New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
Sparse APCA identifies sparse factors in financial returns over time.
problem Analyzing co-movements of high-dimensional panel data over time.
method Sparse asymptotic PCA with truncated power method for sparse factors and sequential deflation for multi-factor cases.
result Identification of nine risk factors influencing the S&P 500 stock market.
Proposes FARM model combining latent factor and sparse regression.
problem Testing adequacy of latent factor and sparse regression models.
method Factor Augmented sparse linear Regression Model (FARM) with FabTest and ANOVA type tests.
result Model robustness and effectiveness validated through experiments.
Deep weight factorization improves neural network training through smooth optimization of sparse penalties.
problem Challenges in applying sparse regularization in neural networks due to non-differentiability of penalties.
method Introduces deep weight factorization, decomposing weights into multiple factors for smooth optimization of L1-penalized networks. result Deep weight factorization outperforms shallow factorization and pruning methods consistently across various architectures and datasets.
Sparse VAE learns latent factors from high-dimensional data.
problem Unsupervised representation learning on high-dimensional data.
method Sparse VAE model that learns latent factors summarizing data associations.
result Sparse VAE can recover true model parameters with infinite data.
Bayesian model infers factor dimensionality and sparse loading matrix adaptively.
problem Inference of high-dimensional sparse factor model with varying sparsity and factor dimensions.
method Adaptive Bayesian sparse factor model with posterior concentration.
result Posterior distribution asymptotically concentrates on true factor dimensionality and sparsity.
Sparse GFA identifies disease factors in FTD subgroups.
problem Heterogeneity in neurological disorders hinders understanding and treatment.
method Sparse Group Factor Analysis (GFA) with regularised horseshoe priors.
result Identified latent disease factors differentially expressed in FTD subgroups.
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and valu…
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a relaxation of the number of nonzero columns in a factorization of the matrix. These nonco…
A new NMF variant tackles underdetermined problems with sparse and separable assumptions.
problem Underdetermined blind source separation, especially multispectral image unmixing.
method Sparse Separable Nonnegative Matrix Factorization (SSNMF) combining separability and sparsity assumptions. Algorithm based on SNPA and sparse nonnegative least squares.
result In noiseless settings, the algorithm recovers true underlying sources.
EFS uses LLMs to optimize sparse portfolios by evolving alpha factors.
problem Sparse portfolio optimization in dynamic market regimes.
method Evolutionary feedback loop with LLM-generated alpha factors.
result Significantly outperforms baselines in diverse datasets.
Study confirms sparse coding in whole brain using MRI data.
problem Sparse coding in the whole brain's neural activities.
method Applied various matrix factorization methods to fMRI data.
result Sparse coding hypothesis in information representation in the whole human brain is confirmed.
New method for disentangling latent factors with sparse dependencies.
problem Disentangling latent factors from observed variables and past factors.
method Mechanism sparsity regularization and sparse causal graphical model.
result Identifiability of latent factors up to a sparse causal graph.
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
The paper tackles tensor factorization and completion from noisy data.
problem Sparse nonnegative tensor factorization and completion from partial and noisy observations.
method Minimizes the sum of maximum likelihood estimation and tensor ℓ0 norm with nonnegativity constraints. result Error bounds and minimax lower bounds are established for the proposed model.
NoTMF forecasts sparse urban road movement speeds with nonstationary temporal matrix factorization.
problem Sparse and nonstationary movement speed data from urban roads.
method Nonstationary Temporal Matrix Factorization (NoTMF) model.
result NoTMF outperforms baseline models in forecasting urban road movement speeds.
New principle for disentangling latent factors using sparse regularization.
problem Disentangling latent factors from complex data.
method Sparse regularization of latent mechanisms to induce disentanglement.
result Recovery of latent variables up to permutation under certain conditions.
Proposes a method for tensor completion with sparse factors and missing data.
problem Recovering nonnegative data from noisy observations with missing values.
method Sparse nonnegative Tucker decomposition with ℓ0 norm for sparsity, maximum likelihood estimation, and error bounds. result The method outperforms existing tensor-based or matrix-based methods in nonnegative tensor data completion.
Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple factors, subspace clustering and low-rank sparse bilinear regression as potential ap…
Proposes a nonparametric tensor factorization for sparse data.
problem Handling sparse tensor data with structural and interpretability benefits.
method Hierarchical Gamma processes and Poisson random measures for tensor-valued process, Dirichlet processes for sampling entry indices, Gaussian processes for values.
result Demonstrates superior performance on benchmark datasets.
Divide-and-conquer method speeds sparse factorization for large matrices.
problem Sparse factorization of large matrices for statistical learning.
method Statistical problem formulation, divide-and-conquer approach, stagewise learning.
result Efficient algorithm with lower complexity than existing 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.
New method for factor analysis using nuclear and ℓ0 norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, ℓ0 norm, and KL divergence. Used alternating minimization algorithm. result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
New method for sparse data using L1-NMF with improved sparsity control.
problem Sparse data with false zeros and heavy-tailed noise.
method Component-wise L1-NMF with weighted penalization and coordinate descent.
result Effective in handling sparse data with false zeros.
Whereas CNNs have demonstrated immense progress in many vision problems, they suffer from a dependence on monumental amounts of labeled training data. On the other hand, dictionary learning does not scale to the size of problems that CNNs can handle, despite being very effective at low-level vision tasks such as denois…
Paper proposes a new method for sparse covariance Cholesky factor estimation.
problem Estimating sparse covariance matrices for ordered data.
method Matrix loss penalization approach for sparse Cholesky factor estimation.
result The proposed method outperforms existing regression-based approaches in simulations and real data.
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization problem that consists of learning the basis set, adapting it to specific data. V…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsit…
Method learns shared and specific factors in multi-study gene expression data.
problem Understanding shared and specific factors in high-dimensional multi-study data.
method Nonlinear multi-study factor model with sparse variational autoencoder.
result Method recovers meaningful shared and specific factors in platelet gene expression data.
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
While matrix factorisation models are ubiquitous in large scale recommendation and search, real time application of such models requires inner product computations over an intractably large set of item factors. In this manuscript we present a novel framework that uses the inverted index representation to exploit struct…
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
Paper develops a new estimator for high-dimensional panel data with common shocks.
problem Cross-sectionally dependent errors driven by common shocks in high-dimensional panel data.
method Factor-augmented sparse-group LASSO estimator combining MIDAS aggregation with latent factors.
result The estimator outperforms standard LASSO for prediction and estimation in settings with cross-sectional dependence.
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
problem Efficiently solving nonlinear PDEs with Gaussian processes and kernel methods.
method Sparse Cholesky factorization for near-linear complexity.
result Near-linear complexity algorithm for working with kernel matrices of nonlinear PDEs.
New Bayesian method for sparse multidimensional item response theory.
problem Sparse interpretable explanations for questionnaire data.
method Bayesian EM algorithm for sparse factor loadings.
result Reliable recovery of factor dimensionality and latent structure.
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being highly ill-posed, that is, there typically exist many different but equivalent facto…
This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a shortcut for very fast computations over zero-valued inputs, and oftentimes result…
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.
Sparse NMF with archetypal regularization aims to robustly represent data points.
problem Representing data points as sparse linear combinations of archetypes.
method Sparse NMF with archetypal regularization, introducing strong and weak robustness.
result Theoretical robustness guarantees hold under minimal assumptions.
A new matrix factorization method for high-dimensional data.
problem Exploiting sparse structures in complex data for better interpretability.
method Bayesian shrinkage priors and flexible sparse patterns modeled through row and column dependencies.
result Demonstrated practical advantages through simulation and soccer heatmap analysis.
New sparse penalty improves biclustering for gene expression data.
problem Identifying significant clusters in gene expression data.
method Prenet penalty applied to SSVD for biclustering.
result Mixed Prenet penalty effectively clusters non-overlapped data.
We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor…
SOFARI improves inference on multi-task learning latent factors.
problem Challenges in precise inference on multi-task learning latent factor matrices.
method High-dimensional manifold-based Neyman near-orthogonality inference on Stiefel manifold structure.
result Easy-to-use bias-corrected estimators for latent factor vectors and singular values with asymptotic normal distributions.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
A new method STMF improves missing value prediction using tropical semiring.
problem Limited capability of linear models to model complex relations.
method Sparse Tropical Matrix Factorization (STMF) using tropical semiring.
result STMF outperforms NMF on real data, especially in handling extreme values.
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for networks, the sparse exchangeable graphs, have been introduced to resolve some imp…