Guarantees uniform convergence for square-root Lipschitz losses.
problem Uniform convergence guarantees for square-root Lipschitz losses.
method Using Rademacher complexity and square root of scalar loss function Lipschitz constant.
result Generalizes previous results and handles non-smooth loss functions.
Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine (ELM) are popular techniques. However, the noise sensitivity is a major bottlene…
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.
Proposes squentropy loss for improved classification accuracy and model calibration.
problem Theoretical and empirical evidence for cross-entropy loss is lacking.
method Introduces squentropy loss as the sum of cross-entropy and average square loss over incorrect classes.
result Squentropy loss outperforms cross-entropy and rescaled square losses in classification accuracy and model calibration.
A novel dictionary-based approach for predicting functions.
problem Functional-output regression with non-orthogonal dictionaries.
method Projection learning (PL) with reproducing kernel Hilbert spaces (KPL).
result KPL offers a flexible and computationally efficient solution.
Paper explores connections between loss functions and consistency in binary classification and regression.
problem Consistency in binary classification and regression applications.
method Characterization of conformable loss functions and derivation of a new Huber-type loss function.
result Margin-based loss functions are equivalent to loss functions of squared standardized logistic regression residuals.
The paper introduces a new FOR framework using Huber and ε-insensitive losses.
problem Handling outliers and sparsity in functional output regression.
method Proposes a flexible FOR framework with infimal convolution losses and computable algorithms.
result Demonstrates efficiency and effectiveness on synthetic and real-world data.
The paper explores how different loss functions impact reinforcement learning algorithms.
problem Improving reinforcement learning algorithms by optimizing loss functions.
method Comprehensive survey on loss functions in reinforcement learning, proving the benefits of specific loss functions.
result Binary cross-entropy loss leads to first-order bounds and is more efficient than squared loss.
Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.
problem Limited theoretical analysis for distributed ERM with general loss functions and hypothesis spaces.
method Derive tight risk bounds under assumptions on hypothesis space and loss function.
result Developed more general risk bound for distributed ERM without strong convexity restriction.
This work investigates square loss in overparametrized neural networks, revealing its advantages in robustness and calibration.
problem Theoretical understanding of square loss in overparametrized neural networks.
method Systematic investigation of square loss in the NTK regime for both separable and non-separable classes.
result Square loss shows fast convergence rates and robustness guarantees for overparametrized neural networks.
Gradient descent on ReLU networks with square loss implicitly favors balanced weights.
problem Understanding implicit regularization in nonlinear neural networks with regression losses.
method Analyzing gradient descent dynamics on ReLU networks with square loss.
result It is impossible to characterize the implicit regularization of ReLU networks with square loss by any explicit function of model parameters.
Classification and regression tasks in overparameterized models show different generalization properties.
problem Comparing classification and regression in overparameterized models.
method Comparison of least-squares minimum-norm interpolation and hard-margin SVM using different loss functions.
result Interpolating solutions generalize well with 0-1 loss but not with square loss.
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.
Paper proposes fitting loss functions to data using source functions from information geometry.
problem Choosing appropriate loss functions for machine learning models.
method Introduces source functions from information geometry to fit loss functions to the domain at hand.
result Significant improvements over state-of-the-art methods in model training.
The past decade has witnessed a successful application of deep learning to solving many challenging problems in machine learning and artificial intelligence. However, the loss functions of deep neural networks (especially nonlinear networks) are still far from being well understood from a theoretical aspect. In this pa…
Study improves H-consistency bounds for regression analysis.
problem Improving H-consistency bounds for regression analysis. method Generalized theorems and novel H-consistency bounds for various surrogate loss functions. result Derives principled surrogate losses for adversarial regression.
The logcosh loss function helps neural networks learn set-valued functions better.
problem Learning set-valued functions with neural networks.
method Using artificial neural networks with logcosh loss.
result Neural networks with logcosh loss can classify samples based on set-valued functions.
This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian for the loss function, we derive an error bound to the true matrix for the non-strict critical points with r…
Develops a new framework for robust regression with EGM.
problem Addressing robust regression with heavy-tailed noise or outliers.
method Empirical gain maximization (EGM) to approximate noise density.
result Unified analysis of robust regression approaches.
This paper presents a learning method for convolutional autoencoders (CAEs) for extracting features from images. CAEs can be obtained by utilizing convolutional neural networks to learn an approximation to the identity function in an unsupervised manner. The loss function based on the pixel loss (PL) that is the mean s…
With the recent advancement in the deep learning technologies such as CNNs and GANs, there is significant improvement in the quality of the images reconstructed by deep learning based super-resolution (SR) techniques. In this work, we propose a robust loss function based on the preservation of edges obtained by the Can…
Previous studies have shown that deep neural networks (DNNs) with common settings often capture target functions from low to high frequency, which is called Frequency Principle (F-Principle). It has also been shown that F-Principle can provide an understanding to the often observed good generalization ability of DNNs. …
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.
Square loss performs comparably or better than cross-entropy in neural architectures for various tasks.
problem The superiority of cross-entropy loss over square loss in classification tasks is debated.
method Comparison of several neural architectures on NLP, ASR, and computer vision datasets using both loss functions.
result Square loss often produces better results in the majority of tasks, especially in NLP and ASR.
The Nyström method improves learning efficiency for convex losses.
problem Improving computational efficiency in empirical risk minimization.
method Using random subspaces to approximate hypothesis spaces in convex loss functions.
result Computational gains can be achieved without sacrificing learning performance for general convex Lipschitz losses.
New loss functions improve extreme classification with missing labels.
problem Large number of infrequent labels and missing labels in XMC.
method Derive unbiased loss functions for XMC, incorporating them into existing algorithms.
result Significant improvement in extreme classification performance (up to 20%) over existing methods.
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine para…
In this work we propose an adversarial learning approach to generate high resolution MRI scans from low resolution images. The architecture, based on the SRGAN model, adopts 3D convolutions to exploit volumetric information. For the discriminator, the adversarial loss uses least squares in order to stabilize the traini…
New method optimizes fairness in predictive models for continuous sensitive attributes.
problem Enforcing full statistical independence on continuous sensitive attributes is too restrictive.
method Functional bilevel optimization (FBO) and ITD algorithms.
result Achieves lowest or near-lowest fairness-accuracy regret on synthetic and real datasets.
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a …
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…
Artificial neural network training with stochastic gradient descent can be destabilized by "bad batches" with high losses. This is often problematic for training with small batch sizes, high order loss functions or unstably high learning rates. To stabilize learning, we have developed adaptive learning rate clipping (A…
In few-shot learning, typically, the loss function which is applied at test time is the one we are ultimately interested in minimising, such as the mean-squared-error loss for a regression problem. However, given that we have few samples at test time, we argue that the loss function that we are interested in minimising…
Paper studies a robust online learning algorithm for regression.
problem Develops a robust online learning algorithm for regression problems.
method Introduces an online learning algorithm with a robust loss function over RKHS.
result The algorithm achieves optimal convergence rates in mean square and RKHS.
Unified framework for non-Euclidean CPD under scalable stochastic mirror descent.
problem Handling non-Euclidean losses in tensor decomposition.
method Tensor fiber sampling strategy-based stochastic mirror descent.
result Global convergence to a stationary point under reasonable conditions.
Deep networks can memorize random labels; symmetric loss improves this.
problem Deep networks can memorize random labels, ignoring standard regularization.
method Empirical studies with MNIST and CIFAR-10 datasets, formal definition of robustness.
result Symmetric loss function improves network's ability to resist memorization.
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.
Introduces Fitzpatrick losses, tighter than Fenchel-Young losses.
problem Improving loss functions for machine learning.
method Introduces Fitzpatrick losses based on the Fitzpatrick function.
result Fitzpatrick losses are tighter than Fenchel-Young losses.
This paper analyzes M-estimators under infinite-variance noise in high dimensions.
problem High-dimensional M-estimation with infinite-variance noise.
method Study of the Fenchel conjugate domain and its impact on risk.
result Exact risk of M-estimators under infinite-variance noise is derived.
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 sparse Gaussian processes by optimizing predictive loss.
problem Optimizing predictive loss in sparse Gaussian processes.
method Direct loss minimization (DLM) for log-loss and square loss, with product sampling (uPS) and biased Monte Carlo (bMC) for non-conjugate cases.
result DLM shows significant performance improvement in both log-loss and square loss cases.
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …
The paper explores conditions for predicting optimization performance.
problem Lack of formal theoretical guarantees linking prediction and optimization performance.
method Exploring conditions for asymptotic convergence and exact quantification of optimization performance.
result Explicit theoretical relationship between prediction and optimization performance.
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. The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…
Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process…
This work introduces a new loss function to improve the efficiency of optimization-based PDE solvers.
problem Optimization-based PDE solvers converge slowly and are inefficient compared to classical iterative solvers.
method Proposes a novel Stabilized Gradient Residual (SGR) loss function to modulate the condition number.
result The SGR loss achieves orders-of-magnitude faster convergence than the MSE loss in both ODIL and PINNs frameworks.
Paper proposes a boosting method with fast learning rates and early stopping.
problem Missing theoretical guarantees for boosting methods in binary classification.
method Fully-corrective gradient boosting with squared hinge loss and ADMM algorithm.
result Derives fast learning rates of O((m/logm)−1/4) and O((m/logm)−1/2).