This paper proposes a mechanism to produce equivalent Lipschitz surrogates for zero-norm and rank optimization problems by means of the global exact penalty for their equivalent mathematical programs with an equilibrium constraint (MPECs). Specifically, we reformulate these combinatorial problems as equivalent MPECs by…
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48 results for “Lipschitz surrogate”
Polynomial-time algorithm for near-optimal community detection in graphs.
problem Node-private community estimation in stochastic block models.
method Explicit Lipschitz surrogate and accept-reject algorithm for sampling community labels.
result Achieves minimax rates for exact recovery with polynomial-time runtime and logarithmic privacy parameter.
New PG losses improve decision optimization in misspecified models.
problem Improving decision optimization in models that are not perfectly specified.
method Introducing Perturbation Gradient (PG) losses to connect decision loss with directional derivatives and optimizing using gradient techniques.
result PG losses yield best-in-class policies asymptotically, even in misspecified settings.
We investigate online classification with paid stochastic experts. Here, before making their prediction, each expert must be paid. The amount that we pay each expert directly influences the accuracy of their prediction through some unknown Lipschitz "productivity" function. In each round, the learner must decide how mu…
New algorithms reduce regret for convex bandits with small comparator norms.
problem Optimizing in bandit convex optimization with varying comparator norms.
method Developed algorithms using techniques from full-information setting and new gradient estimators.
result Regret bounds are small when comparator norm is small.
This manuscript provides optimization guarantees, generalization bounds, and statistical consistency results for AdaBoost variants which replace the exponential loss with the logistic and similar losses (specifically, twice differentiable convex losses which are Lipschitz and tend to zero on one side). The heart of the…
Proposes a new generalization bound for Bayesian deep nets without strict assumptions.
problem Lack of generalization bounds for Bayesian deep nets without strict assumptions.
method Exploits contractivity of Log-Sobolev inequalities to add a loss-gradient norm term to the generalization bound.
result Introduces a new generalization bound for Bayesian deep nets that avoids strict assumptions.
The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is…
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.
Neural networks are dense among Lipschitz functions with fixed Lipschitz constant.
problem Characterizing neural network approximations to Lipschitz functions.
method Analyzing -Lipschitz neural networks and their density in -Lipschitz functions.
result One layer neural networks are dense in the set of all -Lipschitz functions.
Constructs a map with prescribed local Lipschitz constants on a subset of a manifold.
problem Creating a Lipschitz map with specific local Lipschitz constants on a subset of a manifold.
method Constructs a Lipschitz map that matches a given map on a subset and has a local Lipschitz constant defined by a continuous function.
result A Lipschitz map can be constructed with a local Lipschitz constant prescribed by a continuous function.
Maps between certain Lipschitz manifolds are isometries if they preserve volume.
problem Volume preservation and isometry conditions for Lipschitz manifolds.
method Volume-preserving 1-Lipschitz maps from integral currents onto infinitesimally Euclidean Lipschitz manifolds.
result Volume-preserving maps are isometries under given conditions.
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
problem Generalization bounds with strict assumptions like uniformly bounded loss.
method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.
result Proposes a new generalization bound with a surrogate of model complexity.
We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and control flow of the reference simulator. Our surrogates target stochastic simul…
Randomizing the Fourier-transform (FT) phases of temporal-spatial data generates surrogates that approximate examples from the data-generating distribution. We propose such FT surrogates as a novel tool to augment and analyze training of neural networks and explore the approach in the example of sleep-stage classificat…
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 , assigns the original loss val…
The paper proposes a scalable framework for uncertainty quantification and propagation in surrogate-based Bayesian inference.
problem Uncertainty in surrogate models and its impact on inference and decision-making.
method Bayesian inference methods for surrogate models with measurement data.
result Scalable framework for uncertainty quantification and propagation in surrogate models.
Paper proposes hybrid modeling to improve surrogate accuracy using multiple data sources.
problem Improving surrogate model accuracy by integrating simulation and real-world data.
method Two novel probabilistic approaches: separate and combined surrogates with weighting strategy.
result Hybrid models improve predictive accuracy and coverage compared to single-source surrogates.
Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables i…
Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.
problem Deformation of Lipschitz homeomorphisms
method Lipschitz analogues of Siebenmann's and Perelman's homeomorphism theory
result Lipschitz stability theorem and gluing theorem
The paper proposes a method to assess surrogate heterogeneity in non-randomized data.
problem Lack of methods to evaluate surrogate heterogeneity in non-randomized data.
method Proposes a framework using meta-learners to assess surrogate heterogeneity in real-world data.
result Identifies individuals for whom the surrogate is a valid replacement of the primary outcome.
We compute the local Lipschitz constant of ReLU networks precisely.
problem Estimating the local Lipschitz constant of ReLU networks is hard.
method We use a novel approach involving the generalized Jacobian and backpropagation.
result We provide an algorithm to compute the exact Lipschitz constant of ReLU networks.
Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are characterised by their ability to efficiently emulate complex computational models …
This paper develops efficient surrogate models for optimization of complex dynamical systems.
problem Computational expense in solving complex dynamical systems through numerical simulation.
method Combination of proper orthogonal decomposition and radial basis functions for constructing low-dimensional surrogate models.
result Surrogate models reduce computational time for optimization problems while maintaining accuracy.
Study shows infinite distinct outer metric Lipschitz classes for knots in .
problem Lipschitz classification of surface singularities in .
method Outer metric Lipschitz equivalence and topological equivalence of knots.
result Infinitely many distinct outer metric Lipschitz classes for knots in .
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…
This work improves surrogate models for balancing accuracy and cost in multi-fidelity methods.
problem Balancing accuracy and computational cost in multi-fidelity methods.
method Develops context-aware surrogate models for multi-fidelity importance sampling and Bayesian inverse problems.
result Context-aware surrogate models can lead to runtime speedups of up to one order of magnitude.
The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.
problem The expressivity of bi-Lipschitz Normalizing Flows in approximating specific target distributions.
method Characterization of expressivity through lower bounds on Total Variation distance and discussion of potential remedies.
result Several target distributions are difficult to approximate using bi-Lipschitz Normalizing Flows, and lower bounds on their approximation are provided.
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.
Novikov conjecture reduced to Lipschitz cohomology of groups.
problem Novikov higher signature conjecture for groups.
method Introducing Lipschitz cohomology classes and reducing the conjecture.
result Reduced Novikov conjecture to Lipschitz cohomology.
New method simplifies checking consistency of differentiable loss functions.
problem Verifying consistency of differentiable loss functions is difficult.
method Developed a new approach called strong indirect elicitation (strong IE) to simplify checking consistency.
result Strong IE is equivalent to calibration for strongly convex, differentiable surrogates.
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 examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arisi…
Paper introduces new loss functions for multi-class abstention learning.
problem Learning with multi-class classification and the ability to abstain.
method Developed new families of surrogate losses for abstention.
result Proved strong consistency guarantees for new surrogate losses.
Proposal-Guided Greedy Surrogate Refinement for PDE-Driven High-Dimensional Rare-Event Estimationmath.NA
Proposes a method to refine PDE-driven high-dimensional rare-event simulation.
problem Challenges in constructing accurate surrogates for rare-event simulation.
method Adaptive importance sampling framework that refines a locally constructed surrogate.
result Achieves accuracy comparable to true-model adaptive importance sampling with fewer high-fidelity evaluations.
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.
New MIP formulations for neural network Lipschitz constant estimation.
problem Ensuring robustness of neural networks by calculating their Lipschitz constant.
method Reformulating the neural network Lipschitz estimation problem as a Quadratically Constrained MIP (MIQCQP) problem.
result Solutions of the MIQCQP formulations provide bounds on the Lipschitz constant, with conditions for exactness.
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…
A new framework improves reinforcement learning algorithms with policy guarantees.
problem Designing efficient and stable reinforcement learning algorithms.
method A general framework (FMA-PG) based on functional mirror ascent that constructs surrogate functions enabling policy improvement guarantees.
result The proposed framework enables policy improvement guarantees that hold regardless of policy parameterization, and recovers important heuristics.
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…
New method for differentially private optimization with general Lipschitz conditions.
problem Differentially private optimization under general Lipschitz conditions.
method Generalized Lipschitz condition for per-sample gradients, tuning clip norm based on minimum per-sample Lipschitz constant.
result Efficacy of the recommended clip norm tuning method verified on 8 datasets.
The paper studies properties of intrinsically Lipschitz constants in metric spaces.
problem Investigating properties of intrinsically Lipschitz constants.
method Introduced Leibniz and product formulas for intrinsic slope.
result Formulated Leibniz and product formulas for intrinsic slope.
New scalable Lipschitz bounds improve neural network robustness analysis.
problem Computing tight Lipschitz bounds for deep neural networks is challenging and computationally expensive.
method Derived new closed-form Lipschitz bounds using more general feasible points of LipSDP, avoiding SDP solvers.
result Improved scalability and precision of Lipschitz estimation for large neural networks.
The paper studies Lipschitz bounds for integral kernels under differentiability assumptions.
problem Understanding the Lipschitz continuity of feature maps associated with integral kernels.
method Analyzes differentiability assumptions to derive explicit formulas for Lipschitz constants and conditions for non-Lipschitz continuity.
result Explicit formulas and conditions for Lipschitz continuity of feature maps associated with various kernels.
We characterize locally Lipschitz mappings and existence of Lipschitz extensions through a first order nonlinear system of PDEs. We extend this study to graded group-valued Lipschitz mappings defined on compact Riemannian manifolds. Through a simple application, we emphasize the connection between these PDEs and the Ru…
Sobolev-to-Lipschitz property of geodesically complete spaces with curvature bounded from abovemath.DG
Geodesically complete spaces with curvature bounded above have maps with finite energy that are Lipschitz.
problem Analyzing the properties of geodesically complete spaces with curvature constraints.
method Geometric perturbations of geodesics to curves with zero length on singular sets.
result Every Sobolev map in space has a Lipschitz representative with the same Lipschitz constant as its infinity energy.
We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz …
Develops methods to create consistent surrogate models for agent-based simulators.
problem High computational costs and misjudgment of interventions in agent-based models.
method Causal abstractions to learn interventionally consistent surrogate models.
result Surrogates trained for interventional consistency closely mimic the agent-based model's behavior under interventions.