Proposes a transductive matrix completion method with calibration for multi-task learning.
problem Improving multi-task learning with multiple related data sources.
method Transductive matrix completion with calibration constraint.
result The proposed algorithm recovers incomplete feature and target matrices with improved results.
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 deep learning model for matrix completion combining linear and nonlinear relationships.
problem Matrix completion considering only linear or nonlinear relations, ignoring latent relationships.
method Combines linear and nonlinear models in a latent variables framework, using a deep neural network with two branches for columns and rows, and manifold learning as an auxiliary task.
result Experimental results show the proposed method outperforms state-of-the-art matrix completion methods.
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
This paper analyzes privacy threats in federated matrix factorization.
problem Privacy threats in federated matrix factorization models.
method Categorizes federated matrix factorization into three types and analyzes privacy threats.
result This is the first study of privacy threats in federated matrix factorization.
A new machine learning model uses matrix exponentials for universal approximation.
problem Developing a robust and efficient machine learning model.
method Introduces a novel architecture using matrix exponentials as the only nonlinearity.
result The model achieves universal approximation properties and outperforms other models on benchmark tasks.
This work establishes always-valid risk bounds for online matrix completion.
problem Challenges in establishing always-valid concentration inequalities for online matrix completion.
method Combines non-asymptotic martingale concentration and regularized low-rank matrix regression.
result Establishes always-valid risk bound process for online matrix completion.
Federated multi-view matrix factorization learns from multiple data sources without centralizing user data.
problem Cold-start federated recommendations and multi-view data structure.
method Federated learning framework extended to multi-view matrix factorization.
result Federated multi-view matrix factorization outperforms simpler methods in cold-start federated recommendations.
Bayesian parametric matrix models provide uncertainty quantification for spectral learning.
problem Uncertainty quantification in spectral learning for safety-critical applications.
method Bayesian parametric matrix models (B-PMMs) that extend PMMs to provide uncertainty estimates.
result B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling.
Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained a…
New method efficiently learns positive-definite curvature for neural nets.
problem Efficiently learn positive-definite curvature for neural net training.
method Spectral-factorized positive-definite curvature learning approach.
result Efficiently applies arbitrary matrix roots and generic curvature learning.
We provide a proof of backpropagation algorithm in matrix notation.
problem The lack of a full induction proof of backpropagation algorithm in matrix notation.
method We provide a full induction proof of the BP algorithm in matrix notation, situating it in the framework of matrix differential calculus.
result We prove the validity of the backpropagation algorithm in inductive form.
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
GD learns matrix solutions incrementally, revealing insights into generalization.
problem Matrix sensing problem of recovering low-rank matrices from linear measurements.
method Fine-grained analysis of GD dynamics for matrix sensing.
result GD follows an incremental learning procedure, solving matrices of increasing ranks.
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-co…
EDAs with matrix transpose improve Bayesian structure learning performance.
problem Improving Bayesian structure learning performance.
method Introducing a matrix transpose mutation operator for EDAs in Bayesian structure learning.
result EDAs with transpose mutation give markedly better performance than conventional EDAs.
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.
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.
A new algorithm speeds up matrix multiplication without actual multiplication.
problem Efficiently multiplying matrices in machine learning.
method Learning-based algorithm that uses hashing, averaging, and byte shuffling.
result Often runs 100x faster than exact matrix products and 10x faster than current approximate methods.
The paper analyzes stability of random matrix products with Markovian noise.
problem Analyzing stability of random matrix products with Markovian noise.
method Using a super-Lyapunov drift condition and controlled growth of matrix-valued functions, the paper provides an exponential stability result for the p-th moment of random matrix product.
result Finite-time p-th moment bounds for linear stochastic approximation and TD learning algorithms.
Study exact limits of matrix reconstruction from noisy projections.
problem Reconstructing matrices from linear projections with high-dimensional data.
method Asymptotic analysis, universality properties, and generalized linear models.
result Exact asymptotic equations for optimal learning performance.
Paper proposes new costs for learning multiple centers in MDNs.
problem Learning multiple centers for density approximation in MDNs.
method Combines MDNs with contrastive costs using four types of kernelized matrix costs.
result New costs improve data density approximation in MDNs.
In the probabilistic topic models, the quantity of interest---a low-rank matrix consisting of topic vectors---is hidden in the text corpus matrix, masked by noise, and the Singular Value Decomposition (SVD) is a potentially useful tool for learning such a low-rank matrix. However, the connection between this low-rank m…
Teaches matrix calculus for machine learning and optimization.
problem Computing derivatives of functions involving matrices.
method Extends differential calculus to vector spaces, focusing on practical applications in machine learning.
result Introduction of adjoint and reverse-mode differentiation for efficient computation.
Dual-T method improves transition matrix estimation in noisy label learning.
problem Large estimation error in noisy class posterior leads to poor transition matrix estimation.
method Introducing an intermediate class to avoid direct estimation of noisy class posterior, factorizing the transition matrix into two easier-to-estimate matrices.
result The dual-T estimator leads to better classification performances.
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
problem Suboptimal performance in spatiotemporal prediction due to out-of-distribution data.
method Causal Adjacency Learning (CAL) method to discover causal relations over graphs.
result Calculated causal adjacency matrix enhances prediction performance on out-of-distribution test data.
A method learns matrix factorization from diverse matrices and applies the knowledge to unseen matrices.
problem Matrix factorization without shared rows or columns.
method Neural network meta-learned to minimize expected imputation error using MAP estimation.
result The method can impute missing values from unseen matrices efficiently.
New algorithms improve on bandit feedback in matrix games with unknown payoff matrices.
problem Improving performance in matrix games with unknown payoff matrices and bandit feedback.
method Regret analyses of variants of UCB and K-learning.
result New algorithms achieve lower regret compared to adversarial bandit algorithms.
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a subset of the kernel matrix entries, or some form of low-rank matrix approximatio…
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.
Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.
problem Solving least squares problems in machine learning and computer vision.
method Developed novel matrix backpropagation algorithms for QR and LQ decompositions of different matrix sizes and ranks.
result Numerical stability and computational efficiency of the proposed methods.
We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an n×d matrix A, and a parameter k, compute a rank-k matrix A′ that minimizes the approximation loss ∥A−A′∥F. The algorithm uses a training set of input matrices in order to optimize its performance. Specifical…
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.
BLAST optimizes deep model inference by learning efficient matrix structures.
problem Efficient inference of large-scale deep neural networks.
method Introduces BLAST matrix for adaptive structured weights.
result Significant compression and performance improvements for various model sizes.
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
problem Difficult inference for multivariate Gaussian Processes with multiple lengthscale parameters.
method Introduces a self-assembled Wishart prior and uses MCMC for Bayesian inference on kernel hyperparameters.
result Demonstrates the effectiveness of the new prior in GP-based learning with empirical results.
In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense noises, we consider a more powerful adversary who can first observe the data matr…
Paper proposes a transfer learning method for improving matrix completion.
problem Improving estimation of a low-rank target matrix using auxiliary data.
method Transfer learning procedure leveraging prior information on favorable source datasets.
result Method outperforms traditional methods when source datasets are close to the target matrix.
We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario. Although this matrix provides us critical information regarding similarity betw…
New algorithm improves game learning with randomised optimism.
problem Learning in matrix games with unknown payoffs and bandit feedback.
method Integrates evolutionary algorithms into bandit framework for randomised optimism.
result Achieves sublinear regret, outperforming classical methods.
Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast …
Autoencoders are popular among neural-network-based matrix completion models due to their ability to retrieve potential latent factors from the partially observed matrices. Nevertheless, when training data is scarce their performance is significantly degraded due to overfitting. In this paper, we mit- igate overfitting…
Paper analyzes AIRL in high-dimensional spaces using random matrix theory.
problem AIRL's performance challenges in high-dimensional environments.
method Examined the rank of the matrix derived from transition matrix, applied random matrix theory.
result High-dimensional scenarios reveal transfer limitations not inherent to AIRL framework.
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…
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…
Efficiently learns matching rewards in two-sided markets with matrix completion.
problem Learning high-dimensional matching rewards in matching markets with limited data.
method Utilizes matrix completion with a novel approach to handle matching interference.
result Near-optimal guarantees for reward learning under matching interference.
DeepTMR reorders matrices without prior knowledge of structural patterns.
problem Matrix reordering without prior structural knowledge.
method DeepTMR uses a neural network to automatically extract features and reorder matrices.
result Trained network produces denoised mean matrix for visualization.
Optimal transfer learning for missing not-at-random matrix completion using source data.
problem Matrix completion in a Missing Not-at-Random setting with incomplete and noisy source data.
method Active sampling of rows and columns, feature shift in latent space, minimax lower bounds, computationally efficient estimation framework.
result Achieves minimax lower bound for active sampling setting, avoiding incoherence assumptions.
New method estimates large matrices' spectra from small sub-matrices.
problem Estimating large matrices' spectra when full matrix-vector products are not available.
method Free decompression based on free probability theory.
result Estimates eigenspectrum of impalpable matrices from small sub-matrices.