New method predicts binary matrix entries using empirical Bayes and low-rank structure.
problem Predicting unobserved entries in binary matrices.
method Empirical Bayes method motivated by Efron--Morris estimator, exploiting low-rank structure.
result Superior performance in predictive accuracy, calibration, and efficiency compared to existing methods.
A novel BMC model with nonconvex regularizers and accelerated proximal algorithm for binary matrix completion.
problem Recovering a binary matrix from partial observed positive elements.
method Proposes a novel BMC model with nonconvex regularizers and accelerates proximal algorithm for solving the nonconvex optimization problem.
result The proposed model and algorithm outperform other methods in both synthetic and real-world data sets.
Develops a method to complete binary matrices using all types of observed entries.
problem Completing binary matrices from partial observations.
method Combines risks from Davenport et al. (2014) and Hsieh et al. (2015) to use all types of entries.
result Improves matrix completion performance by using all types of entries.
OptComplete efficiently completes matrices with side information, providing insights.
problem Matrix completion with interpretability for side information.
method Binary convex optimization reformulation and stochastic cutting planes.
result OptComplete outperforms state-of-the-art methods in scalability and accuracy.
Paper proposes an efficient algorithm for nonnegative binary matrix factorization.
problem Decomposing binary data using matrix factorization.
method Majorization-minimization algorithm with Beta prior for improved performance.
result Proposed algorithm offers excellent trade-off between performance, complexity, and interpretability.
In this paper, we consider the matrix completion problem when the observations are one-bit measurements of some underlying matrix M, and in particular the observed samples consist only of ones and no zeros. This problem is motivated by modern applications such as recommender systems and social networks where only "like…
Study improves fractional posterior for 1-bit matrix completion.
problem Estimating a binary matrix from observed entries.
method Fractional posterior approach with low-rank factorization and spectral scaled Student priors.
result Concentration results for fractional posterior, demonstrating effectiveness in matrix recovery.
A new method for 1-bit matrix completion that is faster and more accurate.
problem Estimating a low-rank matrix from binary observations.
method Majorization-Minimization Gauss-Newton (MMGN) method.
result MMGN outperforms existing methods in accuracy and speed.
Characterizes uncertainty in low-rank matrix completion with noisy data.
problem Uncertainty quantification in low-rank matrix completion with heterogeneous sub-exponential noise.
method Characterizes the distribution of estimated matrix entries under low-rank estimators with heterogeneous sub-exponential noise.
result Explicit formulas for the distribution of estimated matrix entries under Poisson and Binary noise.
New method predicts activity coefficients for binary mixtures without using physical descriptors.
problem Predicting activity coefficients for unexplored binary mixtures.
method Probabilistic matrix factorization model.
result Method outperforms state-of-the-art models requiring less training effort.
Online algorithm for binary matrix completion with side information.
problem Matrix completion with side information for binary matrices.
method Online algorithm with mistake and regret bounds.
result Novel mistake and regret bounds of the form ildeO(D/γ2). The paper proposes methods for predicting missing values in mixed data matrices.
problem Matrix completion for mixed data types (continuous, binary, ordinal).
method Generalized latent factor models for low-rank matrix estimation with entrywise consistency.
result Tight probabilistic error bounds for the proposed estimators.
Paper solves NP-hard haplotyping problem using matrix completion.
problem Reconstructing inherited genetic variations from DNA sequencing data.
method Binary matrix factorization and alternating minimization.
result The proposed technique achieves lower haplotype reconstruction error.
This work tackles collective matrix completion with multiple and heterogeneous data sources.
problem Reconstructing data from multiple heterogeneous matrices.
method Estimation based on minimizing goodness-of-fit and nuclear norm penalization of the whole collective matrix.
result Proposed estimators achieve fast rates of convergence under two settings.
New method estimates missingness probabilities for MNAR matrix completion.
problem Bias in matrix completion due to missing not at random data.
method Estimate missingness probabilities using nuclear norm structure.
result Improved matrix completion accuracy without auxiliary information.
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic genera…
This paper introduces new methods to improve 1-bit matrix completion by considering cluster effects.
problem Improving 1-bit matrix completion for clustered data.
method Group-Specific 1-bit Matrix Completion (GS1MC) and Cluster Developing Matrix Completion (CDMC).
result GS1MC and CDMC outperform existing methods in synthetic and real-world data.
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and the measurements consist of a subset, either of the exact individ…
Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-c…
Improves matrix completion by exploiting biased observation patterns.
problem Matrix completion with biased observation patterns.
method Mask Nearest Neighbor (MNN) algorithm: two-stage process.
result MNN achieves competitive performance with 28x smaller mean squared error.
A new method fills missing labels in multi-label classification problems.
problem Missing feature and label values in multi-label classification.
method Proposes co-completion (COCO) algorithm based on subgradient descent.
result Demonstrates theoretical and practical effectiveness of COCO.
GMBL uses graph embedding to learn binary codes from multiple views for clustering.
problem Lack of complete structure and complementary information from multiple views in single-view hash clustering methods.
method Graph-based Multi-view Binary Learning (GMBL) using Laplacian matrix to preserve data structure and assign weights to views.
result GMBL outperforms previous methods in clustering performance on multiple datasets.
Two binary matrix factorization methods using dictionary learning are proposed.
problem Efficiently factorizing binary matrices for various applications.
method Binary adaptation of dictionary learning for binary matrices, focusing on speed and scalability.
result Effective factorizations of various data types produced.
We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix M∗. Instead of observing a subset of the noisy continuous-valued entries of a matrix M∗, we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…
Paper develops a new weighted low-rank matrix approximation technique.
problem Matrix completion with missing data.
method Element-wise weighted generalization of low-rank matrix approximation.
result Proposes an algorithm and acceleration techniques for solving the weighted problem.
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix map…
Develops a fast BMF approach for binary matrices.
problem Finding patterns in binary matrices for various applications.
method MEBF (Median Expansion for Boolean Factorization) using geometric segmentation and heuristic submatrix identification.
result Superior performance in reconstruction error and computational efficiency compared to existing methods.
Paper proposes algorithms for BMF using integer programming.
problem Approximating binary input matrix as product of two smaller binary factors.
method Alternating optimization strategy using integer programming to solve subproblems and combine solutions.
result Proposed algorithms outperform state of the art on medium-scale problems.
Federated learning approach for binary matrix factorization.
problem Efficiently factorizing binary data distributed across stakeholders while maintaining privacy.
method Proximal optimization for federated learning of relaxed binary matrix factorization.
result Federated algorithm outperforms state-of-the-art methods in quality and efficacy.
Reverse annealing boosts quantum matrix factorization performance.
problem Improving quantum matrix factorization performance.
method Combining forward and reverse annealing for nonnegative/binary matrix factorization.
result Combination of forward and reverse annealing significantly improves performance.
BIND removes background noise from binary matrices, improving detection accuracy and fairness.
problem Real data often violates the i.i.d assumption for binary matrix entries, leading to inaccurate detection.
method BIND optimizes detection by estimating row- and column-wise mixture distributions and eliminating background noise.
result BIND effectively removes background noise and increases detection accuracy and fairness.
New pruning technique reduces index size for DNNs.
problem Irregular index form in fine-grained pruning limits parallelism and memory usage.
method Proposes a low-rank binary index matrix for efficient compression and decompression.
result Fine-grained pruning with binary matrices achieves lower memory footprint and higher parallelism.
Unified Bayesian NMF models for binary data with automatic dimension selection.
problem Binary data analysis with nonnegative matrix factorization and link functions.
method Bayesian mean-parameterized nonnegative binary matrix factorization (NBMF) models with collapsed Gibbs and variational algorithms.
result Automatic detection of relevant components without manual tuning.
Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and internet-of-things. To reduce the communication, sensing and storage complexity, t…
Paper learns causal structures from data using gradient-based optimization.
problem Learning causal structures from observational data.
method Reformulates SEM with binary adjacency matrix and uses gradient-based optimization.
result Gradient-based method efficiently identifies causal structures from data.
The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA),…
New insights into identifying mixtures of product distributions using Hadamard extensions.
problem Identifying mixtures of product distributions on binary variables.
method Analysis of Hadamard extensions of matrix products.
result Conditions for full column rank of Hadamard extensions.
A Bayesian Boolean Matrix Factorization for cancer genomics
problem Identifying coordinated feature changes in cancer
method Bayesian Boolean Matrix Factorization
result Captures widespread, near-simultaneous chromosome-number changes
Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization heuristics such as alternating minimization. In this paper, we provide provable recover…
The study shows inner-product kernels behave similarly to binary kernels in high dimensions.
problem Understanding the behavior of inner-product kernels in high-dimensional data.
method Investigation of eigenspectrum under binary mixture model using random matrix theory.
result The eigenspectrum of inner-product kernels is asymptotically equivalent to binary kernels.
The paper develops algorithms for Boolean matrix factorization using IP and heuristics.
problem Approximating binary input matrices as products of smaller binary factors.
method Alternating optimization with integer programming and greedy/local-search heuristics.
result Proposed methods improve scalability and performance compared to existing techniques.
Improves causal graph learning on dependent binary data.
problem Challenges in learning causal graphical models from dependent binary data.
method Decorrelation-based approach using latent utility model and EM-like algorithm.
result Significant improvement in accuracy of causal graph learning.
BELIEF framework interprets GLMs using binary linear models.
problem Understanding and interpreting generalized linear models (GLMs) with binary outcomes.
method Developed a framework called binary expansion linear effect (BELIEF) to interpret GLMs through transparent linear models.
result BELIEF framework reveals perfect predictors in complete separation scenarios.
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin to the singular value decomposition, that maximizes the Bernoulli log-likelihoo…
Unified approach optimizes neural network training for various metrics.
problem Training and evaluation of neural network binary classifiers often use different metrics.
method Combines differentiable approximation and probabilistic soft sets.
result Effective in optimizing for metrics like F1-Score across various domains.
The study develops a supervised and unsupervised WTA model for sparse binary projections.
problem Sparse binary projections in high-dimensional spaces.
method Supervised and unsupervised WTA models with efficient algorithms.
result Significantly improved results in similarity search tasks.
Unified framework for nonconvex matrix completion with linearly parameterized factors.
problem Matrix completion with improved accuracy using linearly parameterized factors.
method Unified nonconvex optimization framework with Correlated Parametric Factorization condition.
result Uniform upper bounds for low-rank estimation at any local minimum.
The paper extends ternary algebra concepts using cube roots of unity.
problem Extending algebraic structures from binary to ternary multiplication.
method Introducing ternary associator, commutator, and Lie algebra at cube roots of unity.
result Derived an identity for ternary commutator based on GA(1,5).