We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth l…
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48 results for “projective loss functions”
The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well a…
Exploits class similarity for better machine learning models with confidence labels and projective loss functions.
problem Poor model performance due to confusing similar classes.
method Exploits class similarity with confidence labels and projective loss functions.
result Improved model performance on noisy labels.
Study geometric properties of loss functions to understand neural network performance.
problem Understanding the geometric properties of high-dimensional loss functions to improve neural network performance.
method Combine concepts from high-dimensional probability and differential geometry to study curvature properties in lower-dimensional loss representations.
result Mean curvature in the original loss space determines if saddle points appear as minima, maxima, or flat regions.
Paper develops methods for non-quadratic loss low-rank matrix recovery.
problem Recovery of low-rank matrices with non-quadratic losses.
method Projected gradient method with a regularity projection oracle.
result Projected gradient method converges globally and linearly.
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.
Regularizing activations in neural networks via distribution matching with the Wasserstein metriccs.LG
Regularization and normalization have become indispensable components in training deep neural networks, resulting in faster training and improved generalization performance. We propose the projected error function regularization loss (PER) that encourages activations to follow the standard normal distribution. PER rand…
A bidirectional loss function improves label distribution learning and enhancement.
problem Challenges in label distribution learning and label enhancement.
method Bidirectional loss function to address dimensional gap and label enhancement.
result The bidirectional loss function improves the accuracy of label distribution learning and enhancement.
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.
Improved online learning with time-varying constraints for complex domains.
problem Constrained online convex optimization with time-varying constraints.
method Constructing a composite surrogate loss and using the online Frank-Wolfe method.
result Novel regret and cumulative constraint violation bounds for strongly convex losses.
Optimal convex loss function improves regression coefficient estimation.
problem Asymptotic variance improvement in linear regression estimation.
method Score matching extension for log-concave projection.
result Semiparametric estimator attains minimal asymptotic covariance.
Paper tackles online learning on curved spaces without projections.
problem Online learning on Riemannian manifolds with computational constraints.
method Develops projection-free algorithms for geodesically convex optimization.
result Achieves sub-linear regret guarantees in online geodesically convex optimization.
Benguria and Loss have conjectured that, amongst all smooth closed curves of length in the plane, the lowest possible eigenvalue of the operator was one. They observed that this value was achieved on a two-parameter family, , of geometrically distinct ovals containing the round circle and c…
It is now known that an extended Gaussian process model equipped with rescaling can adapt to different smoothness levels of a function valued parameter in many nonparametric Bayesian analyses, offering a posterior convergence rate that is optimal (up to logarithmic factors) for the smoothness class the true function be…
A new method learns proper multiclass losses and probabilities.
problem Learning proper multiclass losses for complex classification tasks.
method Extends monotonicity to multiclass problems using convex functions.
result Consistently outperforms natural multiclass baseline on up to 1,000 class datasets.
A Likelihood-Based Generative Approach for Spatially Consistent Precipitation Downscalingphysics.ao-ph
New approach combines likelihood and adversarial losses for better precipitation predictions.
problem Spatially inconsistent precipitation projections from likelihood-based models.
method Fuses likelihood-based and adversarial losses for generative models.
result Improves spatial consistency in precipitation downscaling.
Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.
problem Minimizing loss and constraint violations in online convex optimization with smooth penalties.
method Projected gradient descent over a set around the current action.
result Both dynamic regret and constraint violation are bounded by the path-length.
New algorithm reduces adaptive regret without projections.
problem Computational expense of projections in online convex optimization.
method Lazy gradient-based algorithm with set-membership computations.
result Near-optimal adaptive regret bounds for general convex functions.
Improved algorithm reduces communication rounds for distributed online learning.
problem Complicated constraints in distributed online learning with locally light computations.
method Proposed D-BOCG algorithm with delayed update mechanism and redefined surrogate loss function.
result Achieved regret bound with communication rounds for convex losses.
We explore a new approach for training neural networks where all loss functions are replaced by hard constraints. The same approach is very successful in phase retrieval, where signals are reconstructed from magnitude constraints and general characteristics (sparsity, support, etc.). Instead of taking gradient steps, t…
For semi-supervised techniques to be applied safely in practice we at least want methods to outperform their supervised counterparts. We study this question for classification using the well-known quadratic surrogate loss function. Using a projection of the supervised estimate onto a set of constraints imposed by the u…
We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to -generalized Bayesian, MDL, and empirical risk minimization estimators. …
This paper deals with supervised classification and feature selection in high dimensional space. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. A strict control on sparsity is moreover obtained by adding an constraint, here on the ma…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first principal components minimizes the sum of squared errors between the original …
Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also Howcs.LG
New research suggests continual learning should focus on both optimization objective and optimization trajectory.
problem Even with perfect joint loss approximation, continual learning still suffers from forgetting when starting a new task.
method Proposes focusing on both optimization objective and optimization trajectory, combining replay-approximated joint objectives with gradient projection-based optimization routines.
result Combining replay-approximated joint objectives with gradient projection-based optimization routines did not show clear benefits in initial experiments.
Mini-batch sub-sampling in neural network training is unavoidable, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. In this study we specifically distinguish between static mini-batch sub-sampled loss functions, where mi…
Optimizes differentially private kernel learning with random projection.
problem Privacy-preserving learning algorithms with optimal performance.
method Differentially private kernel ERM algorithm based on random projection in reproducing kernel Hilbert space.
result Achieves minimax-optimal excess risk rates for various loss functions.
Paper introduces P-FGD for online quantile regression models.
problem Training nonparametric additive quantile regression models in online settings.
method Projected functional gradient descent algorithm (P-FGD) for pinball loss.
result P-FGD achieves minimax optimal consistency rate .
Investigating the interaction between gradient-only line searches and different activation functionsstat.ML
GOLS finds activation functions affect training robustness, especially ReLU.
problem Investigate how different activation functions impact GOLS in neural network training.
method Identify SNN-GPPs for GOLS, analyze activation function effects on gradient continuity.
result GOLS robust for most activation functions but sensitive to ReLU.
Teaching is critical to human society: it is with teaching that prospective students are educated and human civilization can be inherited and advanced. A good teacher not only provides his/her students with qualified teaching materials (e.g., textbooks), but also sets up appropriate learning objectives (e.g., course pr…
FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.
problem Training neural networks without feedback from downstream layers.
method Forward Projection (FP) method that uses randomised nonlinear projections and closed-form regression.
result FP achieves comparable generalisation to backpropagation methods with a single forward pass, offering significant speedup.
A new algorithm estimates sparse gradients on graphs with improved risk bounds.
problem Estimating sparse gradients on graph-structured data.
method Tree-Projected Gradient Descent algorithm for gradient-sparse parameters.
result Achieves risk bound of .
GOPO optimizes large models in Hilbert space, avoiding Kullback-Leibler's curvature.
problem Optimizing large language models with Kullback-Leibler divergence's curvature issues.
method GOPO uses Hilbert space L2(pi_k) with orthogonality constraints and a work-dissipation functional.
result GOPO achieves competitive generalization with stable gradient dynamics and entropy preservation.
New method improves calibration in multi-output probabilistic models.
problem Challenges in achieving multivariate calibration in multi-output regression.
method General regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions.
result Significant improvement in calibration across all pre-rank functions without sacrificing predictive accuracy.
We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.
problem Traditional generative models struggle with heavy-tailed and multivariate data, leading to unstable training and mode dropping.
method We extend the invariant statistical loss method to handle heavy-tailed and multivariate data using a Pareto-ISL generator trained with input noise from a generalised Pareto distribution.
result Pareto-ISL accurately models the tails of heavy-tailed distributions while capturing central characteristics.
Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a memory-affordable way, we propose an online technique based on functional stochastic …
Robust Distortion Risk Measuresq-fin.RM
Paper quantifies distortion risk measures' robustness to distributional uncertainty.
problem Quantifying risk measures' robustness to distributional uncertainty.
method Employing isotonic projections, the paper derives bounds on distortion risk measures' values.
result Sharp bounds on distortion risk measures' values are provided, especially for Value-at-Risk and Range-Value-at-Risk.
Develops high-dimensional measurement error models for non-linear loss functions.
problem Measurement errors in ultrahigh-dimensional biomedical data.
method Lipschitz loss functions, L1 norm minimization, Lasso analog.
result Improved accuracy in classification and quantile regression problems.
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to c…
We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexit…
Gradient descent at edge of stability stabilizes implicitly, following projected gradient descent.
problem Gradient descent's stability and sharpness behavior at the edge of instability.
method Cubic Taylor expansion analysis of gradient descent dynamics.
result Gradient descent at edge of stability implicitly follows projected gradient descent.
Localized Kernel Projection Outlyingness: A Two-Stage Approach for Multi-Modal Outlier Detectioncs.LG
Two-stage framework detects multi-modal outliers.
problem Detecting outliers in multi-modal data structures.
method Combines global kernel PCA and local clustering stages.
result Significantly outperforms existing methods on challenging datasets.
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
ENSURE framework trains deep image recon algorithms without clean data.
problem Lack of clean, fully sampled ground-truth data for deep learning image reconstruction.
method Introduces ENSURE framework, a generalization of SURE and GSURE to random sampling patterns.
result ENSURE loss function is an unbiased estimate for true mean-square error.
A new method optimizes projection directions for sliced Wasserstein distances.
problem Finding informative projecting directions for sliced Wasserstein distances is computationally expensive.
method Amortized projection optimization to predict directions efficiently.
result Proposed amortized models improve generative modeling performance.
Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly isometrically, known as the restricted isometric property in compressed sensing. In th…
Improves deep learning models by blending gradients from training loss and auxiliary objective.
problem Minimizing a single training loss while encouraging desirable model properties.
method Solves a bilevel optimization problem by combining training loss gradients and orthogonal projections of auxiliary gradients.
result Bloop method leads to better performance than other gradient surgery methods without EMA.
New algorithms optimize actions under time-varying constraints without projecting.
problem Optimizing actions under time-varying constraints without projecting.
method Projection-free algorithms using linear optimization oracle.
result Guaranteed regret and constraints violation.