Develops new shape metrics for high-dimensional objects.
problem Lack of single metrics to describe shape in high dimensions.
method Introduces hyper-Sphericity and hyper-Shape Proportion metrics.
result Discriminates between different shapes in high dimensions.
Proposes a method for modeling random objects in metric spaces using random effects.
problem Modeling random objects in non-Euclidean spaces with random effects.
method Nonlinear Fréchet-based algorithm for M-estimation.
result Consistent estimation of prediction target under random-effects formulation.
The paper shows objective derivatives are covariant derivatives on Riemannian metrics.
problem The definition and interpretation of objective derivatives in continuum mechanics.
method Demonstrates that objective derivatives correspond to covariant derivatives on the manifold of Riemannian metrics.
result Objective derivatives are unified as covariant derivatives on the manifold of Riemannian metrics.
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk patterns by optimizing an objective function, which turns out to be intimately …
New fairness metrics improve collaborative filtering fairness.
problem Collaborative filtering's bias in historical data leads to unfair predictions for minority groups.
method Identified and proposed four new fairness metrics to address different forms of unfairness.
result Our new metrics better measure fairness than baseline metrics and effectively reduce unfairness.
New geometric object for polynomials simplifies complex data.
problem Understanding the combinatorial and geometric properties of polynomials.
method Introducing a compact planar 2-complex for polynomials with distinct roots.
result Extracts combinatorial data from a geometric structure of polynomials.
A framework evaluates synthetic tabular data quality objectively.
problem Lack of an objective interpretation of tabular data metrics.
method Proposes a single mathematical objective for synthetic tabular data distribution, structurally decomposes it, and unifies existing metrics.
result Synthesizers that represent tabular structure outperform other methods, especially on smaller datasets.
A fast k-NN classifier without negative pairs.
problem Efficient k-NN classification without negative pairs. method Ridge regression for learning dissimilarity function.
result Better k-NN classification accuracy than state-of-the-art methods. Bayesian optimization on networks using Gaussian process models.
problem Optimizing expensive black-box functions on network structures.
method Developed Bayesian optimization algorithms with Gaussian process surrogates tailored to network geometry.
result Established regret bounds for smooth objective functions and analyzed practical cases.
We optimize rank-based metrics using blackbox differentiation.
problem Challenges in directly optimizing rank-based metrics due to their non-differentiable and non-decomposable nature.
method Efficient, theoretically sound, and general method for differentiating rank-based metrics with mini-batch gradient descent.
result Competitive performance on standard image retrieval datasets and improved performance on object detectors.
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
A new metric learning algorithm using Deep Forest for better class separability.
problem Improving distance metrics between similar and different classes.
method Discriminative Deep Forest (DisDF) algorithm with weighted decision trees.
result The algorithm reduces distances within the same class and increases between different classes.
Novel method decorrelates batches of triplets for active metric learning.
problem Correlation among triplets degrades active learning performance.
method Proposes a novel method to decorrelate batches of triplets, balancing informativeness and diversity.
result Method outperforms state-of-the-art in active metric learning.
New transportation metric for graph data outperforms existing methods.
problem Computing distances between structured objects like graphs.
method Fused Gromov-Wasserstein (FGW) metric that considers both structure and features.
result FGW outperforms graph kernels and deep graph networks in graph classification.
Unified framework for scalable optimization of ranking-based objectives.
problem Scalability issues in optimizing ranking-based performance metrics.
method Unified framework using building block bounds for scalable optimization.
result Substantial improvement in performance over accuracy-objective baseline.
This paper reviews metrics to assess AI model calibration accuracy.
problem AI model probabilities do not always match their true accuracy.
method Comprehensive review of 82 probability calibration metrics.
result Identified 4 classifier families and 1 object detection family of metrics.
Develops objective metrics to evaluate NFL offensive linemen performance.
problem Objective evaluation of NFL offensive linemen performance is lacking.
method Uses statistical analysis of performance metrics to objectively evaluate offensive linemen.
result Identifies overvalued and undervalued offensive linemen.
OBSER framework infers sub-environments from objects, outperforming scene-based methods.
problem Zero-shot recognition of environments from object distributions.
method Bayesian framework using metric and self-supervised learning models to estimate object distributions in latent space.
result OBSER framework reliably performs inference in open-world and photorealistic environments, outperforming scene-based methods.
A simple trick invoking objective B-fields is employed to refine the concept of characteristic classes for twisted bundles. Then the objective stability and objective Einstein metrics are introduced and a new Hitchin-Kobayashi correspondence is established between them. As an application the SO(3)-instanton moduli spac…
DPE embeds non-Euclidean objects into Hilbert space for independence testing.
problem Testing independence of non-Euclidean random objects.
method Distance Profile Embedding (DPE) maps objects into Hilbert space.
result Unified framework for marginal and conditional independence testing.
Paper proposes IE loss for deep metric learning improving CNN performance.
problem Improving deep learning models' performance in classification tasks.
method IE loss method to force distance between samples and class centers.
result IE loss leads to great improvements on various datasets.
The thesis explores stability conditions and metrics in differential geometry.
problem Understanding extremal objects in differential geometry.
method Introduces and analyzes Z-critical metrics and optimal symplectic connections. result Proves a correspondence between existence of metrics and stability conditions.
Paper enhances speech by estimating RI spectrograms and optimizing multiple metrics.
problem Difficulty in phase estimation and lack of multi-metric optimization in speech enhancement.
method Proposes a CNN model for RI spectrogram estimation and multi-metrics learning.
result Unified objective function improves speech enhancement metrics.
Novel algorithm optimizes decision trees for nonlinear metrics.
problem Optimizing decision trees for nonlinear metrics like F1-score.
method Bi-objective optimisation approach to find optimal trees on Pareto frontier.
result The optimal tree for nonlinear metrics lies on the Pareto frontier.
Paper develops a new objective for hierarchical clustering in Euclidean space.
problem Hierarchical clustering in Euclidean space with dissimilarity scores.
method Develops a new global objective and connects it to bisecting k-means.
result Optimal 2-means solution approximates the new objective, proving bisecting k-means optimizes a natural global objective.
This paper introduces a new financial metric for the art market. The metric is based on the price per unit of area and is applicable to two-dimensional art objects such as paintings.
Novel NAS method balances performance and hardware metrics efficiently.
problem Challenging multi-objective optimization in neural architecture search.
method Parameterizes joint architectural distribution via hypernetwork conditioned on hardware features and preferences.
result Zero-shot transferability to new devices with representative and diverse architectures.
The paper introduces metrics to objectively evaluate interpretability methods.
problem Lack of objective evaluation metrics for interpretability methods.
method Proposes a set of metrics to evaluate interpretability methods along simplicity and broadness.
result Validated metrics on different benchmark tasks and showed their utility in method selection.
Researchers extend the concept of metric spaces to Lorentzian spaces and prove the feasibility of their c-completion.
problem Extending the concept of metric spaces to Lorentzian spaces and proving their c-completion.
method Revisiting Lorentzian metric spaces, constructing c-completion, proving feasibility and endowing with Lorentzian metric space structure.
result The c-completion of Lorentzian metric spaces is feasible and well-suited, completing the original space in a precise sense.
New BO method optimizes multiple objectives under input noise.
problem Optimizing multiple performance metrics in manufacturing processes subject to random input noise.
method Formalizes optimization of multivariate value-at-risk (MVaR) using random scalarizations.
result Significantly outperforms alternative methods in identifying robust designs.
This paper offers a new approach to Riemannian geometry using Takagi's factorization.
problem Analyzing the Riemannian geometry using a novel analytical path.
method Using Takagi's factorization of the metric tensor to analyze Riemannian geometry.
result Provides new conditions for curved vs. flat manifolds and decomposes curvature tensor.
New method detects outliers in object-relational data.
problem Detecting outliers in complex object-relational data.
method Exceptional Model Mining framework applied to object-relational data with probabilistic models and Bayesian networks.
result Novel metric based on likelihood ratio improves outlier detection accuracy.
Many objective Bayesian optimization tackles redundant objectives in expensive black-box functions.
problem Efficiently optimizing multiple expensive and noisy black-box functions with redundant objectives.
method Proposes a metric to identify redundant objectives and a Bayesian optimization algorithm to stop evaluating them.
result Reduces computational cost by stopping evaluation of redundant objectives, improving efficiency.
This paper introduces a new scalarization method for multi-objective optimization.
problem Efficiently optimizing multiple conflicting objectives in black box settings.
method Introduces a novel hypervolume scalarization function and uses it to approximate the hypervolume indicator metric.
result Provable convergence to the entire Pareto frontier using random scalarizations and Bayesian optimization.
The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of…
Given a Finsler space (M,F) on a manifold M, the averaging method associates to Finslerian geometric objects affine geometric objects} living on M. In particular, a Riemannian metric is associated to the fundamental tensor g and an affine, torsion free connection is associated to the Chern-Rund connection. As an il…
Study shows stability of Schwarzschild spacetime under specific perturbations.
problem Linear stability of Schwarzschild spacetime under axial perturbations.
method Complex line bundle interpretation and connection-level object analysis.
result Suitably regular initial data decay to a linearized Kerr metric.
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
Metrics stabilize persistent homology in data analysis.
problem Stabilizing invariants for characterizing connectivity structures in data.
method Using contour functions to define metrics for rank invariants.
result Optimal contours provide robust descriptors of spatial patterns.
Paper explores new Kähler metrics from old, aiming to solve YTD conjecture.
problem Extending classical extremal Kähler metrics to include new objects.
method Surveying recent works on weighted extremal Kähler metrics and the YTD conjecture.
result Survey of recent research on weighted extremal Kähler metrics.
In this paper we study submanifolds of an almost complex manifold with Norden metric which are non-degenerate with respect to the one Norden metric and lightlike with respect to the other Norden metric on the manifold. Relations between the induced geometric objects of some of these submanifolds are given. Examples of …
We embed objects as elliptical distributions using the Wasserstein metric.
problem Embedding complex objects as vectors in low dimensional spaces.
method Embedding objects as elliptical probability distributions with the 2-Wasserstein metric.
result Wasserstein elliptical embeddings provide more intuitive and numerically stable tools than Gaussian embeddings.
Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool in better understanding their smooth counterparts. This article is mostly a surve…
The paper introduces a new metric to quantify uncertainty's impact on multiple objectives.
problem Quantifying the impact of uncertainty on multiple objectives in complex systems.
method Proposes the mean multi-objective cost of uncertainty (multi-objective MOCU) to quantify uncertainty.
result Demonstrates the effectiveness of the multi-objective MOCU in real-world applications.
The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.
TripletBoost learns classifiers from noisy triplet comparisons.
problem Learning from comparison-based data.
method Aggregate weak classifiers from weakly learned triplets, then boost.
result Theoretical guarantees and empirical competitiveness.
Invariant tensors found for specific geometric structures.
problem Finding invariant tensors in specific geometric structures.
method Torsion-free connection and invariant tensors found under twin interchange of metrics and connections.
result Invariant tensors found explicitly in a 4D example.
The paper characterizes spherically symmetric metrics with scalar curvature.
problem Characterizing spherically symmetric metrics with scalar curvature.
method Established a curvature compatibility condition on spherically symmetric Finsler metrics and constructed a Berwald frame.
result Characterized spherically symmetric metrics with scalar curvature.