The paper proves concentration inequalities for two-sample rank processes and applies them to ranking performance criteria.
problem Measuring the performance of ranking statistics between two populations.
method Proves concentration inequalities for two-sample rank processes indexed by VC classes of scoring functions.
result Generalization capacity of empirical maximizers of ranking performance criteria is investigated.
Let G be a rank two finite group, and let $\cH$ denote the family of rank one p-subgroups of G, at all primes where G has p-rank two. We show that a rank two finite group G which satisfies certain group-theoretic conditions admits a finite G-CW-complex X with isotropy in $\cH$, whose fixed sets are homotopy spheres. Ou…
We prove that there does not exist any real hypersurface in complex Grassmannians of rank two with semi-parallel structure Jacobi operator. With this result, the nonexistence of real hypersurface in complex Grassmannians of rank two with recurrent structure Jacobi operator is proved.
In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb v…
We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are proven for all strata in genus three, with the hope that they may shed light on a complete classification of rank two manifolds in genus three.
We give a construction of hyperbolic 3-manifolds with rank two fundamental groups and report an experimental search to find such manifolds. Our manifolds are all surface bundles over the circle with genus two surface fiber. For the manifolds so obtained, we then examine whether they are of Heegaard genus two or not. As…
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.
In this paper, we show that there exists no equifocal submanifold with non-flat section in four irreducible simply connected symmetric spaces of compact type and rank two. Also, we show a fact for the sections of equifocal submanifolds with non-flat section in other irreducible simply connected symmetric spaces of comp…
New methods provide stable ranking without assumptions on data distributions.
problem Stability issues in ranking problems with noisy data.
method Developed a stability framework and two ranking operators.
result Guaranteed stability without assumptions on data distributions.
Researchers study rank two theories with eight supercharges using Lefschetz pencils.
problem Understanding the global Seiberg-Witten geometries for rank two theories with eight supercharges.
method Combining combinatorial methods with geometric analysis of Lefschetz pencils.
result The conjugacy class of mapping class group determines the local singularity, and the global study reduces to questions about MCG.
Unified transformer-based LT-TTD improves ranking efficiency and quality.
problem Decoupled L1 and L2 models in recommendation and search systems cause irreversible error propagation and suboptimal ranking.
method LT-TTD combines two-tower models with transformer expressivity in a unified listwise learning framework, providing theoretical guarantees and UPQE evaluation.
result LT-TTD reduces irretrievable relevant items and achieves better global optimization than disjoint training.
Introduces nondecreasing rank for matrices and tensors, developing methods and applications.
problem Finding low-rank approximations for matrices and tensors with monotonic constraints.
method Developed a variant of hierarchical alternating least squares algorithm for finding low ND rank approximations.
result Low ND rank factorizations can be found and interpreted for real-world datasets.
Two-stage risk control for ranked retrieval systems.
problem Assessing prediction uncertainty and risk control in sequential machine learning systems.
method Developed two-stage risk control methods based on LTT and CRC frameworks, leveraging sequential nature of retrieval and ranking phases.
result The proposed methods provide theoretical guarantees and reduce computational burden compared to prior work.
We propose Top-N-Rank, a novel family of list-wise Learning-to-Rank models for reliably recommending the N top-ranked items. The proposed models optimize a variant of the widely used discounted cumulative gain (DCG) objective function which differs from DCG in two important aspects: (i) It limits the evaluation of DCG …
The paper designs tests for comparing ranked preference data and finds significant differences.
problem Comparing pairwise comparison and ranking data in various applications.
method Developed two-sample tests for pairwise comparison and ranking data, proving upper and lower bounds.
result Upper and lower bounds show tightness of the proposed tests, and significant differences in preferences were found.
The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
problem Recovering tensors with low symmetric rank from symmetric rank-one measurements.
method Covering numbers argument, Carbery-Wright inequality, orthogonal polynomials, Fano's inequality.
result Near-optimal sample complexity bounds for log-concave distributions.
In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the topology of fibers of the rank two prolongations. Moreover, by using properties of …
Research characterizes learnability of multilabel ranking problems.
problem Learnability of multilabel ranking problems with relevance-score feedback.
method Characterizes learnability in batch and online settings for a large family of ranking losses.
result Characterizes two equivalence classes of ranking losses based on learnability.
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.
The purpose of this work is to close the local deformation problem of rank two Euclidean submanifolds in codimension two by describing their moduli space of deformations. In the process, we provide an explicit simple representation of these submanifolds, a result of independent interest by its applications. We also det…
New gossip algorithms improve robustness of rank-based statistics in decentralized systems.
problem Ensuring robustness in decentralized AI and edge intelligence systems, especially in the presence of corrupted or adversarial data.
method Developed asynchronous gossip algorithms for computing rank-based statistics.
result First convergence rate bound for asynchronous gossip-based rank estimation.
We present an attention-based ranking framework for learning to order sentences given a paragraph. Our framework is built on a bidirectional sentence encoder and a self-attention based transformer network to obtain an input order invariant representation of paragraphs. Moreover, it allows seamless training using a vari…
New algorithm ranks players from partial comparisons with optimal rate.
problem Ranking players from partial pairwise comparisons.
method Divide-and-conquer approach, local MLE within groups.
result Optimal ranking algorithm with minimax rate.
In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em partial rankings}). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical frame…
The paper reveals low-rank structure in neural network gradients, influenced by data and model parameters.
problem Investigating low-rank structure in gradients of neural networks under relaxed assumptions.
method Spiked data model, relaxation of isotropy assumptions, analysis of mean-field and neural-tangent-kernel scalings.
result Gradient of input weights is approximately low rank, dominated by two rank-one terms.
RCPO uses ranked choice modeling for better LLM alignment.
problem Pairwise preference optimization limits LLM alignment.
method Unified framework combining preference optimization and ranked choice modeling.
result RCPO outperforms competitive baselines in LLM alignment.
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of da…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices, and proposes two algorithms (for two versions of retractions) based on ma…
Proposes a new IPW-based ranking metric for two-sided markets.
problem Addressing bias in implicit user feedback in two-sided markets.
method Extends IPW estimator to two-sided markets, addressing position bias.
result Proposed estimator is unbiased for ground-truth ranking metric.
The paper proposes methods to identify and sample from mixtures of Mallows models for top-k rankings.
problem Identifying and sampling from mixtures of Mallows models for top-k rankings in a heterogeneous population.
method Efficient sampling algorithms and identifiability proofs for both components of the mixture.
result The identifiability and learnability of the Mallows components' parameters in the mixture.
A new learning-to-rank approach ensures fairness for item providers in dynamic ranking systems.
problem Myopically optimizing user utility can be unfair to item providers in two-sided markets.
method A controller that integrates unbiased estimators for fairness and utility, dynamically adapting as more data becomes available.
result Empirically, the algorithm is highly practical and robust, ensuring amortized group fairness.
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.
Relevance ranking and result diversification are two core areas in modern recommender systems. Relevance ranking aims at building a ranked list sorted in decreasing order of item relevance, while result diversification focuses on generating a ranked list of items that covers a broad range of topics. In this paper, we s…
Partial convexification improves tractability of low-rank spectral optimization problems.
problem Minimizing linear objectives subject to matrix inequalities and low-rank constraints.
method Partial convexification of the domain set, deriving rank bounds, and developing a column generation algorithm.
result The partial convexification LSOP-R is equivalent to the original LSOP under certain conditions and yields high-quality solutions.
The problem of frequent pattern mining has been studied quite extensively for various types of data, including sets, sequences, and graphs. Somewhat surprisingly, another important type of data, namely rank data, has received very little attention in data mining so far. In this paper, we therefore addresses the problem…
Researchers show mixtures of ranking models are generally identifiable.
problem Understanding when and how parameters of mixtures of ranking models can be uniquely determined.
method Algebraic geometry framework applied to verify the number of solutions in polynomial systems.
result Popular mixtures of ranking models with two components are generically identifiable.
There are two different approaches to exhibit submaximal symmetric rank 2 distributions in 5D via Monge equations. In this note we establish precise relations between these models, find auto-equivalences of one family, and treat two special equations.
Object ranking is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects, which are typically represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. Current approaches co…
New algorithms improve RPCA for large matrices with upper rank bounds.
problem Efficiently decompose large matrices into low-rank and sparse parts.
method Combine regularization and matrix multiplication approaches with upper rank bounds.
result Proposed algorithms are faster and more robust than existing methods.
New proof for higher rank subvarieties in genus three.
problem Classifying higher rank invariant subvarieties in genus three.
method Uses recent techniques developed by Apisa and Wright.
result Short and simplified proof of classification.
New method for initializing low-rank neural networks improves performance.
problem Training low-rank neural networks efficiently and accurately.
method Inspired by function approximation, proposes a novel low-rank initialization framework.
result Demonstrates significant gap between spectral and low-rank initialization approaches.
Paper proposes a two-stage ranking for personalized TV recommendations.
problem Improving TV recommendation accuracy and efficiency.
method First, identifies potential candidates using user viewing patterns. Then, ranks them based on user preferences and program textual information.
result The proposed model outperforms in recommendation accuracy and efficiency.
Fast and accurate methods for low-rank learning problems.
problem Partial singular value decomposition and numerical rank estimation of huge matrices.
method Krylov subspaces and Ritz vectors for fast and accurate solutions.
result Advantages over traditional methods in accuracy and speed.
The optimal ranking score between precision and recall is rarely F1 and can be found using specific methods.
problem Finding a meaningful and optimal compromise between precision and recall scores.
method Established a shortest path between precision- and recall-induced rankings, framed the problem as an optimization problem, and provided theoretical tools to find the optimal β.
result F1 and its skew-insensitive version are not optimal tradeoffs between precision and recall scores.
The two main tasks in the Recommender Systems domain are the ranking and rating prediction tasks. The rating prediction task aims at predicting to what extent a user would like any given item, which would enable to recommend the items with the highest predicted scores. The ranking task on the other hand directly aims a…
This work analyzes two methods for combining multiple binary labels in bipartite ranking.
problem Combining multiple binary labels for optimal bipartite ranking.
method Loss aggregation vs. label aggregation approaches.
result Label aggregation is preferable to loss aggregation due to label dictatorship issues.
Study local third Chern class for point singularities on threefolds.
problem Understanding gauge theory singularity contributions on threefolds.
method Local algebraic data and deformation invariance, K-theoretic interpretation.
result Local third Chern class can be computed from family data and is deformation invariant.
Analytic torsion defined for rank 2 distributions on 5-manifolds.
problem Defining and analyzing analytic torsion for rank 2 distributions.
method Proposed an analytic torsion for Rumin complex associated with rank 2 distributions on 5-manifolds, established anomaly formulas, and showed coincidence with Ray-Singer torsion.
result The proposed torsion coincides with Ray-Singer torsion for certain nilmanifolds.