Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mea…
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48 results for “row means”
Improved nearest neighbors for missing data in latent factor models.
problem Estimation with missing data in latent factor models.
method Doubly robust nearest neighbors (NN) that considers both row and column neighbors.
result Provides a consistent estimate and near-quadratic improvement in error.
A clustering algorithm uses the left Gram matrix for high dimensional data.
problem Clustering high dimensional data with many features and few objects.
method The algorithm uses the normalized left Gram matrix G = XX'/P to cluster objects based on row means.
result The algorithm provides the most accurate cluster configuration more than twice as often as competitors.
New algorithm for biclustering with improved performance.
problem Simultaneous clustering of rows and columns with similar patterns.
method Formulated new biclustering problem, developed alternating k-means algorithm.
result Our algorithm finds local minima efficiently and outperforms other methods.
Improved neural network model for predicting latent budgets in compositional data.
problem Predicting response variables in compositional data with non-negativity constraints.
method LBA-NN, a feed forward neural network model that incorporates K-means clustering for interpretation.
result LBA-NN outperforms traditional LBA in prediction accuracy, specificity, recall, and mean square error.
We propose stochastic rank- bandits, a class of online learning problems where at each step a learning agent chooses a pair of row and column arms, and receives the product of their values as a reward. The main challenge of the problem is that the individual values of the row and column are unobserved. We assume tha…
We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples…
An -coreset for Least-Mean-Squares (LMS) of a matrix is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine -dimensional subspace of , up to a factor of . Such coresets are useful…
Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means selecting a subset of nodes and recording all of their edges. This sampling mech…
Paper proposes an adaptive modeling approach for row-type dependent predictive analysis in banking.
problem Accurate prediction of diverse row types within a single dataset.
method Adaptive modeling approach, tailored data pre-processing, feature engineering, traditional and ensemble machine learning models.
result All predictive approaches achieve a precision rate of no less than 90% for different row types.
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.
We prove a central limit theorem for the components of the eigenvectors corresponding to the largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
Double autoencoder improves missing value imputation in recommender systems.
problem Imputing missing values in tables using row-row and column-column relationships.
method Simultaneously uses row-row and column-column relationships through a double autoencoder.
result outperforms state-of-the-art models in recommender systems.
We construct an explicit topological model (similar to the topological Springer fibers appearing in work of Khovanov and Russell) for every two-row Springer fiber associated with the even orthogonal group and prove that the respective topological model is homeomorphic to its corresponding Springer fiber. This confirms …
New method allows generating independent data matrices from summary statistics.
problem Generating independent data matrices from summary statistics like mean and covariance.
method Thinning a Wishart random matrix based on sample mean and covariance.
result It is possible to generate two independent data matrices from summary statistics.
New optimizers control network width scaling, improving stability and transfer across different model sizes.
problem Designing stable optimizers for networks of varying widths.
method Interpreting optimizers as steepest descent under mean-normalized operator norms, enabling layerwise composability and width-independent bounds.
result New optimizers like row normalization and column normalization provide stable learning-rate transfer across different model widths.
In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are…
Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both …
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with pr…
Paper analyzes singular subspace estimation in noisy matrix models.
problem Estimating low-rank signals in noisy matrix data.
method Asymptotic distributional theory, extreme value theory, saddle point approximation, random matrix theory.
result Plug-in test statistic based on two-to-infinity norm has higher power for detecting structured alternatives.
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…
Proposes SROF for row-wise fusion in federated learning for multivariate responses.
problem Heterogeneous client models with shared variable-level structure.
method Sparse Row-wise Fusion (SROF) regularizer and RowFed algorithm.
result Empirically shows consistent error reduction and stronger variable-level cluster recovery.
Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML) frameworks and study the conditions for perfect reconstruction of the original r…
We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an informa…
Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methodsmath.ST
We solve matrix denoising with both row and column correlations, setting limits and designing optimal methods.
problem Matrix denoising with doubly heteroscedastic noise (both row and column correlations).
method Established information-theoretic and algorithmic limits, designed a novel spectral estimator with optimality guarantees.
result The novel spectral estimator achieves positive correlation with the signal and Bayes-optimal error under one-sided heteroscedasticity.
CEDA analyzes large categorical datasets using tree geometry and binary codes.
problem Analyzing large categorical datasets with extreme- samples.
method CEDA uses tree geometry and binary codes to analyze categorical data.
result CEDA discovers patterns and evaluates their reliability in large categorical datasets.
In this paper, we consider the block-sparse signals recovery problem in the context of multiple measurement vectors (MMV) with common row sparsity patterns. We develop a new method for recovery of common row sparsity MMV signals, where a pattern-coupled hierarchical Gaussian prior model is introduced to characterize bo…
The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures and under varying constraints. In this paper we focus on the exclusive row bicl…
Predictive State Representations (PSRs) are powerful techniques for modelling dynamical systems, which represent a state as a vector of predictions about future observable events (tests). In PSRs, one of the fundamental problems is the learning of the PSR model of the underlying system. Recently, spectral methods have …
The paper calculates colored Jones polynomials for specific link configurations.
problem Computing colored Jones polynomials in general is difficult, but the paper provides explicit formulas.
method Uses Kuperberg's skein relation and one-row Young diagrams.
result Derives the tail of -torus links and false theta series.
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many applications, which exhibit both row and column cluster structure, and our goal is …
The paper develops inference methods for high-dimensional multi-task regression with row-sparse coefficients.
problem Inference for high-dimensional multi-task regression with unknown coefficient matrix under row-sparsity.
method Proposes chi-square and normal inference methodologies using MT Lasso with de-biasing scheme and interaction matrix.
result Derives asymptotic normal and chi-square distribution results for valid confidence intervals and ellipsoids.
We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix . This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix rec…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on t…
New algorithm improves matrix estimation with one-sided covariates.
problem Estimating matrix means with unobserved row covariates.
method Proposes an algorithm for nonparametric matrix estimation with observed column covariates.
result Achieves minimax optimal nonparametric rate in moderately proportioned matrices.
This work models the interconnection of company's investment managers' representations and the market attraction of its shares. The models that reflect the connection of the company's market effectiveness indices and parameters of its economic activity are created on the basis of the Mean-Variance Analysis and Regressi…
The paper proposes a new model to analyze directed networks and accurately estimate community memberships.
problem Modeling and estimating community memberships in directed networks with heterogeneous degrees.
method Directed Degree Corrected Mixed Membership (DiDCMM) model and DiMSC algorithm.
result The proposed DiMSC algorithm is asymptotically consistent and provides error bounds for community membership vectors.
Improved co-clustering for robust data analysis.
problem Noise and posterior collapse in co-clustering.
method Fully variational Co-clustering framework with Compositional ELBO.
result Enhanced robustness and accuracy in co-clustering.
Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because they fit well with modern parallel computing architectures. We propose a simple me…
Study one-sided matrix completion with two observations per row.
problem Recover right singular vectors of a low-rank matrix with few observations.
method Impute missing values of and analyze recovery guarantees.
result Provable recovery of with rows, outperforming standard methods.
Conjoined Dirichlet Processstat.ML
Develops a non-parametric Dirichlet process method for probabilistic biclustering.
problem Challenges in finding biclusters with strong co-occurrence in rows and columns.
method Dual Dirichlet process mixture models for row and column clustering, with cluster number determined by data.
result Improves bicluster extraction in text mining and gene expression analysis.
Latent block models are used for probabilistic biclustering, which is shown to be an effective method for analyzing various relational data sets. However, there has been no statistical test method for determining the row and column cluster numbers of latent block models. Recent studies have constructed statistical-test…
Optimized sampling scheme for compressed sensing combining randomness and determinism.
problem Improving compressed sensing performance with deterministic sampling.
method Optimized sampling scheme combining random and deterministic selection of rows.
result Measurable improvements in image compressed sensing for generative and sparse priors.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
problem Efficiently reducing the rank of non-negative matrices.
method Formulated rank reduction as a mean-field approximation using a log-linear model.
result Optimal solution for minimizing KL divergence can be computed in closed form.
New method estimates heterogeneous treatment effects with improved guarantees.
problem Estimating treatment effects in panel data with heterogeneous assignments.
method Matrix completion approach with row-wise error analysis.
result Achieves a row-wise error bound.
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of sid…
A new method preserves useful information in data rows with outlying cells.
problem Preserving useful information in data rows with outlying cells.
method Cellwise robust Minimum Covariance Determinant (cellMCD) method using observed likelihood and a penalty term on cellwise outliers.
result The cellMCD method performs well in simulations and on real data.
New algorithm samples matrix rows proportional to their ℓ_p norm in a turnstile data stream.
problem Sampling rows of a dynamic matrix efficiently in a turnstile data stream.
method Develops a novel algorithm for sampling rows proportional to their ℓ_p norm in a turnstile data stream, returning sampled row indexes and approximated sampling probabilities.
result Achieves approximation for logistic regression in a turnstile data stream with polynomial sketch size.