Compact learning results across various loss functions.
problem Understanding sample complexity in transductive learning.
method Analyzing finite projections and sample complexities for different loss functions.
result Exact compactness of sample complexity holds broadly across realizable and agnostic learning.
We describe loss surfaces using topological Betti numbers.
problem Understanding the complexity and structure of loss surfaces in neural networks.
method Topological analysis using Betti numbers for multilayer neural networks.
result Loss complexity is influenced by the number of hidden units and activation function.
We use barcodes to analyze neural networks' loss surfaces, revealing important properties.
problem Understanding the topology of neural networks' loss surfaces.
method Topological data analysis using Morse complexes and barcodes.
result Barcodes of local minima are located in a small part of the loss function's range and decrease with network depth and width.
New insights into training ReLU networks, especially as data dimensionality increases.
problem Understanding computational complexity of training ReLU networks with varying data dimensions.
method Analyzed the parameterized complexity of two-layer ReLU networks with respect to various loss functions, focusing on the influence of data dimensionality.
result Running time lower bounds and optimal brute-force strategies for training ReLU networks, extending previous results to broader loss functions.
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…
New algorithm improves gradient-based ERM for smooth convex losses.
problem Empirical risk minimization of smooth, strongly convex loss functions.
method Iterative gradient-based method with local polynomial regression.
result Oracle complexity of O((pε−1)d/(2η)) for our algorithm. Near-optimal algorithms for predicting across multiple loss functions efficiently.
problem Predicting optimally across various loss functions simultaneously.
method Developed near-optimal online and offline learning algorithms for omniprediction.
result Achieved near-optimal complexity for both online and offline settings.
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.
A new federated learning algorithm improves on existing methods by exploiting data smoothness.
problem Federated learning optimization with smooth loss functions.
method Federated Low Rank Gradient Descent (FedLRGD) algorithm.
result FedLRGD outperforms Federated Averaging (FedAve) in federated oracle complexity under certain conditions.
Polyak step size GD reaches final radius of convergence after log iterations.
problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.
Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.
problem Optimizing empirical risk minimization loss functions
method Piecewise polynomial interpolation-based gradient descent
result Oracle complexity is reduced for smooth loss functions
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…
As the complexity of neural network models has grown, it has become increasingly important to optimize their design automatically through metalearning. Methods for discovering hyperparameters, topologies, and learning rate schedules have lead to significant increases in performance. This paper shows that loss functions…
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.
PINNs solve differential geometry problems in complex shapes.
problem Solving differential geometry problems in complex shapes.
method Training neural networks with loss functions inspired by differential conditions.
result PINNs are effective for differential geometry problems.
Paper proposes new loss functions for training energy networks.
problem Challenges in computing gradients for training energy networks.
method Proposes generalized Fenchel-Young losses for efficient gradient computation.
result Demonstrates the calibration of excess risk for linear-concave energies.
Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the unde…
We analyze the optimization landscape of α-loss in logistic models.
problem Optimization landscape of α-loss in logistic models.
method Tools from strictly-locally-quasi-convex functions and geometric techniques.
result Evolution of optimization landscape with respect to α.
Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
New algorithms achieve decision calibration without sample complexity dependent on feature dimension.
problem Achieving decision calibration for nonlinear loss functions with polynomial sample complexity.
method Developed smooth relaxation of decision calibration, enabling dimension-free algorithms.
result Efficient algorithms post-process predictors to satisfy decision calibration without worsening accuracy.
Paper addresses ERM in LDP, reducing sample complexity for smooth and convex losses.
problem Achieving error α in ERM with non-interactive LDP, especially for high-dimensional data.
method Developed algorithms using Bernstein polynomial and polynomial approximation techniques.
result For smooth and convex losses, sample complexity is linear in dimensionality.
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 …
Adma proposes a flexible loss function for neural networks.
problem Static loss functions limit neural network performance.
method Introduces a flexible loss function that adapts to ANN complexity and data distribution.
result Flexible loss function achieves state-of-the-art performance.
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.
The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In the context of weakly-supervised CNN segmentation, we demonstrate a well-motivated…
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.
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 …
The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves over which training and test accuracy are nearly constant. We introduce a training procedure to discover these hig…
A new framework learns differentiable structured losses from data.
problem Learning effective losses for complex structured prediction tasks.
method Contrastive learning to learn differentiable structured losses from output data.
result Achieves similar or better performance than kernel-based methods.
Proposes sigmoidF1 loss for multilabel classification, improving performance metrics.
problem Lack of smooth, tractable loss functions for multilabel classification.
method Introduces sigmoidF1, a smooth F1 score surrogate loss function.
result sigmoidF1 outperforms other loss functions on various datasets and metrics.
This work examines uncertainty sampling in binary classification using equivalent loss.
problem Lack of consensus on proper uncertainty definition and theoretical guarantees for active learning.
method Systematically examines uncertainty sampling via equivalent loss, proving its optimality.
result Established that uncertainty sampling optimizes against equivalent loss, providing theoretical guarantees.
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed scenarios. Our results show that the error rate depends on two parameters: one captu…
New algorithm reduces sample complexity for omnipredictors of SIMs.
problem Learning optimal predictors for various loss functions.
method Sharp analysis of Isotron algorithm for agnostic learning.
result Improved sample complexity to ≈ε−2 for bi-Lipschitz link functions. 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.
Optimal algorithms for mixable losses in dynamic environments with reduced redundancy.
problem Online optimization of mixable loss functions in a dynamic environment.
method Introduce online mixture schemes with polynomial and logarithmic time complexities.
result Achieves optimal redundancy up to a constant multiplicity gap.
A novel gradient-based method optimizes decision trees for complex tasks.
problem Training decision trees with arbitrary differentiable loss functions.
method Gradient-based optimization using first and second derivatives of loss functions.
result Improves accuracy and flexibility in decision tree optimization.
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.
Although various linear log-distance path loss models have been developed, advanced models are requiring to more accurately and flexibly represent the path loss for complex environments such as the urban area. This letter proposes an artificial neural network (ANN) based multi-dimensional regression framework for path …
Paper establishes generalization bounds for RNNs and improves existing results.
problem Theoretical understanding and generalization bounds for RNNs.
method New generalization error bound and Rademacher complexity calculation.
result Improved generalization bounds for RNNs, tighter than existing bounds.
We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polyno…
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.
This paper evaluates various loss functions for Transformer models in stock ranking.
problem Evaluating loss functions for Transformer models in stock ranking.
method Systematic evaluation of advanced loss functions (pointwise, pairwise, listwise) on S&P 500 data.
result Different loss functions impact a model's ability to discern profitable relative orderings among assets.
We introduce a tunable loss function called α-loss, parameterized by α∈(0,∞], which interpolates between the exponential loss (α=1/2), the log-loss (α=1), and the 0-1 loss (α=∞), for the machine learning setting of classification. Theoretically, we illustrate a fundamental connection between $…
We use surrogate losses to obtain several new regret bounds and new algorithms for contextual bandit learning. Using the ramp loss, we derive new margin-based regret bounds in terms of standard sequential complexity measures of a benchmark class of real-valued regression functions. Using the hinge loss, we derive an ef…
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and empirical risk minimization. While recent work asks which properties are elicitable, …
We develop a new theoretical framework, the \emph{envelope complexity}, to analyze the minimax regret with logarithmic loss functions and derive a Bayesian predictor that adaptively achieves the minimax regret over high-dimensional ℓ1-balls within a factor of two. The prior is newly derived for achieving the mini…
New approach uses loss functions to extend data depth for anomaly detection.
problem Anomaly detection in high-dimensional data.
method Introducing loss depths to generalize halfspace depth.
result New loss depths improve anomaly detection efficiency and interpretability.
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H-consistency bounds.