Paper develops new patterns for unique matrix completions.
problem Developing unique completions for non-random matrix patterns.
method Formulated low-rank matrix completion using Plucker coordinates.
result Provides two families of patterns for any rank.
New matrix completion method for arbitrary sampling patterns using network flows.
problem Matrix completion under arbitrary sampling patterns.
method Network flow approach to matrix completion.
result Minimax optimal estimation for individual entries.
Unified ML imputation framework for missing data.
problem Invalid inference with incomplete data and ML imputations.
method Stratified by missingness patterns, weights and aggregates complete case information.
result Valid statistical inference for general missingness patterns.
This paper proves a deformation circle pattern theorem, which gives a complete description of those circle patterns with interstices in terms of the combinatorial type, the exterior intersections angles and the conformal structures of interstices. As results, the surface version of Rivin's theorem and the approximation…
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ens…
Study circle patterns on tori, linking symplectic forms and homeomorphisms.
problem Understanding circle patterns on tori and their symplectic properties.
method Investigates the space of circle patterns on closed tori with complex projective structures, embedding it into Teichmüller spaces and analyzing symplectic forms.
result Non-degeneracy of the pulled-back Weil-Petersson symplectic form and homeomorphism between circle patterns and Teichmüller spaces.
GraphDETR detects subgraphs in large graphs using deep learning.
problem Detecting subgraphs in large graphs efficiently and accurately.
method Formulates subgraph detection as a set prediction problem using GraphDETR, a deep learning framework.
result GraphDETR can detect diverse patterns in large graphs, achieving strong performance on molecular functional group detection.
New guarantees for matrix completion from any deterministic sampling patterns.
problem Proving guarantees for low-rank matrix completion from non-random sampling schemes.
method Introduced a graph with observed entries as edges to analyze the performance of constrained nuclear norm minimization algorithm.
result The algorithm can successfully complete the matrix if the observation graph is well-connected and has similar node degrees.
Paper tackles NP-complete subgraph isomorphism counting problem.
problem Counting subgraph isomorphisms in large graphs.
method Learning framework that augments representation learning architectures and iteratively attends pattern and target graphs.
result Scalable learning approach counts subgraph isomorphisms in linear time.
We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sa…
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.
Study identifies clusters of EU countries with similar young mortality patterns.
problem Identify clusters of EU countries with similar mortality patterns in young population.
method Symbolic data analysis (SDA) with age, gender, and main causes of death dimensions.
result Identified clusters of EU countries with similar mortality patterns in young population.
JULIA combines multi-linear and nonlinear models for tensor completion.
problem Complex patterns in real-world tensors require a unified model.
method JULIA unifies multi-linear and nonlinear models with flexible component assignment and efficient alternating optimization.
result JULIA outperforms existing methods in large-scale tensor completion.
New method for tensor completion from specific mode observations.
problem Recovering multiway data tensors from partial observations.
method Tensor train decomposition for fiber-wise observations.
result Deterministic recovery guarantees for specific observation patterns.
Proposes CVKT to complete missing kernel matrices across multiple views.
problem Missing data in multiple views of kernel matrices.
method Cross-View Kernel Transfer (CVKT) with kernel alignment.
result Predicts missing values in kernel matrices using other views' data.
We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). …
We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: under what condition there will be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable. We answer the question fro…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries an…
Information mapping is a popular application of Multivoxel Pattern Analysis (MVPA) to fMRI. Information maps are constructed using the so called searchlight method, where the spherical multivoxel neighborhood of every voxel (i.e., a searchlight) in the brain is evaluated for the presence of task-relevant response patte…
Paper detects common subtrees with identical labels in trees.
problem Finding common subtrees with identical label distribution in tree data.
method Developed an algorithm for tree isomorphism and a new compression scheme for trees.
result The method efficiently finds and compresses common subtrees with identical labels.
CACTI improves tabular data imputation by leveraging missingness patterns and contextual information.
problem Tabular data imputation with improved accuracy and robustness.
method Masked autoencoding approach with median truncated copy masking and contextual information.
result Average R2 gain of 7.8% over the next best method across various datasets and missingness conditions. Extends circle pattern theorem to quasi-simplicial triangulations.
problem Characterize circle patterns on quasi-simplicial triangulated surfaces.
method Use finite covering technique to reduce problem to simplicial case, prove characterization by KAT inequalities.
result Curvature image is characterized by KAT inequalities.
The paper improves tensor completion bounds using spectral gap.
problem Theoretical limitations in tensor completion, especially for deterministic sampling.
method Bounding the generalization error of tensor completion methods using spectral gap.
result Improved bounds on tensor completion error, reducing rank dependence.
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric models are usually built from completely random measures, a Poisson-process based c…
Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete d×N matrix is finitely rank-r completable if there are at …
Paper proposes a new model for imputing missing spatiotemporal traffic data.
problem Missing data and sparsity in spatiotemporal traffic data.
method Low-rank tensor completion (LRTC) framework with truncated nuclear norm (TNN).
result The proposed model outperforms state-of-the-art imputation models in various scenarios.
Moon phases added to stock market analysis for better pattern recognition.
problem Finding meaningful patterns in stock market data using irregular time sampling.
method Incorporating Moon phases into the Gregorian calendar time sampling methods for stock market analysis.
result Moon phases provide unique, irregular sampling features for stock market pattern recognition.
Study compares LRMC algorithms under dependent sampling in various applications.
problem Recovering missing entries in partially observed low-rank matrices with dependent sampling.
method Various LRMC algorithms tested under dependent sampling in different contexts.
result Performance differences among LRMC algorithms under dependent sampling.
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…
Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to an unknown union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and computer vision. Even though the behavior of SSC for complete data is by now well-un…
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing physical connectivity of networked systems only from the event time series their i…
Imputation-Powered Inference improves subpopulation efficiency in missing data settings.
problem Complex missing data patterns challenge standard inference methods.
method Imputation-Powered Inference (IPI) combines blackbox imputation with bias correction.
result IPI provides valid and efficient M-estimation under MCAR blockwise missingness.
New method for matrix completion using Kronecker product approximation.
problem Matrix completion with low Kronecker rank structure.
method Alternative matrix representation using Kronecker product, identification through mean squared error and modified cross-validation.
result Consistency of the method under suitable signal-to-noise ratio conditions.
PPPD framework extracts physical characterizations from stochastic mechanical systems.
problem Complex system behavior requires more than probabilistic descriptions of QoI.
method Probabilistic Performance-Pattern Decomposition (PPPD) framework.
result Decomposes system behaviors into meaningful patterns in response space.
Paper proposes a new tensor imputation method for spatiotemporal traffic data with missing patterns.
problem Imputation of corrupted or incomplete traffic data.
method Truncated tensor Schatten p-norm (TSpN) for spatiotemporal traffic data imputation.
result The proposed method outperforms other state-of-the-art tensor-based imputation models in various missing cases.
A formula for bordered Floer homology of concordances and satellites
problem Computing knot Floer homology for concordances and satellites
method Combinatorial method for bordered Floer homology
result Computation of knot Floer homology cobordism map
Geodesic patterns, shears, and Anosov representations of the modular group.
problem Understanding representations of the modular group into Isom(X).
method Analyzing geodesic patterns, shears, and foliations.
result The Barbot component is homeomorphic to R^2 x [0,∞), with interior and boundary properties.
Model predicts individual insurance claim reserves using activation patterns.
problem Accurately predicting individual claim reserves in insurance contracts.
method Multinomial logistic regression to model claim activation and development.
result The model generates accurate predictions of total and per coverage reserves.
In this paper, we propose and develop the novel idea of treating musical sheets as literary documents in the traditional text analytics parlance, to fully benefit from the vast amount of research already existing in statistical text mining and topic modelling. We specifically introduce the idea of representing any give…
Paper uses tensor completion to estimate HVAC fan power baselines.
problem Estimating HVAC fan power without demand response.
method Tensor completion for multi-dimensional data analysis.
result Tensor completion outperforms existing baselining methods.
Optimizes atomic descriptors to reduce redundancy and improve machine learning models.
problem Redundant descriptors in atomistic machine learning models increase computational burden and limit model expressivity.
method Employing techniques from pattern recognition, we refine and augment existing atomistic representations to produce optimal sets of descriptors.
result New architectures recognize up to 5-body patterns with low computational cost and high accuracy.
This study examines how removing edges from complete graphs affects Ollivier Ricci curvature.
problem Conditions under which Ollivier Ricci curvature changes sign after edge removal.
method Defined and analyzed graphs obtained by removing matching, vertex incident, and cycle edges from complete graphs.
result Ollivier Ricci curvature remains positive or zero for graphs formed by removing edges from complete graphs.
Define the complete n-complex on N vertices to be the n-skeleton of an (N-1)-simplex. We show that embeddings of sufficiently large complete n-complexes in R^{2n+1} necessarily exhibit complicated linking behaviour, thereby extending known results on embeddings of large complete graphs in R^3 (the case n=1) to higher d…
Geo2DR learns graph representations using substructure patterns.
problem Learning distributed representations of graphs efficiently.
method Unsupervised learning with discrete substructure patterns and neural language models.
result Geo2DR achieves high reproducibility and interoperability in graph classification.
Classifies fibered ribbon pretzels, except for a few cases.
problem Classifying fibered ribbon pretzel knots up to mutation.
method Combining lattice embedding techniques with Gabai's classification of fibered pretzel knots, and exhibiting ribbon disks.
result Complete classification except for a few cases.
This paper discusses how usage patterns and preferences of inhabitants can be learned efficiently to allow smart homes to autonomously achieve energy savings. We propose a frequent sequential pattern mining algorithm suitable for real-life smart home event data. The performance of the proposed algorithm is compared to …
Modified RV-coefficient reveals how training affects neural network representations.
problem Understanding how training affects intermediate representations in convolutional neural networks.
method Experimented with modified RV-coefficient (RV2) to compare activation patterns in deep networks trained on varying amounts of data and layers.
result RV2 successfully recovered expected similarity patterns and provided interpretable similarity matrices.
Unified Python package N2 benchmarks NN-based matrix completion methods.
problem Matrix completion with robust NN methods across diverse applications.
method Unified Python package N2 consolidates NN-based methods. result NN-based techniques outperform classical methods in real-world settings.