Surveying nonparametric inference with shape constraints, past and future.
problem Statistical inference under shape constraints.
method Historical overview and future directions.
result Outlook on future research directions.
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48 results for “shape constraints”
Winterbottom shape minimizes capillary functional under volume constraint.
problem Finding the shape that minimizes capillary functional under volume constraint.
method Proved minimality of Winterbottom shape using anisotropic capillary functional.
result Winterbottom shape is a volume-constraint minimizer of the anisotropic capillary functional.
Kernel-based tests for shape constraints in finance.
problem Enforcing shape relations on latent functions in financial econometrics.
method Kernel-based nonparametric framework for mean-variance optimization.
result Established statistical properties and a joint Wald-type statistic for testing shape constraints.
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at…
Unified framework for hard affine SDP constraints in vRKHSs.
problem Incorporating shape constraints into predictive models for rich function classes.
method Unified convex optimization framework using second-order cone tightening.
result Unified and modular approach for handling multiple shape constraints.
Study S-shaped utility maximization with VaR constraint and unobservable drift.
problem Maximizing utility with a Value at Risk (VaR) constraint and unknown drift.
method Bayesian filter, concavification principle, change of measure, semi-closed integral representation, algorithms (Lagrange, simulation, deep neural network).
result Critical wealth level determining solution feasibility and optimal solution existence.
The paper studies how arm selection in a bandit problem changes with shape constraints.
problem Stochastic Thresholding Bandit Problem under shape constraints.
method Investigation of TBP under four shape constraints: monotonic increasing, unimodal, concave, and fixed.
result Minimax rates for regret vary significantly depending on the shape constraint.
Paper tackles hard shape constraints in kernel machines.
problem Enforcing shape requirements in a hard fashion is challenging.
method Tightened second-order cone constrained reformulation for kernel machines.
result Performance guarantees and efficiency demonstrated in various applications.
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
Shape-constrained symbolic regression improves model extrapolation with prior knowledge.
problem Improving model extrapolation with prior knowledge in symbolic regression.
method Shape-constrained symbolic regression using evolutionary algorithms with interval arithmetic.
result Models with shape constraints have improved extrapolation but lower accuracy on test sets.
We solve S-shaped utility portfolio selection with SD constraints using algorithms and neural networks.
problem Optimizing portfolios with S-shaped utility functions under SD constraints.
method First-order SD constraint solution, numerical algorithm for SSD, neural network approach.
result Effective numerical and neural network solutions for SSD constrained problems.
Prediction Rule Reshapingstat.ML
Two methods are proposed for high-dimensional shape-constrained regression and classification. These methods reshape pre-trained prediction rules to satisfy shape constraints like monotonicity and convexity. The first method can be applied to any pre-trained prediction rule, while the second method deals specifically w…
Dynamic risk constraints help limit risky behavior in financial portfolios.
problem Static risk measures fail to control tail-risk-seeking traders.
method Introduces dynamic risk constraints applied throughout the trading horizon.
result Dynamic risk constraints can effectively limit risky behavior in portfolios.
New neural network models extreme value distributions with preserved shape constraints.
problem Modeling multivariate extreme value distributions with preserved shape constraints.
method d-max-decreasing neural network architecture for non-parametric calibration and generation of MEVs.
result The proposed architecture approximates the dependence structure of MEVs at parametric rate and preserves essential shape constraints.
ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.
problem Creating interpretable non-linear models with expert knowledge constraints.
method Gradient Boosting of cubic polynomials with specified constraints.
result ParamBoost outperforms state-of-the-art GAMs in real-world datasets.
Paper proposes a shape-constrained approach to distributionally robust learning.
problem Challenges in statistical learning under distribution shift.
method Shape-constrained approach to distributionally robust learning (DRL). Assumes isotonic density ratio.
result Improved accuracy demonstrated in empirical studies.
Optimization of piecewise smooth shapes under uncertainty using the example of Navier-Stokes flowmath.OC
Optimizes shapes in uncertain Navier-Stokes flow problems.
problem Optimizing shapes with geometric constraints and physical uncertainty.
method Multi-shape calculus and stochastic augmented Lagrangian method.
result Successfully optimized shapes in uncertain Navier-Stokes flow.
Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regressionstat.ME
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
One-dimensional crystals have convex shapes under certain conditions.
problem Determining if one-dimensional crystals have convex shapes.
method Analyzing the free energy under mass constraints and convexity assumptions.
result In one dimension, crystals have convex shapes under given conditions.
We demonstrate how easy it is for modern machine-learned systems to violate common deontological ethical principles and social norms such as "favor the less fortunate," and "do not penalize good attributes." We propose that in some cases such ethical principles can be incorporated into a machine-learned model by adding…
The paper analyzes extreme risk measures with limited distributional information.
problem Investigating risk measures under partial knowledge of distribution moments and shape.
method Employing probability inequalities and modified Schwarz inequality to derive bounds on distortion risk measures.
result Unified framework for calculating best- and worst-case scenarios of distortion risk measures.
Continuous-time model shows insider trading constraints impact market dynamics.
problem Trading constraints faced by insiders in continuous-time models.
method Proved global existence of equilibrium with terminal trading constraint.
result Equilibrium model aligns with empirical market behaviors.
New method for linear connections in ODEs with constraints.
problem Constructing linear connections for ODEs with and without constraints.
method Novel method using submodule covariant derivatives.
result Closed form expressions for Massa-Pagani connection and its extension.
Study minimax risk of score estimation for log-concave distributions.
problem Minimizing risk in score estimation for log-concave distributions.
method Developed subclasses of log-concave densities and constructed a locally adaptive, multiscale estimator.
result Established minimax rates for score estimation over specific subclasses of log-concave densities.
The paper classifies affine hypersurfaces with symplectic structures and constraints on their curvature.
problem Characterizing affine hypersurfaces with symplectic structures and curvature constraints.
method Analyzing hypersurfaces with non-degenerate second fundamental forms and almost symplectic structures.
result The rank of the shape operator is at most one under certain conditions on the almost symplectic form.
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product d…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and constrained single index model. We review some of the theoretical properties of the least …
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surfa…
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
The paper learns pose variations within shape populations using constrained mixtures of factor analyzers.
problem Learning pose variations within a shape population with articulated parts and relative rotations.
method Formulated as mixtures of factor analyzers, segmentation by component posterior probabilities, and constraints on factor loading matrices for rotation matrices.
result Automatic learning of pose variations from shape populations, resulting in smooth and realistic animations.
Proposes Constrained Q-learning for reinforcement learning with constraints.
problem Optimizing multiple objectives while adhering to constraints in reinforcement learning.
method Directly restricts the action space in Q-update to learn optimal Q-function for constrained MDP.
result Improves safety and optimality in high-level decision making for autonomous driving.
We study the supersymmetric Wilson loop as introduced by Caron-Huot, which attaches to lightlike polygons certain edge and vertex operators, whose shape is determined by supersymmetry constraints. We state explicit formulas for the vertex operators to all orders in the Graßmann expansion, thus filling a gap in the lite…
Sparse Shape Reconstructionmath.FA
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set opera…
A framework for generating 3D shapes by sequentially assembling primitives.
problem Combinatorial complexity in generating 3D shapes.
method Bayesian optimization for efficient exploration and exploitation of feasible combinations.
result Successfully generates realistic combinatorial 3D shapes.
New friction model for geometric locomotion systems.
problem Modeling asymmetric friction in locomotion systems.
method Introducing asymmetric friction into geometric locomotion models using Finsler metrics.
result Generalized motility map for systems with asymmetric friction.
Proposes a tuning-free dynamic pricing method for linear valuation models.
problem Dynamic pricing in linear valuation models with unknown market noise distribution.
method Shape-constrained isotonic regression under weaker Hölder continuity assumptions.
result Demonstrates lower empirical regret compared to existing methods.
Design-by-Morphing creates radical airfoil designs without geometric constraints.
problem Design constraints limit airfoil design novelty and small changes.
method Design-by-Morphing (DbM) creates a search space without geometric constraints.
result DbM generates radical airfoils with remarkable lift-over-drag ratio and stall angle tolerance.
The paper solves a thermodynamics problem about crystal shape.
problem Understanding if minimizing free energy with convex potential and mass constraint generates a convex crystal.
method Utilized a stability theorem, convexity, and a new maximum principle approach to prove a three-dimensional convexity theorem.
result Completely settled the Almgren problem in under generic conditions.
Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that integrating multiple input representations leads to state-of-the-art results. In p…
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distanc…
VCAE improves autoencoder quality on MNIST and CelebA.
problem Overfitting and poor generative/reconstruction quality in autoencoders.
method Proposes variance-constrained autoencoder (VCAE) to enforce variance constraint on latent distribution.
result VCAE outperforms Wasserstein Autoencoder and Variational Autoencoder in quality.
A language for specifying complex reinforcement learning tasks.
problem Challenges in specifying and shaping reward functions for complex reinforcement learning tasks.
method Proposes a new language and algorithm for automatically generating and shaping reward functions.
result SPECTRL tool outperforms state-of-the-art baselines.
Method flattens complex surfaces with consistent density and shape.
problem Shape deformations and local geometric distortions in density-equalizing maps for multiply-connected surfaces.
method Formulates density diffusion as a quasiconformal flow, solving an energy minimization problem involving the Beltrami coefficient to ensure bijectivity and control distortion.
result Achieves optimal parameterization of multiply-connected surfaces with bijective and controlled geometric distortions.
Compact hypersurfaces minimize area in convex cones with free boundary.
problem Finding compact hypersurfaces minimizing area in convex cones with free boundary.
method Minimizing an anisotropic area functional under a volume constraint.
result Compact hypersurfaces are contained in a Wulff-shape.
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and ca…