The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.
problem Efficient training and deployment of large-scale deep learning models.
method Complementary theoretical perspectives on low-rank structures during training and convergence, and practical applications of LoRA and masked training.
result Understanding and exploiting low-rank structures can improve efficiency and effectiveness of training and fine-tuning.
FLAMBE tackles RL in low rank MDPs by learning features.
problem Dealing with the curse of dimensionality in RL.
method Develops FLAMBE, a method that engages in exploration and representation learning for RL in low rank transition models.
result FLAMBE efficiently learns features for RL in low rank transition models.
New spectral methods improve matrix estimation in RL with low-rank structure.
problem Estimating matrices with low-rank structure in reinforcement learning.
method Spectral-based matrix estimation approaches.
result Spectral methods efficiently recover singular subspaces and minimize entry-wise error.
Algorithm recovers multiple low-rank matrices from unlabeled data.
problem Learning mixtures of low-rank models from unlabelled data.
method Three-stage meta-algorithm that copes with non-convexity and noise.
result Near-optimal sample and computational complexities under Gaussian designs.
New algorithm improves deep learning models' robustness without sacrificing accuracy.
problem Low-rank methods compromise model robustness against adversarial perturbations.
method Robust low-rank training via approximate orthonormal constraints.
result Ensures well-conditioning and better adversarial robustness without sacrificing model accuracy.
New model-free algorithms learn representations for low-rank MDPs efficiently.
problem Learning representations in reinforcement learning for low-rank MDPs.
method Developed minimax representation learning objective and interleaved with reward-free exploration.
result Proven sample efficiency and scalability to complex environments.
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…
Study the distribution for low-rank matrix learning, improving inference methods.
problem Lack of understanding of underlying probability distributions in low-rank matrix learning.
method Analyze the distribution f(X)∝e−λ∥X∥∗, using differential geometry to design an improved MCMC algorithm and learn penalty parameter λ. result Improved MCMC algorithm and penalty parameter learning for low-rank Bayesian inference.
New nonconvex regularizer speeds up low-rank matrix completion.
problem Low-rank matrix completion with good theoretical and empirical performance.
method Proposes a new nonconvex regularizer with adaptive shrinkage, scalable, and fast optimization.
result Proposed method achieves state-of-the-art recovery performance and is the fastest.
Paper tackles fair low-rank approximation and column subset selection.
problem Minimize loss over sub-populations in machine learning.
method Developed algorithms for fair low-rank approximation and fair column subset selection.
result Achieved polynomial time algorithms for fair low-rank approximation.
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …
Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still a challenge for current methods to handle datasets with both high dimensions and…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…
FedLoRU improves FL efficiency by using low-rank updates.
problem Communication inefficiency and performance reduction in Federated Learning.
method Proposes FedLoRU, a low-rank update framework for FL, which reduces communication costs while maintaining performance.
result FedLoRU achieves convergence rates similar to FedAvg and is robust to heterogeneous and large numbers of clients.
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.
LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.
problem Efficiently solving time-dependent PDEs with deep neural networks.
method Low-rank constraint on network weights using SVD for efficient parameter updates.
result LR-EDNN achieves comparable accuracy to full EDNN with fewer parameters and lower cost.
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…
Bayesian model improves image completion accuracy by automatically learning low rank structure.
problem Improving image completion accuracy with limited data and avoiding overfitting.
method Developed a Bayesian low rank tensor ring model with multiplicative interaction and Student-T distribution for sparse core factors.
result The proposed method outperforms state-of-the-art image completion techniques, especially in recovery accuracy.
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…
Paper improves sample complexity for reward-free RL in low-rank MDPs.
problem Reward-free RL in low-rank MDPs with unknown representation and weights.
method Proposes a novel model-based algorithm RAFFLE with improved sample complexity.
result RAFFLE achieves ε-optimal policy and accurate system identification with significantly fewer samples. New insights into training deep networks with low rank layers.
problem Efficiency in training deep neural networks.
method Analysis of techniques for training in low rank space.
result Falsified common beliefs in training deep networks.
Proposes GTTN for discovering all low-rank structures in deep multi-task learning.
problem Discovering all low-rank structures among tasks in deep multi-task models.
method Introduces GTTN, a convex combination of matrix trace norms of all tensor flattenings, to automatically determine the importance of components.
result Demonstrates the effectiveness of GTTN on real-world datasets.
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
problem Solving large-scale combinatorial optimization problems efficiently.
method Proposed a new computing model for SPIM that can handle low-rank interaction matrices.
result Demonstrated efficient learning, classification, and sampling of MNIST images using the model.
New framework explains why nonconvex methods work well in low-rank matrix estimation.
problem Nonconvex low-rank matrix estimation problems in machine learning.
method Developed a theoretical framework revealing a benign regularizer.
result Nonconvex procedures can behave well due to a disguised convexity.
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.
Survey on factor models and their applications in econometrics.
problem Estimating low-rank structures in high-dimensional models.
method Low-rank recovery techniques for factor model estimation.
result New insights into factor model applications in econometrics.
New algorithm learns low-rank matrices with linear number of samples.
problem Learning low-rank matrices efficiently in latent-variable applications.
method Proposed algorithm that uses linear number of samples in high dimension.
result Learning kimesk, rank-r, matrices requires $Ω( rac{kr}{ε^2})$ samples. GCL-LRR improves node classification in noisy graphs.
problem Noise in real-world graph data impairs GNNs' effectiveness.
method Two-stage transductive learning with low-rank regularization and attention.
result Improved node classification performance in noisy graphs.
New RL algorithm maximizes CVaR in low-rank MDPs with provable efficiency.
problem Maximizing CVaR in large state spaces with function approximation.
method Upper Confidence Bound (UCB) bonus-driven algorithm for low-rank MDPs.
result Achieves sample complexity of O(H^7 A^2 d^4 / τ^2 ε^2) for ε-optimal CVaR.
This work tackles representation learning for RL in low-rank MDPs, improving sample efficiency.
problem How to learn a compact representation for RL in low-rank MDPs efficiently.
method Proposes REP-UCB for online RL and develops an algorithm for offline RL under partial coverage.
result Significantly improved sample complexity for online RL and competitive performance for offline RL.
LoRAs enable efficient adaptation of large models; this paper explores processing LoRA weights with machine learning.
problem Efficient processing of low-rank weight decompositions in large finetuned models.
method Developed symmetry-aware invariant and equivariant LoL models to process LoRA weights.
result LoL models can predict CLIP scores, finetuning data attributes, and accuracy on downstream tasks.
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.
Efficient solver for nonconvex tensor regularization reduces computational cost.
problem Computational inefficiency in extending nonconvex regularization to tensor learning.
method Proximal average algorithm with adaptive momentum, maintaining sparse plus low-rank structure.
result Shows good statistical performance and accuracy on tensor completion problems.
New method normalizes matrix features for robust low-rank approximation.
problem Robust feature normalization for low-rank matrix approximation.
method Learn quantile normalization operators jointly with matrix factorization.
result Improves quality of low-rank representation of data.
Proposes a new model for image restoration combining deep learning and total variation.
problem Restoring images from limited data with low-rank constraints insufficient.
method Regularized Deep Matrix Factorized (RDMF) model using deep neural network's low-rank bias and total variation.
result Outperforms state-of-the-art models in image restoration from few observations.
PowerGossip compresses model differences for decentralized deep learning with low-rank linear compressors.
problem Communication bottleneck in decentralized deep learning models.
method Low-rank linear compressors applied on model differences using power iteration steps.
result Asymptotically independent of network and compression, faster convergence, and comparable performance to tuned compression algorithms.
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the low-rank and the structural constraints onto separate factors. We formulate the optim…
New approach to convex hulls for low-rank problems.
problem Characterizing convex hulls for low-rank sets.
method Matrix perspective function and orthogonal projection matrices.
result Strong relaxations for various low-rank problems.
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. New method improves robust low-rank matrix completion for computer vision.
problem Robust low-rank matrix completion for partially observed data.
method Formulated as a nonsmooth Riemannian optimization problem over Grassmann manifold, solved with an alternating manifold proximal gradient continuation method.
result Demonstrated advantages over existing approaches in background extraction from surveillance videos.
CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.
problem Learning matrix-valued distributions from high-dimensional and incomplete data.
method Low-rank flow model that learns shared row/column subspaces and trains a normalizing flow on the core.
result CoreFlow improves generation quality in few-sample regimes and remains competitive in data-rich settings.
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
problem Improving value function learning in complex reinforcement learning tasks.
method Uncertainty-aware low-rank Q-matrix estimation (UA-LQE) algorithm.
result UA-LQE selectively erases uncertain entries in Q-matrix to improve value function approximation.
New method extends low-rank MDPs to continuous action spaces.
problem Limited applicability of current low-rank MDP methods to continuous action spaces.
method Extending FLAMBE algorithm to continuous action spaces with Hölder smoothness conditions.
result Similar PAC bound achieved for continuous actions with polynomial dependence on smoothness order.
A new method models user-specific parameters as a low-rank plus sparse component for efficient personalization.
problem Efficient personalization of machine learning models for individual users.
method Meta-learning approach that models network weights as a sum of low-rank and sparse components.
result The proposed method, AMHT-LRS, achieves nearly optimal sample complexity for estimating the low-rank and sparse components.
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix…
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.