A new method approximates expected empirical loss for stochastic deep learning tasks.
problem Determining optimal step sizes for stochastic gradient descent in deep learning.
method Applying one-dimensional function fitting to noisy losses of vertical cross sections to approximate expected empirical loss.
result The method leads to a robust and straightforward optimization method that performs well across datasets and architectures.
We present α-loss, α∈[1,∞], a tunable loss function for binary classification that bridges log-loss (α=1) and 0-1 loss (α=∞). We prove that α-loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal y…
The paper proves deep learning can be robust with certain loss functions.
problem The robustness of deep learning models under flawed data.
method Empirical-risk minimization with unbounded, Lipschitz-continuous loss functions.
result These loss functions provide efficient prediction under minimal data assumptions.
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an unbiased gradient estimator of the empirical average loss. In contrast, we develop a co…
CcGAN tackles conditional image generation for continuous labels.
problem Mathematical challenges in conditioning on continuous, scalar labels.
method Proposes novel empirical losses and label input methods for continuous conditional GANs.
result CcGAN generates diverse, high-quality images from continuous labels.
We study differentially private (DP) algorithms for stochastic convex optimization (SCO). In this problem the goal is to approximately minimize the population loss given i.i.d. samples from a distribution over convex and Lipschitz loss functions. A long line of existing work on private convex optimization focuses on th…
New loss function calibrates WW-hinge loss for multiclass SVM.
problem WW-hinge loss not calibrated with 0-1 loss.
method Introduced ordered partition loss and proved WW-hinge loss is calibrated.
result WW-hinge loss is calibrated with ordered partition loss.
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization term…
We study the rates of convergence from empirical surrogate risk minimizers to the Bayes optimal classifier. Specifically, we introduce the notion of \emph{consistency intensity} to characterize a surrogate loss function and exploit this notion to obtain the rate of convergence from an empirical surrogate risk minimizer…
Recent years have seen adversarial losses been applied to many fields. Their applications extend beyond the originally proposed generative modeling to conditional generative and discriminative settings. While prior work has proposed various output activation functions and regularization approaches, some open questions …
DLM for BNNs fails to improve over ELBO optimization.
problem Performance of DLM for Bayesian Neural Networks (BNNs).
method Direct Loss Minimization (DLM) compared to ELBO optimization.
result DLM does not significantly improve over ELBO optimization for BNNs.
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.
Optimizes exp-concave losses with a new risk bound.
problem Optimizing exp-concave losses with stochastic convex optimization.
method Empirical Risk Minimization with a unified geometric assumption and local norms.
result Provides an O(d/n+log(1/δ)/n) excess risk bound. Gradient descent implicitly follows regularization for general losses.
problem The implicit bias of gradient descent methods in machine learning.
method Empirical risk minimization over linear predictors with arbitrary convex, strictly decreasing losses.
result Gradient descent and regularization paths converge to the same direction for non-attained risks.
Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points…
Clarifies model-based RL's theoretical issues and counterexamples for popular losses.
problem Model-based reinforcement learning's empirical performance vs. theoretical properties and popular loss functions.
method Analyzes empirical and theoretical aspects of model-based RL and constructs counterexamples for losses.
result MuZero loss fails in stochastic and deterministic environments, leading to exponential sample complexity.
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.
In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared …
Optimizes hybrid insurance contracts for heavy-tailed losses.
problem Providing insurance against heavy-tailed losses with finite expected loss.
method Combines traditional and parametric insurance, using a Pareto-type criterion for optimization.
result The hybrid contract outperforms traditional contracts in simulations and real data.
The paper analyzes and proposes methods for privately sharing individual privacy losses using per-instance differential privacy.
problem The standard differential privacy framework provides a worst-case bound that may not accurately reflect individual privacy losses.
method The paper analyzes per-instance differential privacy and proposes methods to privately and accurately publish per-instance privacy losses.
result The methods privately and accurately publish per-instance differential privacy losses with minimal additional privacy cost.
Study analyzes landscape complexity of empirical loss functions with correlated data.
problem Understanding the complexity of loss landscapes in machine learning with structured data.
method Kac-Rice formula and random matrix theory applied to high-dimensional empirical loss functions.
result Characterizes the average number of critical points in loss functions with structured data.
EnsLoss combines multiple loss functions to prevent overfitting in classification.
problem Preventing overfitting in classification models.
method EnsLoss is an ensemble method that combines loss functions, ensuring calibration and consistency.
result EnsLoss improves classification accuracy compared to fixed loss methods.
We design simple screening tests to automatically discard data samples in empirical risk minimization without losing optimization guarantees. We derive loss functions that produce dual objectives with a sparse solution. We also show how to regularize convex losses to ensure such a dual sparsity-inducing property, and p…
Listwise learning-to-rank methods form a powerful class of ranking algorithms that are widely adopted in applications such as information retrieval. These algorithms learn to rank a set of items by optimizing a loss that is a function of the entire set -- as a surrogate to a typically non-differentiable ranking metric.…
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.
Study on using random subspaces for ERM with various loss functions.
problem Improving learning accuracy with computational savings from random subspaces.
method Random subspaces of a hypothesis space, considering data-dependent subspaces.
result Unified analysis showing computational efficiency can be improved without performance loss.
Proposes neuron alignment to optimize mode connectivity in neural networks.
problem Understanding and optimizing mode connectivity in deep neural networks.
method Introduces neuron alignment to approximate optimal weight permutations and improve mode connectivity.
result Neuron alignment significantly alleviates robust loss barriers and improves model robustness and accuracy.
Paper analyzes high-dimensional portfolio risks and finds empirical out-of-sample relative loss is more reliable.
problem Analyzing risks in high-dimensional portfolios using empirical variance.
method Derives asymptotic behavior of out-of-sample variance and relative loss in high-dimensional settings.
result Empirical out-of-sample relative loss is more reliable than variance in high-dimensional portfolios.
New algorithm optimizes PAC-Bayes bound without surrogate loss.
problem Mismatch between optimisation objective and generalisation bound in stochastic neural networks.
method Proposes a novel training algorithm that optimizes the PAC-Bayesian bound directly.
result Empirical results show improved performance over existing PAC-Bayesian training methods.
Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…
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.
Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors? Better understanding of this question of generalization may improve practical applications of deep networks. In this paper we show that with cross-entropy loss it is surprisingly simple to ind…
Loss-guided training accelerates node embedding methods on graphs.
problem Training efficiency in graph learning methods with implicit positive examples.
method Dynamic adjustment of training distribution based on loss values.
result Significant acceleration in training and computation over static methods.
Study on neural networks with quadratic activation functions, focusing on optimization and generalization.
problem Understanding the dynamics and generalization of neural networks with quadratic activation in the over-parametrized regime.
method Teacher-student scenario, empirical loss landscape analysis, gradient descent dynamics, numerical experiments.
result Conditions for the neural network to recover the teacher and achieve small generalization error.
AMP regularization improves deep learning models by favoring flat minima.
problem Improving deep learning model generalization and avoiding overfitting.
method AMP regularization uses adversarial model perturbation to minimize a norm-bounded perturbation of the empirical risk.
result AMP regularization leads to state-of-the-art performance across various deep architectures.
A new method estimates the learning coefficient using empirical loss.
problem Estimating the learning coefficient in complex models.
method Numerical estimation using Empirical Loss.
result Our method outperforms existing techniques in terms of bias and variance.
Improves Bayesian predictive performance in misspecified models.
problem Misspecification gap between inferential and predictive risks.
method Develops a multi-sample loss (PACm) to bridge the gap. result Empirical study shows improved predictive distribution.
The problem of estimating a high-dimensional sparse vector θ∈Rn from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…
New margin-based learning guarantees improve generalization bounds.
problem Improving generalization bounds for machine learning models.
method Relative deviation margin bounds using empirical margin loss and Rademacher complexity.
result Distribution-dependent generalization bounds for unbounded loss functions.
New approach ties loss curvature to model performance in deep learning.
problem Understanding the relationship between loss curvature and model performance in deep learning.
method Empirical analysis of loss Hessians and theoretical results on input-output Jacobians.
result Novel generalization bound in terms of empirical Jacobian.
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.
Develops a framework for consistent loss functions with variable transformations.
problem Lack of theoretical understanding of variable transformations in consistent loss functions.
method Formal characterizations of consistency for transformed loss functions in two cases: realization and prediction variables.
result Establishes new identifiable and elicitable functionals for complex predictive tasks.
Sampling a fraction of pairs can match full evaluation in machine learning losses.
problem High computational cost of full pairwise loss evaluation.
method Survey sampling techniques targeting informative pairs.
result Performance close to full pairwise evaluation achieved with frugal sampling.
In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literat…
Paper introduces a new topological loss for better convergence.
problem Optimizing topological losses for model's desired topological behavior.
method Introduces a new regularized topology-aware loss function.
result Guarantees efficient optimization of the new loss function.
The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.
problem Risk-sensitive learning aims to minimize risk-averse measures of loss.
method Proposes learning bounds for empirical OCE minimizers based on Rademacher average and variance.
result Provides two learning bounds on the performance of empirical OCE minimizers.
Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while …