A structured prediction method for ranking labels.
problem Solving label ranking problems as structured output regression.
method Two-step approach: regression in feature space followed by pre-image solving.
result Efficiency on real-world datasets for partial and complete rankings.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
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.
We present surrogate regret bounds for arbitrary surrogate losses in the context of binary classification with label-dependent costs. Such bounds relate a classifier's risk, assessed with respect to a surrogate loss, to its cost-sensitive classification risk. Two approaches to surrogate regret bounds are developed. The…
New bounds show polyhedral surrogates are optimal for generalization.
problem Proving generalization rates for polyhedral loss functions.
method Developed two general results for polyhedral surrogates.
result Polyhedral surrogates provide linear surrogate regret bounds, translating directly to target rates.
Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Improved robustness in kernel-based regression via novel loss function and IRLS.
problem Noise sensitivity in kernel-based regression methods.
method Proposed ℓs-loss function and iteratively reweighted least squares (IRLS) optimization. result Improved noise robustness in kernel-based regression methods.
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of output labels, we first estimate the conditional risk function by solving a (possi…
STORM enables edge computing for empirical risk minimization.
problem Training models on edge devices for streaming data.
method Online sketching for empirical risk minimization.
result STORM can estimate least-squares objective accurately.
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.
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.
Paper develops a least-squares framework for learning discrete losses.
problem Learning strategies for discrete losses (e.g., multilabeling, ranking).
method Least-squares framework to systematically design learning algorithms for discrete losses.
result Improved results with explicit dependence on the number of labels and faster learning rates.
Study on H-consistency bounds for machine learning surrogates.
problem Estimating target loss error relative to surrogate loss error in machine learning.
method Developed H-consistency bounds for various surrogates and loss functions. result Stronger guarantees than existing methods, offering distribution-dependent and -independent bounds.
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. Paper analyzes proper losses and their performance in machine learning tasks.
problem Understanding the performance of estimators and forecasters in machine learning tasks.
method Analyzes surrogate regret and convergence rates for strictly proper losses.
result Strongly proper losses achieve the optimal convergence rate.
The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. …
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.
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…
Optimizes maps with controlled distortion for geometric tasks.
problem Free-boundary diffeomorphism optimization in geometric modeling.
method Least-squares quasiconformal (LSQC) operator and Spectral Beltrami Network (SBN).
result LSQC minimizer well-posed under mild conditions, stable under mesh refinement.
3D GAN improves MRI image quality from low-res scans.
problem Improving MRI image quality from low-resolution scans.
method Adversarial learning using 3D convolutions and least squares loss.
result 3D GAN generates high-quality 3D MRI images from low-resolution scans.
Efficient method for high-dimensional American option pricing and hedging.
problem High-dimensional American option pricing and hedging.
method Gradient-enhanced sparse Hermite polynomial expansions combined with least squares Monte Carlo.
result Outperforms state-of-the-art methods in high dimensions with comparable computational cost.
Improved machine learning model performance through data augmentation, custom loss functions, and transfer learning.
problem Poor performance of a traditional engineering model due to limited training data.
method Data augmentation, custom loss functions, transfer learning.
result Improvement of at least 38% in performance across five models.
A new autoregressive SPO method improves decision-making for dependent data.
problem Improving decision-making for dependent data in stochastic optimization.
method An autoregressive Smart Predict-then-Optimize (SPO) method for time series data.
result Generalization bounds and uniform calibration results for the SPO loss in autoregressive models.
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.
Paper uses deep learning to solve PDEs without supervision.
problem Solving elliptic PDEs without labeled data.
method Uses deep neural networks and least-squares functionals.
result Demonstrates effectiveness on 1D second-order elliptic PDEs.
Bayesian optimization reduces hyperparameters for mixed variable design problems.
problem Optimizing designs with a large number of mixed continuous, integer, and categorical variables.
method Adaptive dimension reduction using partial least squares for fewer hyperparameters.
result Significant improvement in performance compared to genetic algorithms.
The paper explores trading off consistency and dimensionality in convex surrogates for multiclass classification.
problem Designing consistent surrogate losses for multiclass classification with high-dimensional outcomes.
method Investigates embedding outcomes into convex polytopes and examining consistency under low-noise assumptions.
result Consistency can be achieved with less than n−1 dimensions, but hallucination occurs for some distributions. Exact expressions for double descent and implicit regularization in over-parameterized models.
problem Understanding the generalization error of over-parameterized models like deep neural networks.
method Surrogate random design to replace standard i.i.d. design, leading to exact expressions for mean squared error and implicit regularization.
result Exact non-asymptotic expressions for double descent and implicit regularization in over-parameterized models.
Study shows squared loss is robust for binary classification with noisy features.
problem Learning binary classifiers with noisy features.
method Sy-De and Asy-In attribute noise models, analyzing l0−1 and lsq losses. result Squared loss is robust in Sy-De model but not in Asy-In model.
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) 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-supervised method…
Algorithm solves robust linear regression with block Lewis weights.
problem Group distributionally robust least squares problem.
method Algorithm based on geometric construction and block Lewis weights, using accelerated proximal methods.
result Improves over known methods for moderate accuracy regimes and matches state-of-the-art guarantees.
The conditional-mean barrier helps diagnose deterministic surrogates missing uncertainty.
problem Uncertainty in deterministic surrogates for complex systems.
method Developed diagnostics to locate the conditional-mean barrier and prove its necessity for distributional objectives.
result Crossing the barrier requires a loss that scores distributions, not point predictions.
EPGP surrogate outperforms finite elements in solving wave equations.
problem Benchmarking Gaussian Process surrogates vs. finite elements for wave equation solutions.
method EPGP uses penalized least squares and exponential-polynomial bases; CN-FEM employs Crank--Nicolson time stepping.
result EPGP achieves lower error than CN-FEM under matched degrees-of-freedom.
Bayesian optimization selects wavelengths for sugar content estimation in NIR spectroscopy.
problem Improving prediction accuracy and interpretability of spectral data for sugar content estimation.
method Formulated as a binary black-box optimization problem, proposed method uses Bayesian optimization with a sparse quadratic surrogate model and Thompson sampling.
result Improves prediction accuracy of partial least squares regression and yields more consistent wavelength regions.
Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large number of function evaluations. Gradient-enhanced kriging has the potential to r…
Optimal multiscale learning of linear operators
problem Statistical and computational limits of learning bounded linear operators between Sobolev spaces
method Reformulate as an infinite-dimensional matrix regression problem with heterogeneous multiscale structure
result Establish minimax rates and construct a finite-resolution blockwise least-squares estimator attaining these rates
EASE estimator improves probabilistic value estimation efficiency.
problem Efficiently estimating probabilistic values like Shapley and semivalues.
method Developed an Efficiency-Aware Surrogate-adjusted Estimator (EASE) that minimizes first-order mean squared error.
result EASE consistently outperforms existing estimators for various probabilistic values.
The paper explores machine learning methods for proxy modeling in life insurance solvency capital requirements.
problem Life insurance companies need to estimate solvency capital requirements from full loss distributions, but computational limitations restrict full simulations.
method The paper presents various adaptive machine learning approaches to approximate the risk-dependent proxy function using least-squares Monte Carlo.
result The machine learning methods significantly improve the accuracy and efficiency of proxy modeling compared to traditional regression techniques.
New algorithm improves regression error bounds and accelerates performance for low noise.
problem Nonparametric least square regression in RKHS with optimal error bounds.
method Kernel Truncated Randomized Ridge Regression (KTRRR) with optimal generalization error bounds.
result Faster finite-time and asymptotic rates on low noise problems.
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In this approach, one gets a surrogate dataset by sampling from the full data, and …
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…
MFNets constructs efficient multifidelity surrogates from diverse information sources.
problem Creating accurate surrogates from multiple, potentially costly or inaccurate data sources.
method Directed acyclic graph of connections, gradient-based minimization of least squares objective, flexible information source structure.
result Error reduction by orders-of-magnitude, especially in low-data scenarios.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O(d/n) in bounded distributions. Improves Bayesian optimisation for engineering design problems with many variables.
problem Efficiently searching for global minima in high-dimensional design spaces.
method Integrates input and output data to identify a reduced latent subspace using probabilistic partial least squares.
result Significant improvements in convergence to the global minimum compared to existing methods.
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…
Efficient surrogate losses and regularization methods for structured prediction.
problem Efficiency and performance in structured prediction with rich label structures.
method Development of bi-criteria surrogate losses and shared Frobenius norm for regularization.
result Improved efficiency and performance in inference and optimization for structured prediction.
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 K principal components minimizes the sum of squared errors between the original …
This paper introduces new loss functions for balanced multi-class classification.
problem Balancing class imbalance in multi-class classification.
method Introduces two new surrogate loss families: GLA and GCA.
result GCA losses offer stronger theoretical guarantees in imbalanced settings.