This paper approximates Gaussian process emulators with constraints and noisy data.
problem Realistic stochastic emulators with inequality constraints and noisy observations.
method Monte Carlo and Markov Chain Monte Carlo methods with noise term.
result Improved performance of MC and MCMC samplers with noisy observations and constraints.
Proposes a method to impose linear inequality constraints on neural networks.
problem Imposing prior knowledge on neural network activations.
method Directly incorporates constraints into the network architecture using stochastic gradient descent.
result Significantly speeds up inference at test time with up to two orders of magnitude improvement.
Novel GP-modulated Cox process framework with linear inequality constraints.
problem Modeling point patterns with positiveness and inequality constraints.
method Directly impose positiveness and inequality constraints on the Gaussian process without restrictions on covariance functions.
result Accurate inference of intensity functions with improved results for monotonic processes.
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017) which can satisfy inequality conditions everywhere (either boundedness, monoton…
A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.
problem Solving variational inequality problems with multiple functional constraints efficiently.
method Constrained Gradient Method (CGM) for Minty variational inequality problems.
result The Constrained Gradient Method achieves complexity similar to projection-based methods but with cheaper oracles.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…
Detects causal scenarios with inequality constraints among classical correlations.
problem Classifying causal structures and identifying those with inequality constraints.
method Using d-separation, e-separation, incompatible supports, and HLP condition.
result Resolved all but three causal scenarios with up to 4 observed variables.
Sharp inequalities in unit ball with constraints on moments.
problem Establishing Sobolev trace inequalities with constraints.
method Constructing smooth test functions for higher order moments.
result Almost optimal Sobolev trace inequalities for 2nd and 4th orders.
New loss function handles uncertain constraints in CSLO problems.
problem Handling uncertain inequality constraints in CSLO with machine learning predictions.
method Introduces SPO-RC loss and SPO-RC+ surrogate, trains on truncated datasets, corrects bias.
result SPO-RC+ effectively manages constraint uncertainty and improves performance.
Additive Gaussian process framework handles monotonicity constraints in high dimensions.
problem Handling monotonicity constraints in high-dimensional data.
method Additive Gaussian process framework with MaxMod algorithm for dimension reduction.
result Framework enables to satisfy monotonicity constraints everywhere in the input space.
The paper develops a method for Gaussian Process regression with linear operator constraints.
problem Modeling functions with multiple linear constraints in high-consequence engineering systems.
method Develops a method for constrained Gaussian Process regression using linear operator constraints.
result Derives the exact posterior for a conjugate likelihood under linear operator constraints.
FISAR uses neural networks to optimize safe reinforcement learning with forward-invariant constraints.
problem Safe reinforcement learning with constraints in safety-critical environments.
method Imposing linear constraints on policy parameters' updating dynamics, using a DNN-based optimizer to satisfy these constraints.
result The policy decreases constraint violation and maximizes cumulative reward monotonically.
DiffSlack learns neural networks with nonlinear constraints via learnable slack variables.
problem Enforcing nonlinear inequality constraints in neural networks.
method DiffSlack reformulates inequalities as equalities with learnable slack variables, predicting them as part of the network output.
result DiffSlack achieves higher planning success rates and stronger geometric constraint satisfaction compared to existing methods.
Paper derives inequalities for eigenvalues of Witten-Laplacian under fixed volume constraint.
problem Eigenvalue inequalities of Witten-Laplacian on bounded domains.
method Rearrangement technique and trial functions under fixed weighted volume constraint.
result Several isoperimetric inequalities for eigenvalues of Witten-Laplacian.
Improved Moser-Trudinger-Onofri inequality with constraints on sphere.
problem Improving constant in Moser-Trudinger-Onofri inequality with constraints.
method Generalization to higher order moments and perturbation method.
result New inequalities with similarity to Lebedev-Milin type inequalities.
Proves existence of solutions to Einstein constraints with specific boundary conditions and verifies Penrose inequality.
problem Existence of asymptotically hyperbolic solutions to Einstein constraints with marginally outer trapped boundaries.
method Constant mean curvature conformal method.
result Verification of Penrose inequality for certain Schwarzschild-AdS black hole perturbations.
New proof of Sobolev inequality with constraints on sphere.
problem Improving Sobolev inequality on sphere with constraints.
method Careful study of extremal problem on sphere.
result Explicit determination of constant in second order moments case.
New method uses logical relations to derive bounds and inequality constraints from causal models.
problem Recovering bounds and inequality constraints from unobserved confounding.
method Using rules of probability and restrictions on counterfactuals implied by causal graphical models.
result Powerful method to recover known and novel bounds and constraints.
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to reduce the interval programming problem with uncertain objective and constraints …
New inequality criterion for a mean field equation on spheres.
problem Finding uniqueness in a mean field equation on spheres.
method Established a new Moser-Trudinger-Onofri inequality with a constraint on moments deviation.
result A threshold for deviation is a uniqueness criterion for the mean field equation.
OLLA framework efficiently samples from constrained distributions with nonconvex constraints.
problem Sampling from constrained distributions with nonconvex constraints is challenging.
method Overdamped Langevin with Landing (OLLA) framework that handles both equality and inequality constraints.
result OLLA converges exponentially fast to the constrained target density in W 2 W_2 W 2 distance. Proves strict inequality for minimizers of Willmore energy under isoperimetric constraints.
problem Minimizing the Willmore energy under isoperimetric constraints.
method Connected sum approach, building on previous work by Keller-Mondino-Rivière.
result Existence of minimizers for the isoperimetric constrained Willmore problem in every genus.
Recent work has shown that a country's productive structure constrains its level of economic growth and income inequality. Here, we compare the productive structure of countries in Latin America and the Caribbean (LAC) with that of China and other High-Performing Asian Economies (HPAE) to expose the increasing gap in t…
The paper explores optimal algorithms for linear regression under covariate shift, proving the optimality of certain transformations and SGD variants.
problem Optimal algorithms for linear regression under covariate shift with ellipse-shaped constraints.
method Establishes a tight lower generalization bound via Bayesian Cramer-Rao inequality, proves the optimality of certain transformations, and analyzes SGD variants.
result Optimal estimators and SGD variants achieve optimality under specific conditions.
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
Proves Hölder-type inequality for Lagrangians' distance.
problem Understanding the symplectic geometry of Lagrangians.
method Developed methods from previous works to establish the inequality.
result Established a Hölder-type inequality for the Hausdorff distance between Lagrangians.
Paper finds inequalities for eigenvalues of buckling problems on special metric spaces.
problem Eigenvalue inequalities for buckling problems of drifting Laplacian.
method Investigated on bounded domains in complete smooth metric measure spaces (SMMSs) with special functions.
result General inequalities for eigenvalues derived under curvature constraints.
A new algorithm speeds up elliptical slice sampling for truncated multivariate normals.
problem Efficiently sampling from truncated multivariate normal distributions with linear constraints.
method Adapting elliptical slice sampling to linearly truncated multivariate normals, with an algorithm for ellipse-polytope intersection in O(m log m) time.
result The algorithm enhances numerical stability, speeds up running time, and is easy to parallelize.
In this article we give a criterion for the existence of a metric of curvature 1 1 1 on a 2 2 2 -sphere with n n n conical singularities of prescribed angles 2 π ϑ 1 , … , 2 π ϑ n 2π\vartheta_1,\dots,2π\vartheta_n 2 π ϑ 1 , … , 2 π ϑ n and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in $\vartheta_1,\dot…
We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of R n \mathbb{R}^n R n . Our result applies to…
Method solves nonconvex constrained optimization problems with a new augmented Lagrangian approach.
problem Nonconvex composite functional constraints with inequality constraints.
method First-order augmented Lagrangian method with smoothed prox-linear reformulation.
result Explicit convergence rates for the proposed method in terms of KKT residual.
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that mod…
Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.
problem Optimizing hypothesis testing with quantized samples and communication constraints.
method Developed a polynomial-time algorithm achieving near-optimal sample complexity under communication constraints.
result Achieved near-optimal sample complexity under communication constraints, with a logarithmic factor increase over unconstrained setting.
This paper describes a simple framework for structured sparse recovery based on convex optimization. We show that many structured sparsity models can be naturally represented by linear matrix inequalities on the support of the unknown parameters, where the constraint matrix has a totally unimodular (TU) structure. For …
Paper presents a method to solve variational inequalities with general constraints without requiring analytic solutions.
problem Solving variational inequalities with general constraints.
method A primal-dual approach using approximate subproblem solutions and warm-starting.
result The method converges with a rate of O ( 1 K ) O(\frac{1}{\sqrt{K}}) O ( K 1 ) for L L L -Lipschitz and monotone operators. Optimization with inequality constraints using embedded gradient vector field method
problem Optimization with inequality constraints
method Geometric framework using quadratic slack variables
result Derives Lagrange multiplier functions and second-order optimality conditions
Sharp inequalities on curved spaces with bounded curvature.
problem Establishing inequalities on curved spaces with curvature constraints.
method Using Sobolev and Moser-Trudinger inequalities on noncompact Riemannian manifolds with Ricci curvature bounded below.
result Best constants for inequalities on curved spaces with curvature constraints.
Paper solves optimization problems with convex expectation constraints using a new algorithm.
problem Minimizing convex expectation functions with inequality convex expectation constraints.
method Stochastic Augmented Lagrangian-Type Algorithm (Stochastic Linearized Proximal Method of Multipliers).
result Algorithm achieves O ( K − 1 / 2 ) O(K^{-1/2}) O ( K − 1/2 ) convergence rates for objective reduction and constraint violation. The paper classifies energy-minimizing sets in specific domains.
problem Classifying volume-constraint local energy-minimizing sets.
method Proved a Poincaré-type inequality for stable sets.
result Relative boundary of energy-minimizing sets is smooth.
Study optimal consumption with drawdown limits over a fixed time frame.
problem Maximizing utility with consumption limits during a fixed period.
method Extended utility maximization problem with drawdown constraint, using PDE arguments and dual transform.
result Existence and uniqueness of classical solution to HJB variational inequality, with explicit free boundaries.
Research shows finiteness in triangulations with girth constraints.
problem Finiteness of cellular partial triangulations with girth constraints.
method Characterization of sparse graphs and contraction-minimal graphs.
result There are finitely many (3,6)-tight and (3,3)-tight graphs.
A new method combines SciML and UQ with physical constraints.
problem Uncertainty quantification in scientific machine learning tasks.
method Physics-constrained polynomial chaos expansion.
result Effective uncertainty quantification and SciML integration.
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
Develops inequalities for high-dimensional linear processes with dependent innovations.
problem Estimating high-dimensional VAR(p) systems and HAC covariance estimation.
method Concentration inequalities for l ∞ l_\infty l ∞ norm of vector linear processes with sub-Weibull, mixingale innovations. result Obtained concentration bounds for the maximum entrywise norm of lag- h h h autocovariance matrices. A new metric learning scheme for structured data combining graph and feature-space information.
problem Learning a metric from structured data while respecting metric constraints.
method Training metric-constrained linear combinations of dissimilarity matrices, applying graph-based optimization under constraints.
result Our approach can reduce computational complexity by one order of magnitude for some cases.
New algorithm tackles stochastic optimization with inequality constraints.
problem Stochastic optimization with inequality constraints in various applications.
method Active-set stochastic sequential quadratic programming (StoSQP) with a differentiable exact augmented Lagrangian.
result Global convergence for any initialization, KKT residuals converge to zero almost surely.
A new GP method enforces physical constraints in probabilistic terms.
problem Unbounded model in GP regression leading to infeasible values.
method Introduces a new GP method using QHMC to enforce soft inequality and monotonicity constraints.
result Improves accuracy and reduces variance in GP model.