Paper shows unique decomposition of 3-manifolds and multiplicative property of Reidemeister torsion.
problem Unique decomposition of compact 3-manifolds.
method Study of adjoint Reidemeister torsion on disk sum decompositions.
result Adjoint Reidemeister torsion has a multiplicative property on unique decompositions.
We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…
The study improves theoretical understanding of using multiple synthetic datasets for better model accuracy.
problem Lack of theoretical understanding of using multiple synthetic datasets for supervised learning.
method Derive bias-variance decompositions for multiple synthetic datasets settings.
result A simple rule of thumb to select the appropriate number of synthetic datasets.
New method evaluates multiple social disparities using machine learning.
problem Reduction of educational disparities across multiple dimensions.
method Triply-Robust Machine Learning Approach for Causal Decomposition Analysis.
result Simultaneous interventions across multiple domains reduce disparities.
The paper improves risk bounds for learning multiple components with sparsity-inducing regularization.
problem Learning multiple components with sparsity-inducing regularization.
method Derives efficient error bounds using known decompositions of Rademacher complexity.
result Proposes a method to derive tighter risk bounds without excessive effort.
A new method combines multiple node embeddings using tensor decomposition.
problem Generating accurate node embeddings for complex networks.
method TenSemble2Vec: combines multiple embeddings via tensor decomposition.
result Improves node embeddings by leveraging complementary information from different methods.
Graphical notation simplifies tensor operations and decompositions.
problem Complex tensor operations are difficult to understand and represent.
method Introduces graphical notation to represent tensor operations.
result Simplified representation of tensor operations and decompositions.
Unified theory for curved shell deformations with elastic and inelastic components.
problem Coupled nonlinear elastic and inelastic deformations of curved thin shells.
method Multiplicative decomposition of surface deformation gradient, detailed kinematics analysis, surface balance laws, constitutive relations derived from thermodynamics.
result Unified constitutive relations for growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity of shells.
No arbitrage in financial markets with special semimartingales.
problem Proving the absence of arbitrage in non-numéraire financial markets.
method Proving the absence of arbitrage using a multiplicative special semimartingale deflator.
result The market is free of arbitrage if and only if there exists a multiplicative special semimartingale deflator.
Solution to sparse PCA tuning problem using Empirical Bayes.
problem Sparse PCA multiple tuning problem (MTP).
method Empirical Bayes covariance decomposition for penalized PCA.
result Empirical Bayes approach efficiently solves MTP in sparse PCA.
Proposes BHT-ARIMA for forecasting multiple short time series.
problem Forecasting multiple short time series with mutual correlations.
method Block Hankel tensors, Tucker decomposition, generalized tensor ARIMA.
result Improves forecasting accuracy and reduces computational cost.
Develops a tensor decomposition method with side information.
problem Identifying the relationship between a high-dimensional tensor and side information.
method Supervised tensor decomposition incorporating multiple feature matrices.
result Captures effective dimension reduction of the data tensor in feature space.
BIDIFAC+ factorizes linked matrices for cancer studies.
problem Integrating multiple omics platforms across various cancer types.
method Flexible approach to simultaneous factorization and decomposition of linked matrices using BIDIFAC+.
result Identifies shared and specific modes of variability across multiple omics platforms and cancer types.
Given a handle decomposition of a 4-manifold with boundary, and an open book decomposition of the boundary, we show how to produce a trisection diagram of a trisection of the 4-manifold inducing the given open book. We do this by making the original proof of the existence of relative trisections more explicit, in terms…
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
We give a formula of the connected component decomposition of the Alexander quandle: Z[t±1]/(f1(t),…,fk(t))=⨆i=0a−1Orb(i), where a=gcd(f1(1),…,fk(1)). We show that the connected component Orb(i) is isomorphic to Z[t±1]/J with an expli…
Identifies conditions for multiple invariant probabilities in Markov kernels.
problem Global irreducibility and recurrence do not guarantee uniqueness of invariant probabilities.
method Uses Jordan decomposition of the difference of two invariant probabilities.
result A Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition.
Paper predicts multiple types of miRNA-disease associations using tensor decomposition.
problem Predicting miRNA-disease associations, especially multi-type ones.
method Represented miRNA-disease-type triplets as a tensor and used Tensor Decomposition methods.
result Tensor Decomposition methods improve a recent baseline by up to 38% in top-1 F1.
We consider knots whose diagrams have a high amount of twisting of multiple strands. By encircling twists on multiple strands with unknotted curves, we obtain a link called a generalized augmented link. Dehn filling this link gives the original knot. We classify those generalized augmented links that are Seifert fibere…
New hierarchical tensor decomposition model for complex data.
problem Lack of natural generalization of hierarchical NMF to tensors.
method Proposes a new hierarchical nonnegative tensor decomposition (HNTF) model.
result Model more naturally illuminates topic hierarchy.
A new method for analyzing multi-source, multi-way data reduces dimensionality and reveals shared and individual structures.
problem Analyzing multi-source, multi-way data from different high-throughput technologies.
method Multiple Linked Tensor Factorization (MULTIFAC) extending CP decomposition with L2 penalties and EM algorithm for incomplete data.
result MULTIFAC approximates underlying signal, identifies shared and unshared structures, and imputes missing data.
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data…
New examples show some manifolds can't be decomposed.
problem Existence of open book decompositions for certain manifolds.
method Using signature non-multiplicativity in fibre bundles.
result Closed manifolds with no open book decomposition exist.
Non-orthogonal joint diagonalization (NJD) free of prewhitening has been widely studied in the context of blind source separation (BSS) and array signal processing, etc. However, NJD is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single da…
New methods estimate interventional effects with multiple mediators using machine learning.
problem Estimating interventional effects with multiple mediators.
method Flexible machine learning techniques for estimation, with weak convergence results for confidence intervals.
result Closed-form confidence intervals and hypothesis tests for interventional mediation effects.
Paper explores how design matrix patterns affect regression performance in over-parameterized models.
problem The impact of covariance matrix degeneracy and covariate dependence on regression performance in over-parameterized models.
method Derives deterministic equivalents for prediction risk in a vanishing-ridge regime, using graph theory to identify singular configurations.
result Degeneracy of covariance matrices and dependence can lead to multiple descent in regression performance.
LSTM-MSNet forecasts time series with multiple seasonal patterns using a unified model.
problem Forecasting time series with multiple seasonal cycles.
method Decomposition-based, unified prediction framework using LSTM.
result LSTM-MSNet outperforms state-of-the-art methods on various datasets.
Proposes D-CDLF for multi-view data decomposition.
problem Uncorrelatedness between common and distinctive latent factors.
method Decomposes data into common, distinctive, and noise components.
result Effective uncorrelatedness between distinctive latent factors from different views.
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.
MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.
problem Dequantization bottleneck in LLM inference on modern AI accelerators.
method MSD decomposes high-precision activations into multiple low-precision components for direct multiplication with quantized weights.
result MSD avoids INT8-to-BF16 weight conversion, reducing dequantization cycles and HBM traffic.
Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the most widely studied and used decompositions, especially in data mining and machi…
Paper analyzes electricity price and demand TSs using decomposition to detect cyber-attacks.
problem Detecting cyber-attacks in electricity price and demand time series data.
method Performed time series decomposition using additive and multiplicative methods, tested error term for patterns.
result Found a chance of cyber-attacks in the error term of decomposed TSs.
The paper introduces new measures to quantify variability in decision tree models due to observational multiplicity.
problem The variability in decision tree models due to observational multiplicity.
method Introduces leaf regret and structural regret to decompose observational multiplicity.
result Structural regret is the primary driver of observational multiplicity, accounting for over 15 times the variability of leaf regret in some datasets.
ST-MTM models complex time series by decomposing and masking seasonal and trend components.
problem Forecasting complex time series with intricate temporal variations.
method Seasonal-Trend Decomposition with Masking and Contrastive Learning.
result ST-MTM achieves superior forecasting performance compared to existing methods.
New method groups genetic data into coherent topics for disease insights.
problem Analyzing large, multi-dimensional genetic data sets.
method Conditional Hierarchical Bayesian Tucker Decomposition for genetic data analysis.
result Our models are more coherent than baseline models.
Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…
VecHGrad solves complex tensor decomposition problems more accurately and efficiently.
problem Complex tensor decomposition with multiple matrices and diagonal tensors.
method VecHGrad algorithm using gradient, Hessian-vector product, and adaptive line search.
result VecHGrad converges faster and more accurately than existing methods.
The paper describes decompositions of geometric measures on Anosov homogeneous spaces.
problem Decomposing geometric measures on Anosov homogeneous spaces.
method Ergodic decompositions of Burger-Roblin and Bowen-Margulis-Sullivan measures.
result The space of non-trivial invariant ergodic measures is homeomorphic to a product space.
Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the 20th century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decomposi…
Left invariant affine structures in a Lie group G are in one-to-one correspondence with left-symmetric algebras over its Lie algebra g=TeG (``over'' means that the commutator [x,y]=xy−yx coincides with the Lie bracket; left-symmetric algebras can be defined as Lie-admissible algebras such that the mult…
A new decomposition explains over-parameterized models' counterintuitive behaviors.
problem Understanding predictive error in over-parameterized models.
method Introducing the Generalized Aliasing Decomposition (GAD) to explain predictive performance.
result The GAD decomposes predictive error into three parts: model insufficiency, data insufficiency, and generalized aliasing.
This article is motivated by soccer positional passing networks collected across multiple games. We refer to these data as replicated spatial passing networks---to accurately model such data it is necessary to take into account the spatial positions of the passer and receiver for each passing event. This spatial regist…
New algorithm reduces matrix multiplication time for sparse matrices.
problem Efficiently multiply large sparse matrices with limited space.
method Exploits sparsity to reduce QR decompositions and time complexity.
result Time complexity reduced to $\widetilde{O}\left((
nz(X)+
nz(Y))\ell+n\ell^2
ight)$ in expectation.
New AMP algorithms reveal phase transitions in tensor recovery.
problem Understanding algorithmic behavior of low-rank tensor decompositions.
method Derive Bayesian AMP algorithms and use dynamic mean field theory.
result Reveals phase transitions between easy, hard, and impossible inference regimes.
This paper derives a portfolio decomposition formula when the agent maximizes utility of her wealth at some finite planning horizon. The financial market is complete and consists of multiple risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with drift and volatility b…
Classifies 4D metric Lie algebras with parallel skew-symmetric tensors.
problem Classifying 4D metric Lie algebras with parallel skew-symmetric tensors.
method Complete classification up to isometric isomorphism and scaling.
result Classification of 4D metric Lie algebras with parallel skew-symmetric tensors.
Develops methods to analyze feature-outcome associations in subpopulations.
problem Challenges in understanding feature-outcome associations in high-dimensional data.
method Geometric decomposition framework using gradient flow and co-monotonicity decomposition.
result Identifies context-dependent patterns and improves statistical power and interpretability.
This paper introduces ∞- and n-fold vector bundles as special functors from the ∞- and n-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of n-fold vector bundles and we prove that any n-fold vector bundle admits a non-canonical isomorphism to a decomposed …