Column normalization doesn't ensure good sparse recovery for random matrices.
problem Ensuring good sparse recovery properties for column-normalized random matrices.
method Constructing a random vector and showing that column normalization doesn't lead to desired recovery properties.
result Column-normalized random matrices do not satisfy exact reconstruction property with high probability.
MuonEq improves training of matrix-valued parameters by rebalancing momentum before orthogonalization.
problem Training matrix-valued parameters with orthogonalized-update optimizers like Muon.
method MuonEq introduces three lightweight pre-orthogonalization equilibration schemes: two-sided row/column normalization (RC), row normalization (R), and column normalization (C).
result Row/column normalization acts as a zeroth-order surrogate for whitening and improves the geometry seen by orthogonalization.
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…
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.
NMF with specific constraints is equivalent to LDA.
problem Dimensionality reduction of non-negative data.
method NMF with ℓ1 normalization constraints and Dirichlet prior. result NMF with these constraints is equivalent to LDA.
We introduce a new measure of dimension for binary datasets.
problem Defining the effective dimensionality of sparse binary datasets.
method Adapted fractal dimension concept for binary data and introduced normalized fractal dimension.
result Normalized fractal dimension measures the degree of dependency structure of binary datasets.
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…
DCoM uses deep neural networks to detect semantic data types from raw column values.
problem Detecting semantic data types from dirty and unseen data.
method DCoM employs multi-input NLP-based deep neural networks trained on 686,765 data columns.
result DCoM outperforms existing methods significantly on 78 different semantic data types.
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.
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns. Bittorf, Recht, Ré and Tropp (`Factoring nonnegative matrices with linear programs', …
New design method improves Lasso performance in sparse regression.
problem Sparse linear regression with correlated design columns.
method Introduces partially-rotated designs to improve Lasso's RE constant.
result Lasso achieves better prediction error with high probability.
New method recovers matrix column space with active sampling for better results.
problem Recovering column space of partially observed matrices with limited data.
method Alternating minimization with active sampling strategy.
result Active sampling improves convergence to true column space with higher probability.
The paper proposes an interpretable off-policy learning algorithm for medical treatments.
problem Lack of interpretable methods for personalized treatment decisions from observational data.
method Hyperbox search approach for interpretable policies in disjunctive normal form.
result The proposed algorithm outperforms state-of-the-art methods in terms of regret and is rated highly interpretable by clinical experts.
We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to numerous real-world data applications such as population genetics summarization,…
This paper studies quandles with one non-trivial column and their properties.
problem Understanding quandles with exactly one non-trivially permuted column.
method Investigates automorphism groups, polynomials, cohomology, and hom quandles of quandles with one non-trivial column.
result The properties of these quandles relate to linking number.
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
The paper completes matrices from non-uniformly sampled entries, especially when columns are randomly selected and fully observed.
problem Matrix completion from non-uniformly sampled entries, including fully and partially observed columns.
method First, recover the column space from fully observed columns. Then, for each partially observed column, find a vector in the recovered column space with the observed entries. For low-rank matrices, recover them from Ω(rnlnn) entries. result The algorithm can exactly recover a low-rank matrix from merely Ω(rnlnn) entries. Proposes a Bayesian approach for integrating multiple linked matrices.
problem Integrating multiple linked matrices for diverse applications.
method Empirical Bayes Linked Matrix Decomposition (EB-LMD).
result Efficient estimation algorithm with no tuning parameters.
The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples whic…
SQUEAK reduces space complexity for Nystrom approximations in KRR.
problem Large datasets in KRR require impractical storage space.
method SQUEAK uses unnormalized ridge leverage scores for incremental updates.
result Space complexity improved with constant factor worse than exact RLS.
Double autoencoder Ae2I 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 Ae2I outperforms state-of-the-art models in recommender systems. Neuromorphic column performs online unsupervised clustering.
problem Real-time clustering of streaming data.
method Localized, spike timing-dependent plasticity (STDP) neural column.
result Prototype column performs similarly to k-means clustering.
A new test validates ensemble models against the null hypothesis.
problem Validating ensemble models against the null hypothesis of a constant response.
method Randomized permutation test on SVEM model predictions.
result The test maintains Type I error rate even with more parameters than observations.
Paper tackles low-rank matrix recovery with column ℓ2,0-norm regularization.
problem Low-rank matrix recovery problems with column sparsity constraints.
method Developed alternating majorization-minimization (AMM) methods with extrapolation and hybrid AMM.
result Global convergence analysis and superior performance in matrix completion problems.
A new method for learning row and column structures with missing data.
problem Learning row and column structures in data with missing values.
method A three-component unsupervised approach: estimating a complete matrix, computing pairwise distances, and constructing representations.
result Our method outperforms other methods in data visualization and clustering.
RECol generates error columns to improve outlier detection.
problem Outlier detection in data with complex relationships.
method Generates reconstruction error columns for leave-one-out feature sets.
result Improves ROC-AUC and PR-AUC values of common outlier detection methods.
New method for matrix completion with row and column similarities.
problem Matrix completion with row and column similarities.
method Iterative model selection with Hutchinson estimator.
result Effective model selection for optimal smoothing parameters.
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one…
The paper identifies redundant columns in matrices for feature selection and clustering.
problem Identifying redundant columns in matrices for feature selection and clustering.
method Proves that after re-ordering columns, a matrix can be block-diagonalized revealing linearly dependent columns.
result Identifies redundant columns in matrices, aiding in feature selection and clustering.
Paper proposes using CNN for stock trading with data normalization.
problem Improving stock trading accuracy in volatile markets.
method Developed CNN-based trading framework with novel data normalization.
result CNN-based framework outperforms other methods on 29 stocks.
TGAN models tabular data using GAN for realistic synthetic data.
problem Modeling tabular data with mixed discrete and continuous columns.
method Conditional GAN for modeling tabular data.
result TGAN outperforms Bayesian methods on most real datasets.
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.
Sherlock uses deep learning to accurately detect data types from column headers.
problem Detecting accurate semantic types of data columns for data science tasks.
method Sherlock is a multi-input deep neural network trained on a corpus of 686,765 data columns.
result Sherlock achieves a support-weighted F1 score of 0.89, outperforming existing methods.
This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return arbitrarily poor results, if even a single column is corrupted. One direct appl…
Efficient algorithm for cell detection and segmentation in crowded images.
problem Instance segmentation in biological images with overlapping cells.
method Column generation approach with exact optimization and odd set inequalities.
result Rapid and accurate instance segmentation on multiple datasets.
We consider a column of a rotating stationary surface in Euclidean space. We obtain a value l0>0 in such way that if the length l of column satisfies l>l0, then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature…
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…
New algorithm approximates large matrices by sampling column blocks, reducing overhead.
problem Approximating large matrices using limited row or column sampling.
method Sampling predefined blocks of columns, providing guarantees for approximation quality.
result Effective algorithm for distributed matrix approximation, demonstrated with real-world biometric data.
The Sinkhorn-Knopp algorithm converges quickly but the number of iterations is poorly understood.
problem Understanding the number of iterations required for the Sinkhorn-Knopp algorithm to converge.
method Analyzing the Sinkhorn-Knopp algorithm for matrices with a specific density threshold.
result The Sinkhorn-Knopp algorithm requires Ω(n1/2/ε) iterations for matrices with density γ<1/2. This paper defines a generalized column subset selection problem which is concerned with the selection of a few columns from a source matrix A that best approximate the span of a target matrix B. The paper then proposes a fast greedy algorithm for solving this problem and draws connections to different problems that ca…
The paper uses Column Generation for faster construction of binary decision trees.
problem Constructing efficient univariate binary decision trees for classification tasks.
method Proposes an Integer Linear Programming (ILP) formulation and solves it via Column Generation based heuristic.
result The approach is competitive with state-of-the-art ILP-based algorithms and can handle large datasets.
It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use column generation, a classical optimization technique, to address these limitations…
The paper tackles one-for-many counterfactual explanations using column generation.
problem Minimizing the number of explanations needed for a group of instances with sparsity constraints.
method Developed a novel column generation framework to efficiently search for explanations for any black-box classifier.
result The column generation framework outperforms existing methods in scalability, computational performance, and solution quality.
This paper improves neural network efficiency by combining filter columns and retraining, boosting array utilization and accuracy.
problem Efficient implementation of sparse convolutional neural networks on systolic arrays.
method Column combining of filter matrices, retraining of remaining weights, joint optimization for high utilization and accuracy.
result Significantly increased systolic array utilization efficiency (e.g., ~4x) and maintained high classification accuracy.
PSMM method optimizes matrix sufficient dimension reduction.
problem Feature matrices with row- and column-wise interpretations require efficient dimension reduction.
method PSMM method converts matrix problem into classification problems using rank-1 normal matrix.
result PSMM outperforms existing methods and provides strong interpretability.
New algorithms find important data columns in corrupted big data.
problem Sampling from corrupted big data with low rank structure.
method Robust and scalable column/row sampling algorithms.
result Outperforms state-of-the-art robust sampling algorithms.
New robust PCA algorithm for matrices with both sparse and outlying elements.
problem Simultaneous sparse and outlying corruption in matrices.
method Sparse approximation of a sparsely corrupted column to distinguish inliers from outliers.
result Robust PCA algorithm can handle both sparse and outlying corruptions.
Solves portfolio optimization with cardinality constraints using column generation.
problem Portfolio optimization with cardinality constraints.
method Column generation method applied to a subset of assets in a master convex quadratic problem, using dual information to propose new assets.
result Solves portfolio optimization problems efficiently with cardinality constraints.