Develops methods to estimate high rank tensors from noisy data.
problem Estimating high rank tensors from noisy observations.
method Generative latent variable tensor model, polynomial-time spectral algorithm.
result Achieves computationally optimal rate for signal tensor estimation.
Sparse sampling method for tensor factorization and completion of high rank tensors.
problem Completion of high rank tensors with missing data in recommendation systems.
method Sparse measurements and message-passing algorithms in a high-dimensional limit.
result Theoretical insights and performance analysis of tensor factorization in dense limit.
Truncated SVD provides a simple yet effective method for approximating high-rank matrices.
problem Estimating high-rank positive semi-definite matrices from partial observations or noisy data.
method Truncated SVD applied to an estimate of the matrix.
result Truncated SVD produces a multiplicative approximation of the original matrix in Frobenius norm.
New model for high rank matrix completion with online and batch methods.
problem Matrix completion for high rank matrices with latent structure.
method Kernel trick to map data into a high dimensional feature space, explicit parametrization of low dimensional subspace, online fitting procedure.
result Online method can handle streaming data and adapt to non-stationary latent structure.
New bound explains why high-rank neural nets generalize well.
problem Understanding why high-rank neural networks generalize well.
method Using Koopman operators, group representations, and RKHSs, a new Rademacher complexity bound is derived.
result Derives a bound for a wider range of realistic models.
Low-precision quantization improves kernel approximation under memory constraints.
problem Training kernel approximation methods efficiently with limited memory.
method Low-precision quantization of random Fourier features (LP-RFFs).
result LP-RFFs can match the performance of full-precision RFFs and Nyström method with significantly less memory.
Paper introduces HRPCFD for efficient training of stochastic processes.
problem Discontinuities in stochastic processes over time.
method High Rank Path Development method and HRPCFD metric.
result Efficient algorithm for training HRPCFD from data.
We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.
DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.
problem Missing labels in multi-label learning.
method DM2L imposes local low-rank structures and global high-rank structures on predictions of instances from the same and different labels, respectively.
result DM2L outperforms state-of-the-art methods in multi-label learning with missing labels.
Flora uses random projections to achieve high-rank updates with low memory usage.
problem Excessive memory usage in large neural networks during training.
method Flora approximates LoRA using random projections to enable high-rank updates with sublinear space complexity.
result Flora achieves high-rank updates with significantly reduced memory usage compared to LoRA.
RKPCA improves robustness of PCA for high-rank matrices.
problem Robust recovery of high-rank matrices corrupted by sparse noises.
method RKPCA decomposes matrices into sparse and low-rank components.
result RKPCA provides high recovery accuracy with theoretical guarantees.
The paper recovers missing data entries of high-rank matrices using polynomial polynomials.
problem Recovering missing entries of high-rank matrices with low intrinsic dimension.
method Developed a new polynomial matrix completion method using the kernel trick and relaxation of rank objective.
result Identified complete matrix of minimum intrinsic dimension by minimizing rank in high-dimensional feature space.
New algorithm improves partition function approximation for graphical models.
problem Computing partition function of graphical models is computationally hard.
method Spectral mean-field scheme using FPTAS for low-rank matrices, and approximation of high-rank matrices.
result The proposed algorithm is more robust and accurate than previous methods.
SANs estimate feature importance in neural models, identifying interactions and high-ranked features.
problem Understanding and interpreting black-box neural network models.
method Self-Attention Network (SAN) architecture for feature importance estimation.
result SANs identify similar high-ranked features and feature interactions as other methods, improving predictive performance.
New method for matrix completion using algebraic varieties.
problem Matrix completion with high-rank data.
method Algebraic variety mapping and kernel trick.
result Algorithm recovers data up to sampling complexity bounds.
A method for learning complex functions from data with reduced memory usage.
problem Learning highly nonlinear, multivariate functions from examples.
method Transforming function learning into tensor reconstruction, incrementally building tensors from rank-one terms.
result Efficient gradient-based algorithm with linear time complexity in sample size and tensor dimensions.
New method solves nonsmooth low-rank matrix optimization problems efficiently.
problem Nonsmooth and low-rank matrix optimization problems in statistics and machine learning.
method Low-rank Extragradient Method with warm-start initialization.
result The extragradient method converges to an optimal solution with rate O(1/t) and requires only two low-rank SVDs per iteration. Given a compact Riemannian spin manifold with positive scalar curvature, we find a family of connections ∇At for t∈[0,1] on a trivial vector bundle of sufficiently high rank, such that the first eigenvalue of the twisted Dirac operator DAt is nonzero and becomes arbitrarily small as t→1. Howeve…
DoRA improves adaptation efficiency for large models by factoring norms and fusing kernels.
problem High-rank DoRA is computationally expensive and infeasible on common GPUs.
method Factored norms and fused Triton kernels to reduce memory and speed up computation.
result Fused implementation is up to 2.0x faster for inference and 1.9x faster for gradient computation.
Study mapping class group actions on cohomology of configuration spaces.
problem Understanding the action of mapping class groups on cohomology.
method Examined the nth rational cohomology of configuration spaces and compared kernels. result Found high-rank abelian subgroups in the quotient of kernels and Johnson subgroups.
Flow-SSN improves segmentation efficiency and accuracy.
problem Challenges in medical imaging segmentation, especially high-rank pixel-wise covariances.
method Generative segmentation model using discrete-time autoregressive and continuous-time flow variants.
result Flow-SSNs can estimate high-rank pixel-wise covariances efficiently without assuming rank or storing parameters.
Classifies GL(2,R)-invariant subvarieties in complex geometry.
problem Classifying GL(2,R)-invariant subvarieties.
method Classification of natural subvarieties including double covers and Teichmüller space.
result Classification of high rank invariant subvarieties and new examples.
We prove the holomorphic rigidity conjecture of Teichmüller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichmüller space as a complex manifold. The method of proof is through harmonic maps. We prove that the singular set of a harmonic map from a smooth n-dim…
Unified bounds for neural networks incorporating physical laws.
problem Limitations in existing generalization analyses for PINNs and VPINNs.
method Unified framework using Taylor expansion and Koopman-based analysis.
result High-rank networks can generalize well even with differential operators.
New method clusters incomplete data by fusing subspaces.
problem Learning low-dimensional structures from highly incomplete data.
method Assign each datum to its own subspace, then fuse subspaces of the same cluster.
result Our method performs comparably to state-of-the-art with complete data and better with missing data.
A new method reduces rank in Frank-Wolfe steps for nuclear norm problems.
problem High rank intermediate iterates in Frank-Wolfe algorithm for nuclear norm problems.
method Rank-drop steps to ensure rank decreases and feasibility.
result Reduced rank of solutions compared to Frank-Wolfe and variants.
New saddle network architectures preserve convex-concave geometry in optimization problems.
problem Optimization models with convex x and concave y components.
method Structured separable decomposition and saddle network architectures.
result Proven one-dimensional approximation theorem and high accuracy on various test functions.
New method estimates tensors from noisy data with missing entries.
problem Tensor estimation from noisy observations with missing entries.
method Sign series representation for tensor completion, addressing low- and high-rank signals.
result Excess risk bounds, estimation error rates, and sample complexities established.
We find a rank effect in commodity prices that yields higher returns.
problem Understanding the pricing dynamics of commodities over time.
method Nonparametric econometric methods to demonstrate the rank effect as a consequence of stationary relative asset price distribution.
result A portfolio of lower-ranked, lower-priced commodities yields 23% higher annual returns than a portfolio of higher-ranked, higher-priced commodities.
NoL approach improves adversarial robustness by modeling random noise during training.
problem Improving neural network robustness against adversarial attacks.
method Implicit generative modeling of random noise during training.
result Models trained with NoL perform better against a wide range of adversarial attacks.
Improves tensor networks for classifying medical images.
problem Classifying 2D and 3D medical images efficiently.
method Develops LoTeNet, a tensor network that treats small image regions as orderless and aggregates local representations hierarchically.
result LoTeNet achieves comparable or superior performance to other methods with less computational resources.
Polynomial sketch approximates functions of low-rank matrices efficiently.
problem Approximating element-wise functions of low-rank matrices without full access.
method Combining polynomial approximation and tensor sketch for monomials.
result Efficient algorithm with lower complexity than full matrix access.
Wide & Deep combines linear and deep learning for better app recommendations.
problem Sparse user-item interactions lead to less relevant recommendations.
method Jointly trains wide linear models and deep neural networks.
result Wide & Deep significantly increases app acquisitions compared to wide-only and deep-only models.
This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full r…
New method recovers matrices with nonlinear structures using optimization on Grassmann manifold.
problem Recovering high-rank matrices with nonlinear structures like subspaces or clusters.
method Formulated as rank minimization of a nonlinear feature map, approximated by constrained non-convex optimization on the Grassmann manifold, using Riemannian and alternating minimization schemes.
result Global convergence and worst-case complexity bounds for alternating minimization scheme, leading to unique limit point.
This paper proposes a probabilistic imputation method with uncertainty quantification.
problem Missing value imputation with uncertainty estimation for large datasets.
method Low Rank Gaussian Copula framework that augments PPCA with column-specific transformations.
result The method yields state-of-the-art imputation accuracy and well-calibrated uncertainty estimates.
SGD can jump from high rank minima to low rank minima in DLNs, but not back.
problem SGD's tendency to get stuck in high rank minima in DLNs.
method Analysis of the L2-regularized loss function of DLNs and the definition of absorbing sets. result SGD has a non-zero probability to jump from high rank minima to low rank minima but zero probability to jump back.
The paper explores how kernel eigenalignments affect generalization in KRR.
problem Achieving robust generalization in kernel methods.
method Direct connection between generalization and matrix eigenvectors/eigenvalues, focusing on finite-sample settings.
result Strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between eigenvalues.
The paper introduces a method to incorporate feedback into tree-based anomaly detection to reduce false positives.
problem Difficulty in human analysts examining high-ranking anomalies due to false positives.
method Incorporates simple binary feedback into tree-based anomaly detectors, focusing on the Isolation Forest algorithm.
result Significantly improves the performance of the Isolation Forest algorithm by reducing false positives.
VLM judges rank well but score poorly; task difficulty and annotation quality affect interval width.
problem VLMs as judges lack reliability indicators in multimodal evaluations.
method Conformal prediction using score-token log-probabilities.
result Evaluation uncertainty is task-dependent, affecting interval width and reliability.
Bayesian approach optimizes crowdsourced ranking with limited budget.
problem Efficiently collect high-quality pairwise comparisons for accurate ranking.
method Bayesian Markov decision process for dynamic item and worker selection.
result Proposed policy achieves high ranking accuracy with lower labeling cost.
SGD with mini-batches can solve convex low-rank matrix problems efficiently.
problem Solving large-scale convex low-rank matrix problems efficiently.
method Stochastic Gradient Descent with mini-batches and low-rank projections.
result SGD with mini-batches produces low-rank iterates with high probability.
Novel method extracts hierarchical brain connectivity patterns from fMRI.
problem Functional hierarchical organization of the human brain.
method Sparse Connectivity Patterns (SCPs) with hierarchy of sparse overlapping patterns, deep factorization of correlation matrices.
result Reproducible multi-scale hierarchical SCPs more stable than single-scale patterns.
We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence assumptions on the matrix row space that are necessary for passive sampling procedures. Fo…
This review synthesizes missing data imputation across diverse fields.
problem Missing data hinders analysis across various disciplines.
method Systematic review of imputation methods and their application across domains.
result Critical challenges and future directions identified.
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…
Develops a new nonparametric trace regression model for high-dimensional data.
problem Violation of known functional form and global low-rank structure assumptions in trace regression.
method Structured sign series representations for nonparametric trace regression models.
result Establishes excess risk bounds and sample complexities for the proposed model.
Improved tensor rank learning for CPD models using a generalized hyperbolic prior.
problem Inaccurate tensor rank determination leads to overfitting or underfitting in CPD models.
method Introduced a generalized hyperbolic prior for automatic tensor rank learning in probabilistic CPD models.
result Significantly improved performance in learning both low and high tensor ranks, even for low SNR cases.