Extended Rank-One Theorem to special metric spaces.
problem Extending a theorem to new types of spaces.
method Applied to a new class of metric measure spaces.
result Rank-One Theorem proven for spaces.
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48 results for “Ranking Metrics”
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of functionals for evaluating financial positions.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
Paper extends ranking metrics theory for financial positions.
problem Developing a new class of performance evaluation methods.
method Axiomatic framework based on monotonicity and cash-quasiconcavity.
result Linking ranking metrics to families of acceptance sets and risk measures.
In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, simply-connected geodesic metric space of non-curvature in the sen…
We propose a low-rank approach to learning a Mahalanobis metric from data. Inspired by the recent geometric mean metric learning (GMML) algorithm, we propose a low-rank variant of the algorithm. This allows to jointly learn a low-dimensional subspace where the data reside and the Mahalanobis metric that appropriately f…
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.
Study higher rank inner products and their tilings to describe tori degenerations.
problem Understanding metric degenerations of tori.
method Introduce higher rank inner products and their tilings, use to describe degenerations.
result Describe metric degenerations of polarized tori and Hausdorff limits of tilings.
We prove an obstruction at the level of rational cohomology in small degrees to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As an application, we provide evidence for a generalized conjecture of Hopf that says that no symm…
Completes the space of vector-valued one-forms on manifolds.
problem Metric incompleteness of the space of full-ranked one-forms.
method Distance equality and quotient structures.
result Concrete description of the metric completion of the space of full-ranked one-forms.
Derives smooth homogeneous structures for low-rank tensors.
problem Understanding the geometry of low-rank tensors.
method Analyzes sets of fixed CP, multilinear, and TT rank tensors to derive smooth homogeneous manifolds.
result Derives Riemannian metrics with complete geodesics.
Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.
problem Finding compatible harmonic metrics for rank 3 Higgs bundles in the Hitchin section.
method Defined a symmetric pairing and studied spectral curves as 2-sheeted branched coverings.
result Gave a condition for Higgs bundles on or to have compatible harmonic metrics.
Proposes a cross entropy loss for better ranking algorithms.
problem Improving the theoretical understanding and performance of ranking algorithms.
method Introduces a cross entropy-based loss function that is a convex bound on NDCG and consistent with NDCG.
result Empirically, the proposed method outperforms existing algorithms in quality and robustness.
FLRML efficiently handles large-scale, high-dimensional data for metric learning.
problem Metric learning for large-scale, high-dimensional datasets is computationally expensive and memory-intensive.
method FLRML reformulates low-rank metric learning as an unconstrained optimization problem on the Stiefel manifold, enabling efficient mini-batch processing.
result FLRML achieves high accuracy with significantly reduced computational and memory costs.
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.
New method to rank metrics on non-shuffled traffic.
problem Position bias in ranking metrics due to item display order.
method Leverage stochasticity of recommendation policy to mitigate position bias.
result Improved ranking metrics without shuffling recommendations.
Counterfactual Cross-Validation: Stable Model Selection Procedure for Causal Inference Modelsstat.ML
A new metric for stable model selection in CATE prediction.
problem Model selection in conditional average treatment effect (CATE) prediction.
method Analysis of model performance ranking and formulation of a novel metric.
result Our metric outperforms existing metrics in model selection and hyperparameter tuning.
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric as , the problem can be cast as looking for a linear map between two …
We reduce variance in monetization metrics for ranking experiments.
problem Heavy-tailed monetization metrics lead to unreliable conclusions in A/B experiments.
method Post-stratification combined with CUPED.
result Significant reduction in variance and improved decision stability.
New metrics reveal oversmoothing in GNNs more accurately than traditional methods.
problem Oversmoothing in graph neural networks reduces model performance.
method Rank-based metrics to measure oversmoothing in GNNs.
result Rank-based metrics consistently capture oversmoothing, while energy-based metrics often fail.
We obtain Ricci flat Kähler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics of Biquard-Gauduchon in the Hermitian case and obtain in addition several new metri…
StochasticRank optimizes ranking metrics efficiently and guarantees global convergence.
problem Optimizing discrete ranking metrics due to their ill-posed nature.
method Stochastic smoothing, gradient estimate, debiasing, and Stochastic Gradient Langevin Boosting.
result Global convergence and superior performance on ranking datasets.
Researchers classify geodesic orbit spaces for compact Lie groups of rank two.
problem Identifying geodesic orbit spaces for compact Lie groups of specific rank.
method Classification of simply connected geodesic orbit spaces where G is a compact Lie group of rank two.
result Only certain spheres and projective spaces, with metrics induced from Hopf fibrations, are geodesic orbit spaces for compact Lie groups of rank two.
The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.
We study a remarkable class of paracontact metric manifolds which have no contact metric counterpart: the paracontact metric -spaces which are not paraSasakian (i.e. have ). We present explicit examples with of every possible constant rank and some with non-constant r…
New metrics defined for full-rank correlation matrices, ensuring unique operations.
problem No suitable problem statement as the abstract does not describe a problem to be solved.
method New Riemannian metrics defined on full-rank correlation matrices, providing unique operations.
result Unique Riemannian logarithm and Fréchet mean defined for full-rank correlation matrices.
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes 2012) in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show ho…
We extend the recently introduced theory of Lovasz-Bregman (LB) divergences (Iyer & Bilmes, 2012) in several ways. We show that they represent a distortion between a 'score' and an 'ordering', thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show h…
New method optimizes collaborative filtering for better ranking metrics.
problem Improving recommendation quality metrics like top-N ranking.
method Actor-critic reinforcement learning to directly optimize ranking metrics.
result The method outperforms state-of-the-art baselines on real-world datasets.
The paper introduces metrics to rank potential outcomes for better decision-making.
problem Optimal action selection in uncertain situations using causal reasoning.
method Introducing two new metrics: probabilities of potential outcome ranking (PoR) and probability of achieving the best potential outcome (PoB). Establishing identification theorems and deriving bounds for these metrics, and presenting estimation methods.
result The estimators' finite-sample properties and their application to a real-world dataset are demonstrated.
Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmuller space equipped with either the Teichmuller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse geometry of these spaces. We show that the quasi-Lipschitz image in X of a box i…
Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We first o…
Ranking recommendation algorithms across datasets using Bradley-Terry model
problem Comparing recommendation algorithms across different datasets
method Introduce a novel data-driven ranking methodology based on Bradley-Terry model
result The obtained ranking depends on key dataset statistics
New approach to handle ranking function variation in zero-shot NAS.
problem Variation in ranking function outputs due to randomness.
method Viewing ranking function output as a random variable and constructing a stochastic ordering.
result Stochastic ordering boosts performance in neural architecture search.
This paper improves model robustness to underrepresented groups using ranking metrics and reweighting.
problem Underrepresented groups suffer from low accuracy in models trained via ERM.
method Proposes Discounted Cumulative Gain (DCG) and Discounted Rank Upweighting (DRU) methods.
result Models trained with DRU show superior generalization to unseen groups.
We study non-paraSasakian paracontact metric -spaces with (equivalent to but ). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of . We will also give explicit examples of every possible constant rank of .
We generalize Mallows model to learn distance metrics from data.
problem Learning optimal distance metrics from noisy ranking data.
method Propose distances and develop FPTAS for sampling and MLE.
result Strong consistency of estimators for various and .
Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.
problem Linear perturbations of Spin(7) metrics.
method Applying the method of linear perturbations to Spin(7)-structures.
result Only rank one nilpotent matrices determine nontrivial perturbations.
Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In practical settings, the task often reduces to estimating a rank functional of an object …
We define and study the renormalized volume for geometrically finite hyperbolic -manifolds, including with rank- cusps. We prove a variation formula, and show that for certain families of convex co-compact hyperbolic metrics $g_\eps$ degenerating to a geometrically finite hyperbolic metric with rank- cus…
Compressing data helps learn Mahalanobis metrics effectively.
problem Learning Mahalanobis metrics in high-dimensional spaces.
method Randomly compress data to train a full-rank metric in a reduced feature space.
result Theoretical guarantees on error for Mahalanobis metric learning, independent of ambient dimension.
Paper improves image retrieval quality using nonlinear rank approximations.
problem Improving image retrieval quality in high-dimensional feature spaces.
method Computes normalized approximated ranks, converts to similarities, and uses them in a new loss function.
result Significant improvement in image retrieval quality on multiple datasets.
New Einstein metrics found on specific Lie algebras.
problem Finding special Einstein metrics on solvable Lie algebras.
method Concrete procedure to construct Einstein pseudo-Kähler and para-Kähler metrics.
result Existence of Einstein pseudo-Riemannian metrics on specific Lie algebras.
This paper introduces depth functions for ranking data, improving statistical summaries.
problem Lack of comprehensive statistical summaries for ranking data.
method Metric-based depth functions on symmetric group to define rankings, depths, and procedures.
result Novel depth functions provide a more informative summary of ranking data.
Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.
problem Identifying all invariant contact metric structures on tangent sphere bundles of compact rank-one symmetric spaces.
method Explicitly obtained all structures, distinguishing K-contact, Sasakian, and 3-Sasakian structures.
result There is a unique Sasakian-Einstein metric on tangent sphere bundles of spheres and real projective spaces.
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) w…
Affine maps reveal higher rank structures in certain spaces.
problem Characterizing spaces with higher rank structures.
method Using Hadamard spaces with geometric group actions and affine maps.
result Affine maps not dilations indicate higher rank structures.
We give an explicit description of all complete -invariant Ricci-flat Kähler metrics on the tangent bundle $T(G/K)\cong G^\bbC/K^\bbC$ of rank-one Riemannian symmetric spaces of compact type, in terms of associated vector-functions.
Compact rank one symmetric spaces are rigid under certain curvature conditions.
problem Rigidity of compact rank one symmetric spaces under curvature constraints.
method Examined compact symmetric spaces with metric of rank one, and another metric with sectional curvature bounded by 0 to 1.
result If equals outside a convex subset, then is isometric with .