependence on the number of labels and faster learning rates.
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…
New method guarantees simultaneous decomposition of tensor components.
problem Existing methods fail to recover all tensor components simultaneously.
method S-ASI method using slicing initialization and subspace iterations.
result Guaranteed recovery of top r components simultaneously for symmetric tensors.
The paper improves asymmetric causality tests by addressing inefficiencies and statistical significance issues.
problem Inefficiencies and statistical significance issues in asymmetric causality tests.
method Improved asymmetric causality tests via partial cumulative sums for positive and negative components, explicitly testing differences between causal parameters.
result Efficiently tested hypotheses on asymmetric causal interaction between financial markets.
New algorithms estimate Jacobian matrices for large-scale machine learning.
problem Efficiently computing search directions for large nonlinear least squares.
method Exploit low-rank structure in Hessian to estimate Jacobian matrices.
result Two algorithms perform well compared to state-of-the-art methods.
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-s…
LSGANs improve GANs by using least squares loss, leading to better image quality and stability.
problem Vanishing gradients in GANs during training.
method Introducing LSGANs with least squares loss for both discriminator and generator.
result LSGANs generate higher quality images and are more stable during training.
3D GAN improves MRI image quality from low-res scans.
problem Improving MRI image quality from low-resolution scans.
method Adversarial learning using 3D convolutions and least squares loss.
result 3D GAN generates high-quality 3D MRI images from low-resolution scans.
Optimal weight windows are symmetric rectangles centered at peak.
problem Finding the best weight windows for weighted least squares.
method Investigated symmetric and tapered rectangle window weights, showing the best rectangle window is optimal.
result The best rectangle window is optimal for all tapered rectangle window definitions.
Paper uses deep learning to solve PDEs without supervision.
problem Solving elliptic PDEs without labeled data.
method Uses deep neural networks and least-squares functionals.
result Demonstrates effectiveness on 1D second-order elliptic PDEs.
This paper improves VAEs with regularization for better image reconstruction.
problem Improving image reconstruction quality in Variational Autoencoders.
method Least square loss function with regularization for better approximation of data.
result Least square loss function leads to better reconstructed images and faster training.
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised method…
Algorithm solves robust linear regression with block Lewis weights.
problem Group distributionally robust least squares problem.
method Algorithm based on geometric construction and block Lewis weights, using accelerated proximal methods.
result Improves over known methods for moderate accuracy regimes and matches state-of-the-art guarantees.
Paper proposes a new method to improve classification performance over PCA.
problem Improving classification performance over PCA for classification problems.
method Minimizes the difference in margin distribution between original and projected data.
result Proposed method typically outperforms PCA in classification tasks.
Study binary choice with asymmetric loss, offering simple solutions.
problem Binary choice with asymmetric loss in data-rich environments.
method Loss-based reweighting of logistic regression or machine learning techniques.
result Valid decisions on binary outcomes with general loss functions.
Optimal multiscale learning of linear operators
problem Statistical and computational limits of learning bounded linear operators between Sobolev spaces
method Reformulate as an infinite-dimensional matrix regression problem with heterogeneous multiscale structure
result Establish minimax rates and construct a finite-resolution blockwise least-squares estimator attaining these rates
The paper explores machine learning methods for proxy modeling in life insurance solvency capital requirements.
problem Life insurance companies need to estimate solvency capital requirements from full loss distributions, but computational limitations restrict full simulations.
method The paper presents various adaptive machine learning approaches to approximate the risk-dependent proxy function using least-squares Monte Carlo.
result The machine learning methods significantly improve the accuracy and efficiency of proxy modeling compared to traditional regression techniques.
A new method approximates loss functions asymmetrically to prevent catastrophic forgetting.
problem Catastrophic forgetting in deep neural networks.
method Approximating a true loss function using an asymmetric quadratic function with one side overestimated.
result Achieves state-of-the-art accuracy close to upper-bound performance on benchmark datasets.
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
A new pinball loss function improves SVQR model's prediction and sparsity.
problem Improving prediction accuracy and sparsity in SVQR models.
method Proposed asymmetric ε-insensitive pinball loss function for SVQR.
result Significantly improved prediction ability and sparsity in SVQR model.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O(d/n) in bounded distributions. This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
We consider the problem of predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. When the input distribution is known, there already exists an algorithm having an expected excess…
Proposes a method to generate prediction intervals using weighted asymmetric loss functions.
problem Generating reliable prediction intervals for neural network models.
method Uses a weighted asymmetric loss function to estimate prediction intervals.
result The method produces reliable prediction intervals in complex machine learning scenarios.
Paper improves RLS for sparse outlier detection in linear models.
problem Outliers contaminate linear regression models infrequently.
method Hierarchical-optimization recursive least squares with sparsity-inducing regularization.
result The method robustly estimates linear filters/systems with outliers.
A new asymmetric contrastive loss improves performance on imbalanced datasets.
problem Improving performance on imbalanced datasets using contrastive learning.
method Introducing an asymmetric contrastive loss (ACL) and asymmetric focal contrastive loss (AFCL).
result AFCL outperforms CL and FCL in terms of weighted and unweighted classification accuracies on imbalanced datasets.
Least Squares Estimators are suboptimal for 5D convex functions.
problem Suboptimality of Least Squares Estimators in estimating multidimensional convex functions.
method Analysis of natural subclasses of convex functions in random and fixed design settings.
result Risk of LSE is n−2/d while minimax risk is n−4/(d+4) for d≥5. A method for structured prediction using conditional risk minimization.
problem Structured prediction in complex output spaces.
method Minimizing estimated conditional risk functions through regularized least squares problems.
result Efficient training and inference without convex surrogates for discontinuous loss functions.
EIM improves prediction interval tightness without distributional assumptions.
problem Generating tight prediction intervals for asymmetric distributions.
method Expanded Interval Minimization (EIM) using minibatch statistics for coverage and width optimization.
result EIM produces on average 1.37x tighter prediction intervals than prior techniques.
Extends return extrapolation to nonlinear, asymmetric functions under stochastic volatility.
problem Behavioral anomalies in portfolio choice under stochastic volatility.
method Smooth, nonlinear, asymmetric extrapolation function; CRRA investor; Heston stochastic volatility; Hamilton-Jacobi-Bellman equation; Numerical solutions (finite-difference ADI, deep learning-driven iterative).
result Saturation acts as an endogenous correction mechanism, reducing welfare loss.
Risk-aware linear bandits optimize against adverse outcomes.
problem Optimizing decisions under risk in sequential decision-making problems.
method Proposed an optimistic UCB algorithm for contextual bandits with convex loss minimization.
result Regret guarantees similar to generalized linear bandits with convex optimization at each round.
We extend return extrapolation to incorporate asymmetry and saturation, finding that asymmetric nonlinear extrapolation leads to lower welfare loss.
problem Optimal portfolio choice under stochastic volatility
method Smooth, nonlinear extrapolation function with sentiment and variance hedging
result Lower welfare loss with asymmetric nonlinear extrapolation
The study develops a test for GARCH models with unknown power.
problem Testing adequacy of asymmetric power GARCH models with unknown power.
method Derive asymptotic behavior of squared residuals autocovariances, deduce portmanteau test.
result Asymptotic results and adequacy test for GARCH models with unknown power.
Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.
New method quantifies life insurance risk using Monte Carlo simulations.
problem Quantifying long-term risks in insurance portfolios over a one-year horizon.
method Least-squares Monte Carlo methods to quantify impact of new experience.
result Model can be used as an internal model under Solvency II or SST.
Improved robust regression for heavy-tailed and contaminated data.
problem Linear regression with heavy-tailed and adversarially contaminated covariates and responses.
method Applying a filtering algorithm to covariates and then using Huber regression, least trimmed squares, or least absolute deviation estimators on the remaining data.
result Near-optimal error rates achieved for the Huber regression estimator.
We provide a pointwise confidence bound for non-linear least-squares with fixed design.
problem Confidence estimation in non-linear ℓ2-regularized least squares. method Pointwise confidence bound for local minimizers, using weighted norm involving inverse-Hessian.
result The proposed confidence bound scales with the test input's similarity to the training data.
A structured prediction method for ranking labels.
problem Solving label ranking problems as structured output regression.
method Two-step approach: regression in feature space followed by pre-image solving.
result Efficiency on real-world datasets for partial and complete rankings.
New algorithms improve scalar quantization by optimizing sparse least squares.
problem Improving efficiency and accuracy of scalar quantization for neural networks.
method Sparse least square optimization, iterative and clustering-based methods.
result Proposed algorithms outperform existing methods, especially in bit-width reduction scenarios.