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.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “rank d measurements”
Rank-one measurements limit feasible sets for low-rank PSD matrices.
problem Feasibility of PSD matrices under rank-one measurements.
method Characterization of feasible sets for PSD matrices given rank-one projections.
result Radius of feasible sets determines singleton solution sets for low-rank matrices.
The paper proves rigidity and ergodicity of horospherical foliations.
problem Rigidity and ergodicity of horospherical foliations in higher rank.
method Establishes higher rank extensions of rigidity theorems for representations of discrete subgroups of divergence type, using conformal measures and boundary maps.
result Proves conformal measure rigidity and ergodicity of horospherical foliations for hypertransverse subgroups.
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.
A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its t…
Analytic proof for minimal rank Sard conjecture.
problem Proving the minimal rank Sard conjecture in the analytic category.
method Using subanalytic abnormal distribution from [4], we establish a proof.
result The set of points accessible through singular horizontal curves of minimal rank has Lebesgue measure zero.
Classifies measures for Anosov subgroups in higher ranks.
problem Classifying horospherical invariant measures for Anosov subgroups.
method Geometric approach, not relying on flows or ergodic theorems.
result Extends results from rank one to higher ranks, solving open problems.
Proves finite measure implies product structure for certain discrete subgroups.
problem Classifying discrete subgroups with finite Bowen-Margulis-Sullivan measure.
method Product structure of leafwise measures and high entropy method.
result Proves virtually a product structure for certain subgroups.
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.
Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
problem Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
method Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
result Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
Paper develops a theory for Patterson-Sullivan measures in higher rank symmetric spaces.
problem Establishing existence and uniqueness of Patterson-Sullivan measures in higher rank symmetric spaces.
method Develops theory for vector-valued horofunction boundaries and shadows.
result Proves existence and uniqueness of Patterson-Sullivan measures for transverse groups.
In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME r…
This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements …
Convex optimization method recovers low-rank matrices from rank-one projections efficiently.
problem Recovering low-rank matrices from limited rank-one projections.
method Unlifted convex optimization with subgradient method.
result The estimator succeeds with high probability if the number of measurements exceeds up to logarithmic factors.
Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterizationcs.LG
Gradient descent recovers low-rank matrices from corrupted measurements with double over-parameterization.
problem Robust recovery of low-rank matrices from grossly corrupted measurements.
method Gradient descent with discrepant learning rates for double over-parameterized models.
result Gradient descent with discrepant learning rates provably recovers the underlying matrix without prior knowledge on rank or sparsity.
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…
Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…
Paper proves finite BMS measure for SPR groups in higher rank Lie groups.
problem Finite measure for certain groups in higher rank Lie groups.
method Developed SPR property and proved finite BMS measure.
result Finite Bowen-Margulis-Sullivan measure for SPR groups in higher rank Lie groups.
Given a measurement graph and an unknown signal , we investigate algorithms for recovering from pairwise measurements of the form ; . This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distribute…
Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Banditsstat.ML
Novel method for efficient low-rank matrix estimation and bandit algorithms.
problem Low-rank matrix estimation and bandit problems.
method LowPopArt method for low-rank matrix estimation and novel experimental design criterion.
result Improved recovery guarantees and regret bounds for low-rank bandit algorithms.
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With random measurements of a positive semidefinite matrix of rank and condition number …
Improved stability for matrix recovery from rank-one measurements.
problem Phase retrieval problem of recovering rank-one positive semidefinite matrices.
method Developed a smoothing Newton method based on Bures-Wasserstein gradient descent.
result Superlinear convergence with rigorous guarantees and stable implementation.
In this paper we investigate two variants of association rules for preference data, Label Ranking Association Rules and Pairwise Association Rules. Label Ranking Association Rules (LRAR) are the equivalent of Class Association Rules (CAR) for the Label Ranking task. In CAR, the consequent is a single class, to which th…
Sub-gradient method recovers low-rank matrices robustly from noisy measurements.
problem Recovering low-rank matrices from noisy measurements with unknown rank.
method Sub-gradient method with small initialization, robust to over-parameterization and noise.
result Sub-gradient method converges exponentially fast to the true solution under noisy and over-parameterized conditions.
Paper characterizes minimax regret rates for online ranking with top-k feedback.
problem Analyzing online ranking with partial feedback.
method Developed techniques from partial monitoring to characterize minimax regret rates.
result Full characterization of minimax regret rates for Precision@n.
Study robust recovery of low-rank matrices from corrupted measurements without rank prior.
problem Robust recovery of low-rank matrices from corrupted Gaussian measurements with unknown rank.
method Subgradient method with diminishing stepsizes for nonconvex nonsmooth problem.
result Subgradient method converges to exact low-rank solution at sublinear rate under RDPP condition.
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.
New framework assesses LM uncertainty without thresholding.
problem Uncertainty quantification for LMs, especially comparing different measures.
method Rank-Calibration framework to assess uncertainty and confidence measures.
result Higher uncertainty correlates with lower generation quality.
Melanoma is the deadliest form of skin cancer. Computer systems can assist in melanoma detection, but are not widespread in clinical practice. In 2016, an open challenge in classification of dermoscopic images of skin lesions was announced. A training set of 900 images with corresponding class labels and semi-automatic…
Tensor Restricted Isometry Property Analysis For a Large Class of Random Measurement Ensemblesstat.ML
In previous work, theoretical analysis based on the tensor Restricted Isometry Property (t-RIP) established the robust recovery guarantees of a low-tubal-rank tensor. The obtained sufficient conditions depend strongly on the assumption that the linear measurement maps satisfy the t-RIP. In this paper, by exploiting the…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coeffic…
New algorithms handle phase retrieval with rank d measurements, revealing phase transitions.
problem Phase retrieval with rank d measurements.
method Random duality theory (RDT) and descending phase retrieval algorithms (dPR).
result Minimal sample complexity ratio for dPR's success exhibits phase transitions.
Unified approach for learning quantum operations from measurements.
problem Accurate reconstruction of unknown quantum operations from noisy measurements.
method Matrix sensing techniques, randomized measurement design, blockwise measurement design, alternating least squares (ALS).
result The proposed method provides theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise.
Ranking models are typically designed to provide rankings that optimize some measure of immediate utility to the users. As a result, they have been unable to anticipate an increasing number of undesirable long-term consequences of their proposed rankings, from fueling the spread of misinformation and increasing polariz…
Proves is 1-taut, concluding studies of rank-one Lie groups.
problem Tautness of rank-one Lie groups of non-compact type.
method Proves is 1-taut.
result Concludes the study of -tautness of rank-one Lie groups of non-compact type.
New guarantees for recovering matrices as low-rank plus sparse from fewer measurements.
problem Recovering matrices as the sum of a low-rank and sparse matrix from a limited number of measurements.
method Developed guarantees for recovery of low-rank plus sparse matrices from measurements, using semidefinite programming and gradient descent algorithms.
result Guarantees for recovery of low-rank plus sparse matrices from fewer measurements than previously possible.
Concentration Inequalities for Two-Sample Rank Processes with Application to Bipartite Rankingmath.ST
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.
We address some theoretical guarantees for Schatten- quasi-norm minimization () in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…
Study positive entropy actions by higher-rank lattices, proving rigidity and conjugacy results.
problem Positive entropy actions by higher-rank lattices in Lie groups.
method Analysis of sub-actions, fiber entropy upper semicontinuity, and conjugacy arguments.
result Actions by higher-rank lattices in are conjugate to affine actions on (infra-)tori.
Sign-RIP improves robust low-rank matrix recovery by preserving norms even with corrupted measurements.
problem Robust low-rank matrix recovery in the presence of corrupted measurements.
method Proposed Sign-RIP, a robust restricted isometry property.
result Sign-RIP guarantees uniform convergence of subdifferentials in robust low-rank matrix recovery.
We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface are not dense in the set of probability measures invariant by the geodesic flow. F…
Anosov groups in rank ≤3 have unique ergodic horospherical actions.
problem Characterizing unique ergodicity of horospherical actions for Anosov groups.
method Analyzing -action on for in the limit cone.
result Unique ergodicity holds for and in the limit cone.
The problem of ranking a set of objects given some measure of similarity is one of the most basic in machine learning. Recently Agarwal proposed a method based on techniques in semi-supervised learning utilizing the graph Laplacian. In this work we consider a novel application of this technique to ranking binary choice…
We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial ti…
New tensor completion method reduces impact of outliers.
problem Recover tensors from incomplete data with outliers.
method Proposes a new correntropy-based objective function and half-quadratic minimization.
result Demonstrates robust performance with real and synthetic data.
Study shows how to detect representation extendability using conformal measures.
problem Detecting extendability of representations using conformal measures.
method Using higher rank conformal measures and self-joinings of groups.
result Affirmative answer to detect extendability of representations.