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.
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.
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.
We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing …
In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with standard results in the literature, which either make distributional assumption…
Transformer-based models overfit financial time series data, leading to increased prediction variance.
problem Forecast collapse of transformer-based models under squared loss in financial time series.
method Theoretical analysis and numerical experiments on high-frequency EUR/USD exchange rate data.
result Increased model expressivity in Transformer-based models leads to spurious fluctuations without reducing bias, resulting in higher prediction variance.
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.
Feature selection is a technique to screen out less important features. Many existing supervised feature selection algorithms use redundancy and relevancy as the main criteria to select features. However, feature interaction, potentially a key characteristic in real-world problems, has not received much attention. As a…
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 show that learning methods interpolating the training data can achieve optimal rates for the problems of nonparametric regression and prediction with square loss.
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a long-standing gap between upper and lower bounds. Moreover, we show that our al…
The study explains delayed spikes in batch-normalized models.
problem Delayed spikes in batch-normalized models.
method Analyzing batch-normalized linear models, deriving conditions for delayed onset and waiting time.
result Explicit conditions for delayed-onset and waiting time in whitened square-loss linear regression.
We consider the problem of learning linear classifiers when both features and labels are binary. In addition, the features are noisy, i.e., they could be flipped with an unknown probability. In Sy-De attribute noise model, where all features could be noisy together with same probability, we show that 0-1 loss ($l_{…
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.
AEW estimator achieves optimal risk in expectation for large enough temperatures.
problem Understanding minimax-rate optimality of AEW estimator in model selection aggregation.
method Analyzing AEW estimator with exponential weights for squared loss under random design.
result AEW achieves excess risk Tlog(M)/(n+1) in expectation for large enough temperatures. 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 goal of temporal alignment is to establish time correspondence between two sequences, which has many applications in a variety of areas such as speech processing, bioinformatics, computer vision, and computer graphics. In this paper, we propose a novel temporal alignment method called least-squares dynamic time war…
Information-maximization clustering learns a probabilistic classifier in an unsupervised manner so that mutual information between feature vectors and cluster assignments is maximized. A notable advantage of this approach is that it only involves continuous optimization of model parameters, which is substantially easie…
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.
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.
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…
We consider the setting of online linear regression for arbitrary deterministic sequences, with the square loss. We are interested in the aim set by Bartlett et al. (2015): obtain regret bounds that hold uniformly over all competitor vectors. When the feature sequence is known at the beginning of the game, they provide…
We study tensor completion in the agnostic setting. In the classical tensor completion problem, we receive n entries of an unknown rank-r tensor and wish to exactly complete the remaining entries. In agnostic tensor completion, we make no assumption on the rank of the unknown tensor, but attempt to predict unknown …
AutoML simplifies two-sample tests for detecting distribution shifts.
problem Detecting distribution shifts between datasets.
method Uses mean discrepancy of a witness function with squared loss minimization.
result AutoML simplifies and improves two-sample testing performance.
Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrained mirror descent algorithms applied to the unregularized empiri…
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…
Analytical method finds deeper optima in two-layer ReLU networks.
problem Training two-layer ReLU networks with analytical methods.
method Analytically finding critical points of the loss function for one layer while keeping the other fixed.
result Significantly smaller training loss values on real datasets compared to gradient descent methods.
Neural networks perform differently when regression is treated as classification.
problem Understanding why neural networks perform better when regression is treated as classification.
method Analyzing two-layer ReLU networks and their feature spaces, focusing on the cross entropy loss vs. square loss.
result The support of the measure induced by the square loss differs from that of the cross entropy loss, indicating optimization difficulties.
Sharp rates found for learning with dependent data, avoiding sample size deflation.
problem Learning with dependent data and square loss.
method Combining weak sub-Gaussian class and mixed tail generic chaining.
result Achieves a rate that only depends on class complexity and second order statistics.
Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challeng…
This work introduces a new method for coupling base and target densities in generative models.
problem Generating samples from complex target distributions using simple base distributions.
method Developed a framework of stochastic interpolants with data-dependent couplings.
result Constructing dynamical transport maps that serve as conditional generative models.
Optimizes neural networks' last layer with closed-form solutions.
problem Optimizing neural networks' last layer with stochastic gradient descent.
method Adapting closed-form last layer optimization for stochastic gradient descent, alternating between backbone and last layer updates.
result The method converges to optimal solutions and outperforms standard SGD and Adam in regression tasks.
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.
We consider the problem of computing the best-fitting ReLU with respect to square-loss on a training set when the examples have been drawn according to a spherical Gaussian distribution (the labels can be arbitrary). Let opt<1 be the population loss of the best-fitting ReLU. We prove: 1. Finding a ReLU wit…
In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a …
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.
Efficiently removes specific data subsets without retraining for GDPR compliance.
problem Efficiently removing specific data subsets to comply with GDPR regulations.
method Statistical framework for machine unlearning with minimax optimality for squared loss.
result Developed Unlearning Least Squares (ULS) achieving minimax optimality for estimating model parameters.
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total squared loss compared against the best isotonic (non-decreasing) function in hi…
This paper introduces a new transfer learning method for regression.
problem Boosting predictive power in scenarios with scarce data.
method Affine model transfer, following expected-square loss minimization.
result The affine model transfer method encompasses various existing methods and clarifies its theoretical properties.
Two novel methods estimate multiple FDR directions for binary categorical responses.
problem Estimating multiple FDR directions for categorical responses.
method Information maximization and square loss mutual information.
result Statistical consistency of the proposed methods established.
New DAM method improves AUC scores in medical image classification.
problem Maximizing AUC in large-scale medical image classification.
method Proposes AUC margin loss for robust optimization, conducts extensive empirical studies.
result Improves performance on four medical image classification tasks, achieving 1st place on Stanford CheXpert.
Improved neural network training by coupled initialization reduces neuron count.
problem Training neural networks efficiently with fewer neurons.
method Coupled initialization of weights into pairs of identical Gaussian vectors.
result Significantly reduced number of neurons required for network convergence.
New algorithms adapt to model misspecification in contextual bandits.
problem Design efficient algorithms for contextual bandits that handle model misspecification gracefully.
method Oracle-efficient algorithms for ε-misspecified contextual bandits using square loss regression.
result First algorithm achieving optimal regret bound for unknown misspecification level in linear contextual bandits.
In "Dictionary Learning" one tries to recover incoherent matrices A∗∈Rn×h (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors x∗∈Rh with a small support of size hp for some 0<p<1 while having access to observations $y \in \mathbb{…
The study establishes SQ lower bounds for learning halfspaces and ReLUs under Gaussian marginals.
problem Agnostically learning halfspaces and ReLUs under Gaussian marginals.
method Statistical Query (SQ) lower bounds analysis.
result Proves SQ lower bounds of dpoly(1/ε) for both problems. Theoretical justification for deep networks' performance with regularization techniques.
problem Understanding the performance of deep networks trained with the square loss.
method Analysis of gradient flow and theoretical justification of regularization techniques.
result Convergence to solutions with smaller Frobenius norms leads to better classification error bounds.