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…
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48 results for “distance constraints”
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.
We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors of the data items. The relative-distance constraints used in this work are part…
Expands newsvendor model with moment constraints using Wasserstein distance.
problem Optimizing order quantity under distributional ambiguity.
method Formulates infinite dimensional primal problem, derives finite dimensional dual problem using problem of moments duality.
result Distributional ambiguity affects optimal order quantity and profits/costs.
New algorithm clusters data and learns kernels without relaxing constraints.
problem Learning kernels or distance metrics from pairwise constraints without losing generalization.
method Joint clustering and kernel learning without relaxing constraints.
result Outperforms existing approaches on diverse datasets.
Study knots with genus one, finds Gordian distance and cosmetic crossing constraints.
problem Understanding knots with genus one and their properties.
method Using HOMFLT polynomials to find obstructions for Gordian distance and cosmetic crossings.
result Proves the (generalized) cosmetic crossing conjecture for genus one pretzel knots.
Optimal transport framework for density estimation with constraints.
problem Density estimation under expectation constraints.
method Minimizes Wasserstein distance subject to expected value constraints and regularization.
result Framework effectively addresses non-smooth constraints through annealing-like algorithm.
Paper relaxes the Lipschitz constraint in WGANs to improve performance.
problem WGANs do not always outperform other GAN variants due to imperfect implementation of the Lipschitz condition.
method Proposes a new dual form of Wasserstein distance (Sobolev duality) that relaxes the Lipschitz constraint but maintains gradient property.
result SWGAN, based on Sobolev duality, outperforms existing methods in experiments.
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.
Recent work in distance metric learning has focused on learning transformations of data that best align with provided sets of pairwise similarity and dissimilarity constraints. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the better adapted distance or similar…
Distance metric learning is an important component for many tasks, such as statistical classification and content-based image retrieval. Existing approaches for learning distance metrics from pairwise constraints typically suffer from two major problems. First, most algorithms only offer point estimation of the distanc…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for anal…
Motivated by an application of eliciting users' preferences, we investigate the problem of learning hemimetrics, i.e., pairwise distances among a set of items that satisfy triangle inequalities and non-negativity constraints. In our application, the (asymmetric) distances quantify private costs a user incurs when s…
Quantum channels' contraction under privacy constraints studied.
problem Understanding the privacy constraints on quantum channel contractions.
method Established upper bounds on contraction coefficients for specific divergences under QLDP constraints.
result Upper bounds and full characterization of contraction coefficients for specific quantum distances.
DAG-WGAN learns causal structures using Wasserstein distance.
problem Learning causal structures from data with combinatorial challenges.
method Combines Wasserstein distance, auto-encoder, and acyclicity constraint.
result Demonstrates good performance compared to state-of-the-art models.
ExDAG solves DAG learning problems with low structural Hamming distance.
problem Learning DAGs with low structural Hamming distance under identifiability assumptions.
method Mixed-integer quadratic programming (MIQP) with branch-and-bound-and-cut algorithm and lazy constraints.
result ExDAG guarantees global convergence and provides a real-time quality assessment.
A Cramér Distance perspective on Quantile Regression based Distributional Reinforcement Learningstat.ML
This work connects Cramér distance to QR-DQN for DRL.
problem Improving performance in DRL by capturing full distribution of returns.
method Proves Cramér distance's equivalence to 1-Wasserstein distance and proposes a low-complexity algorithm to compute Cramér distance.
result Cramér distance and quantile regression losses yield collinear gradients under non-crossing constraints.
Unified framework for hyperbolic embeddings from mixed data types.
problem Computing hyperbolic embeddings from noisy metric and non-metric data.
method Semidefinite programming and spectral factorization methods.
result Efficient computation of hyperbolic embeddings from arbitrary data.
We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponen…
Develops a framework for stuck knots with rigid constraints and invariants.
problem Rigidity constraints on knot diagrams restrict allowable isotopies.
method Formalizes stuck crossings as rigid configurations, introduces unstick move, and constructs invariants.
result Rigidity contributes independent information even when knot type remains fixed.
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item is closer to item than item ". Ordinal constraints like this often come from human judgments. To account for errors and variation in jud…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a numbe…
Sphere theorems for specific manifolds with curvature constraints.
problem Sphere theorems for Riemannian manifolds with scalar curvature bounds and non-collapsed spaces.
method Analysis of scalar curvature and mean distance constraints.
result Established sphere theorems for the specified manifolds.
Optimal payoff choice constrained by Bregman-Wasserstein divergence.
problem Maximizing utility under a deviation constraint from a benchmark.
method Solving the problem using Bregman-Wasserstein divergence with a convex function φ.
result Provided the optimal payoff choice in this setting.
-NN classifier is one of the most famous classification algorithms, whose performance is crucially dependent on the distance metric. When we consider the distance metric as a parameter of -NN, learning an appropriate distance metric for -NN can be seen as minimizing the empirical risk of -NN. In this paper,…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as users' implicit feedbacks and citations among articles. As a result, these constra…
The role of distances in the World Trade Webphysics.soc-ph
In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. Howe…
Optimal testing for densities under local differential privacy constraints.
problem Testing goodness-of-fit for densities under privacy constraints.
method Estimation of quadratic distance and minimax separation rates.
result First minimax optimal test under local differential privacy constraints.
Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet constraints. However, the number of constraints is quadratic or even cubic in the number o…
The paper studies the properties of maps with free boundaries, focusing on the obstacle case.
problem Properties of the projected image and its regularity in maps with free boundaries.
method Dividing the map into distance and projected image parts; applying classical obstacle problem methods and proving higher regularity for the projected image.
result The projected image is at most of class and globally of class , locally of around the regular part of the free boundary.
On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminantsstat.ML
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified theoretical analysis of multilabel Fisher discriminants with algebraic and statistical guarantees.
result Unified characterization of multilabel Fisher objectives and their equivalence under orthogonality constraints.
Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.
problem Ensuring privacy in robust statistical estimation.
method Derive private minimum Hellinger distance estimators satisfying Hellinger differential privacy.
result Private minimum Hellinger distance estimators retain robustness and efficiency under privacy constraints.
New method identifies latent relationships in deep models without additional constraints.
problem Latent representations in deep latent variable models are not statistically identifiable.
method Identifies relationships between latent variables (distances, angles, volumes) under mild model conditions.
result Empirically demonstrates more reliable latent distances without additional labeled data.
As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neura…
Recent work in distance metric learning has focused on learning transformations of data that best align with specified pairwise similarity and dissimilarity constraints, often supplied by a human observer. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the bette…
Optimizes decisions in time-varying distributions using online stochastic methods and Wasserstein distance.
problem Optimizing decisions in time-varying distributions using Wasserstein distance.
method Online proximal-gradient method, exact penalty method, constraint-tightening approach.
result Dynamic regret bounds for tracking and estimation error.
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the known algorithms may perform arbitrarily poorly. Amending this issue, by obtaini…
The paper proves stability of manifolds with boundary under volume and distance constraints.
problem Stability of manifolds with boundary under volume and distance constraints.
method Volume preserving intrinsic flat convergence of metrics with boundary constraints.
result The stability of manifolds with boundary under volume and distance constraints is proven.
Sub-twistor metricsmath.DG
The paper studies metrics on hyperkähler manifolds using sub-twistor constraints.
problem Understanding metrics on hyperkähler manifolds with non-holonomic constraints.
method Introducing and analyzing sub-conic metrics, showing they are sub-Finsler.
result Explicit description of Finsler norms for sub-twistor metrics.
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep learning has become a hot research topic in the field of hyperspectral remote s…
Unified framework for DRO using OT with constraints.
problem Handling ambiguity in likelihood ratios and outcomes.
method Unified framework leveraging optimal transport with conditional moment constraints.
result Unified approach enables adversarial perturbation of likelihood ratios and outcomes.
A parametric approach to the estimation of convex risk functionals based on Wasserstein distanceq-fin.RM
Estimates risk in finance using Wasserstein distance and parametric models.
problem Assessing risk in financial models with model uncertainty.
method Parametric approach based on Wasserstein distance for convex risk functionals.
result Developed a numerical method using neural networks to estimate risk and optimal perturbations.
WDL models density curves using Wasserstein distance and flexible mixture models.
problem Modeling entire distribution and non-negativity constraints.
method Wasserstein distance, Semi-parametric Conditional Gaussian Mixture Models (SCGMM), Majorization-Minimization optimization.
result WDL better characterizes nonlinear dependence of conditional densities.
A new algorithm solves the metric nearness problem efficiently.
problem Finding the nearest distance matrix that satisfies triangle inequalities.
method Delayed constraint generation with semismooth Newton based proximal augmented Lagrangian method (PALM).
result Solves problems with up to 10^8 variables and 10^13 constraints efficiently.
On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminantsstat.ML
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified algebraic and statistical analysis of multilabel Fisher discriminants with Stiefel orthogonality constraints.
result Equivalence of four Fisher objectives under the Stiefel constraint and improved discriminant dimensionality.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
problem Matching objects between incomparable spaces using the Gromov-Wasserstein distance.
method Semi-definite programming (SDP) relaxation of the GW distance.
result The SDP relaxation provides globally optimal solutions for the GW distance in some instances.
Introduces MSW distances to improve SW metrics.
problem Redundant projections in SW distance.
method Imposes Markov structure on projecting directions.
result MSW distances improve SW metrics.
Paper finds robust -quantiles equal to extremal distributions.
problem Investigating robust models for -quantiles with partial loss information.
method Extending classical quantiles using -quantiles and applying results from robust quantiles.
result Robust -quantiles equal to -quantiles of extremal distributions.