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 bounds convergence rate of adversarial surrogate risk.
problem Vulnerability of binary classification models to adversarial attacks.
method Characterizes conditions for adversarial consistency and provides surrogate risk bounds.
result Surrogate risk bounds quantify the rate of convergence of adversarial classification risk.
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…
Adversarial consistency depends on the uniqueness of adversarial Bayes classifiers.
problem Consistency of adversarial surrogate losses is not guaranteed.
method Connected consistency of adversarial surrogate losses to the uniqueness of adversarial Bayes classifiers.
result A convex surrogate loss is statistically consistent for adversarial learning if and only if the adversarial Bayes classifier is unique.
Develops a SAS approach for high-dimensional risk prediction using unlabeled data.
problem Challenges in risk modeling with EHR data due to lack of direct disease outcomes and high dimensionality.
method Surrogate Assisted Semi-supervised Learning (SAS) approach leveraging unlabeled and labeled data.
result Valid inference for predicted risk even when underlying model is dense and mis-specified.
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…
In statistical learning theory, convex surrogates of the 0-1 loss are highly preferred because of the computational and theoretical virtues that convexity brings in. This is of more importance if we consider smooth surrogates as witnessed by the fact that the smoothness is further beneficial both computationally- by at…
We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.
problem Establishing linear regret bounds for convex smooth losses.
method Constructing a convex smooth surrogate loss using Fenchel-Young losses generated by the convolutional negentropy.
result We derive a smooth loss with a linear surrogate regret bound.
Active learning is a type of sequential design for supervised machine learning, in which the learning algorithm sequentially requests the labels of selected instances from a large pool of unlabeled data points. The objective is to produce a classifier of relatively low risk, as measured under the 0-1 loss, ideally usin…
We provide novel theoretical insights on structured prediction in the context of efficient convex surrogate loss minimization with consistency guarantees. For any task loss, we construct a convex surrogate that can be optimized via stochastic gradient descent and we prove tight bounds on the so-called "calibration func…
New method optimises learning via surrogate PAC-Bayes bounds.
problem Computational intractability of optimising generalisation bounds.
method Iteratively optimising surrogate training objectives derived from PAC-Bayes bounds.
result Iteratively optimising surrogates implies optimising original generalisation bounds.
Derivative-informed models improve financial surrogates for accurate hedging and risk management.
problem Developing fast surrogate models for financial derivatives and risk quantities.
method Derivative-informed operator learning framework combining neural operators, random features, and tangent sensitivity equations.
result The framework reduces hedging and risk errors by 40-76% compared to standard surrogates.
New method integrates real and synthetic data to improve machine learning models.
problem Expensive or impractical collection of high-quality data limits machine learning.
method Weighted empirical risk minimization approach for integrating surrogate data.
result Integrating surrogate data can significantly reduce test error on the original distribution.
This research improves PAC-Bayesian bounds for classification tasks using convexified loss.
problem Deriving generalization bounds for classification tasks with non-convex loss functions.
method Shift focus to misclassification excess risk bounds for PAC-Bayesian classification using convex surrogate loss and leveraging PAC-Bayesian relative bounds in expectation.
result Improved PAC-Bayesian bounds for classification tasks with convex surrogate loss.
Model predicts insolvency risks in banks due to liquidity and credit risks.
problem Determining insolvency regions in banks due to non-linear interaction between liquidity and credit risks.
method Developed a continuous-time structural dynamic model integrating Basel III requirements into a stochastic optimal control framework. Used Hamilton-Jacobi-Bellman (HJB) equation to solve for insolvency boundary. Derived surrogate analytical approximation for real-time monitoring.
result Calibrated model reveals significant non-linear threshold effects and accelerates insolvency transition.
This research analyzes the consistency of convex and nonconvex surrogate losses for adversarially robust classification.
problem Ensuring classifiers are robust to adversarial perturbations.
method Analysis of convex and nonconvex surrogate losses through the lens of calibration.
result No convex surrogate loss is calibrated with respect to the adversarial 0-1 loss for linear models, but nonconvex losses can be calibrated under certain conditions.
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 studies consistency of surrogate loss procedures under constrained classifiers.
problem Consistency of surrogate loss approaches under constrained classifiers without correct specification.
method The paper develops theoretical results and hinge loss based procedures for a constrained classification problem.
result Hinge losses are the only surrogate losses that preserve consistency in second-best scenarios.
New method uses surrogate outcomes and single-record data to improve suicide risk modeling.
problem Lack of historical information in single-record patients hinders modeling rare medical events.
method Hybrid framework combining supervised and unsupervised learning to integrate concurrent and single-record data.
result Single-record data and concurrent diagnoses provide valuable information for improving suicide risk modeling.
We study the interplay between surrogate methods for structured prediction and techniques from multitask learning designed to leverage relationships between surrogate outputs. We propose an efficient algorithm based on trace norm regularization which, differently from previous methods, does not require explicit knowled…
New active learning framework for multiclass classification beyond realizability assumption.
problem Active learning in non-realizable settings with convex model classes.
method Surrogate risk minimization, epoch-based fitting, aggregation of models.
result Achieves label and sample complexity comparable to prior work in non-realizable settings.
We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many predictions (e.g.\ rankings) as a point in Rd, assigns the original loss val…
This paper investigates recently proposed approaches for defending against adversarial examples and evaluating adversarial robustness. We motivate 'adversarial risk' as an objective for achieving models robust to worst-case inputs. We then frame commonly used attacks and evaluation metrics as defining a tractable surro…
In this paper we refine the process of computing calibration functions for a number of multiclass classification surrogate losses. Calibration functions are a powerful tool for easily converting bounds for the surrogate risk (which can be computed through well-known methods) into bounds for the true risk, the probabili…
A new method SLIDE ensures fairness in AI models.
problem Ensuring fairness in AI models while maintaining computational feasibility.
method Proposes a new surrogate fairness constraint SLIDE.
result SLIDE ensures fairness in AI models asymptotically and converges fast.
Sharp analysis of knowledge distillation for high-dimensional regression.
problem Characterizing the risk of target models in high-dimensional settings.
method Sharp non-asymptotic bounds for ridgeless regression under model and distribution shifts.
result Identifies optimal surrogate models and reveals benefits and limitations of discarding weak features.
Area under ROC (AUC) is an important metric for binary classification and bipartite ranking problems. However, it is difficult to directly optimizing AUC as a learning objective, so most existing algorithms are based on optimizing a surrogate loss to AUC. One significant drawback of these surrogate losses is that they …
We propose to study the generalization error of a learned predictor h^ in terms of that of a surrogate (potentially randomized) predictor that is coupled to h^ and designed to trade empirical risk for control of generalization error. In the case where h^ interpolates the data, it is interesting to con…
This paper improves risk bounds and calibration for smart predict-then-optimize method.
problem Improving risk bounds and calibration for smart predict-then-optimize method.
method Develops risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss.
result Empirical minimizer of the SPO+ loss achieves low excess true risk with high probability.
LOL-GP model improves surrogate modeling of expensive simulators.
problem Costly computer simulations for complex systems.
method Local transfer learning Gaussian process.
result Improved surrogate performance over existing methods.
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 …
We propose a robust adversarial prediction framework for general multiclass classification. Our method seeks predictive distributions that robustly optimize non-convex and non-continuous multiclass loss metrics against the worst-case conditional label distributions (the adversarial distributions) that (approximately) m…
Tensor network surrogate for efficient option pricing in large portfolios.
problem Large-scale portfolio revaluation problems in market risk management.
method Tensor-train (TT) approximation for high-dimensional price surfaces, direct inference using Laplacian kernel and TT representations.
result Tensor surrogate achieves lower test error and faster evaluation times compared to standard GPR.
Human stablecoin transactions predict political risk in cryptocurrency markets.
problem Predicting political risk in cryptocurrency markets.
method Structural break analysis and surrogate-based robustness tests.
result Human-driven stablecoin transactions shift significantly before major political events.
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
In this dissertation, we focus on several important problems in structured prediction. In structured prediction, the label has a rich intrinsic substructure, and the loss varies with respect to the predicted label and the true label pair. Structured SVM is an extension of binary SVM to adapt to such structured tasks. I…
MRCs minimize worst-case expected 0-1 loss and provide performance guarantees.
problem Minimizing expected 0-1 loss in classification.
method Minimizes worst-case expected 0-1 loss over uncertainty sets defined by linear constraints.
result Achieves efficient learning and generalization with performance guarantees.
Paper tackles regression with cost-based rejection, balancing prediction and rejection costs.
problem Regression with cost-based rejection, balancing prediction and rejection costs in a continuous target space.
method Formulated expected risk, derived Bayes optimal solution, proposed surrogate loss function.
result Bayes optimal solution can be recovered by the proposed surrogate loss function.
A new method for learning to defer decisions with expert advice improves over standard methods.
problem Learning to defer decisions with expert advice in systems where expert information can be modified after selection.
method An augmented surrogate that operates on the composite expert-advice action space, providing consistency guarantees and excess-risk bounds.
result The method improves over standard Learning-to-Defer and adapts its advice acquisition behavior to the cost regime.
UREs lead to overfitting in complex models, especially in complementary label learning.
problem Overfitting in weakly supervised learning with complementary labels.
method Proposed a surrogate complementary loss (SCL) framework to reduce gradient variance.
result SCL mitigates overfitting and improves URE-based methods.
This paper develops convex surrogates for optimizing the multi-label F-measure.
problem Optimizing the F-measure for multi-label classification is computationally hard.
method Designing convex surrogate losses calibrated for the F-measure.
result The F-measure for multi-label problems has a rank of at most s2+1. New algorithm reduces online logistic regression regret without exponential constant.
problem Improper learning in online logistic regression with logarithmic regret.
method Regularized empirical risk minimization with surrogate losses.
result Regret scaling as O(B log(Bn)) with low computational complexity.
Paper extends SMM to weakly convex and multi-convex surrogates for non-convex optimization.
problem Non-convex optimization with weakly convex or multi-convex surrogates.
method Stochastic majorization-minimization with proximal regularization or block-minimization.
result Convergence rates for empirical and expected losses under non-i.i.d. data.
This paper characterizes and designs loss functions for robust classification with abstention.
problem Ensuring robustness against adversarial attacks and knowing when to abstain from prediction.
method Proposes adversarial robust reject option loss and characterizes surrogates for calibration.
result Shifted Double Ramp Loss and Shifted Double Sigmoid Loss satisfy the calibration conditions.
Symmetric losses improve classifier robustness from corrupted labels.
problem Improving classifier performance from corrupted labels.
method Symmetric losses that satisfy a certain condition.
result Symmetric losses enhance robust classification from corrupted labels.
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.
Unified market making controls risk, arbitrage, and volatility surfaces.
problem Market making risk, arbitrage, and volatility surface consistency.
method Constrained RL and stochastic control for risk-sensitive execution and hedging.
result Agent achieves positive P&L with zero calendar and butterfly violations.
New method improves solving combinatorial optimization problems with smoothed policies.
problem Solving combinatorial optimization problems repeatedly with varying instances.
method Smoothed policies with controlled random perturbations to linear oracle, leading to differentiable surrogate risk.
result Generalization bound decomposes excess risk into bias, estimation, and optimization components.