A new tensor decomposition method using a dictionary for better interpretability.
problem Ensuring interpretability in tensor decomposition models.
method Dictionary-based tensor canonical polyadic decomposition with sparse coding.
result Improves parameter identifiability and estimation accuracy in tensor decomposition.
Improves PARAFAC tensor decomposition rank estimation for better interpretability and accuracy.
problem Estimating the optimal number of latent factors in PARAFAC tensor decomposition.
method Automatically determines the rank using Core Consistency Diagnostic (CORCONDIA) and explores the trade-off between interpretability and predictive accuracy.
result Striking a good balance between interpretability and accuracy benefits rank estimation.
Paper applies ANOVA decomposition for interpretable data approximation.
problem High-dimensional data interpretation and dimensionality reduction.
method ANOVA decomposition and Grouped Transformations for interpretability.
result Ability to rank variable interactions and unimportant variables.
CTD efficiently decomposes tensors for fast, accurate, and interpretable patterns.
problem Finding patterns and anomalies in tensors efficiently and interpretably.
method CTD: a sampling-based tensor decomposition method.
result CTD-S is 17-83x more accurate and 5-86x faster than state-of-the-art methods.
Neural Decomposition breaks down VAE latent structure for better interpretability.
problem Limited interpretability of VAE latent representations.
method Adapted functional ANOVA to VAEs, applying constraints for identifiability.
result Decomposes data variation into latent and fixed input effects.
SCTD extracts interpretable spatio-temporal modes from high-dimensional data.
problem Analyzing complex, multivariate data with temporal dependencies.
method Shape Constrained Tensor Decomposition using sparse representations.
result More interpretable spatio-temporal modes extracted.
SurvFD and SurvSHAP-IQ provide interpretable survival models by analyzing feature interactions.
problem Non-additivity of hazard and survival functions limits standard additive explanation methods.
method SurvFD decomposes higher-order effects into time-dependent and time-independent components, extending Shapley interactions to time-indexed functions.
result SurvFD and SurvSHAP-IQ offer a new perspective on survival explanations, explicitly characterizing feature interactions.
New algorithms for interpreting complex multivariate functions.
problem Hard interpretation of multivariate functions due to many parameters.
method Filtered tensor decompositions of derivative information.
result Nonparametric estimates of smooth decoupled functions.
New networks interpret kernel decompositions for signal analysis.
problem Mode decomposition in signal analysis.
method Programmable and interpretable regression networks using kernels and data.
result Near machine precision recovery of signal modes under regularity and separation assumptions.
APD method decomposes neural network parameters into simple, faithful components.
problem Understanding the internal mechanisms learned by neural networks.
method Attribution-based Parameter Decomposition (APD) method.
result Demonstrated effectiveness in recovering features, separating computations, and identifying representations.
The paper proposes a new method for online image decomposition using auto-encoders.
problem Building a part-based representation of image datasets for interpretation and online computation.
method Sparse, non-negative auto-encoder with deep encoder and shallow decoder for online computation.
result The method outperforms state-of-the-art online methods on MNIST and Fashion MNIST datasets.
New method quantifies model complexity for better interpretation.
problem Complex models produce misleading interpretation results.
method Functional decomposition to quantify model complexity.
result Post-hoc interpretation of complex models is more reliable and compact.
New insights into when NMF decompositions are not unique.
problem Non-identifiability of NMF decompositions.
method Characterization of non-identifiability conditions.
result Characterized when and how non-uniqueness can occur in NMF.
Paper proposes a method to interpret neural networks by decomposing them into simpler tasks.
problem Understanding the complex nonlinear relationships in trained neural networks.
method Non-negative matrix factorization applied to a trained layered neural network.
result Reveals the roles of hidden units in terms of their contribution to each principal task.
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
problem Performing global sensitivity analysis on black-box models with dependent inputs.
method Proposes a novel framework based on probability theory, functional analysis, and combinatorics to handle dependencies.
result Any square-integrable, real-valued function of random elements with mild dependence assumptions can be uniquely additively decomposed.
SWoTTeD discovers hidden temporal patterns in EHR data.
problem Complex temporal patterns in EHR data.
method Sliding Window for Temporal Tensor Decomposition (SWoTTeD) with constraints and regularizations.
result SWoTTeD achieves at least as accurate reconstruction as state-of-the-art models and extracts meaningful temporal phenotypes.
This paper reviews methods for discovering patient subgroups from EHR data.
problem Discovering subgroups of patients and co-occurring medical conditions from EHR data.
method Low-rank data approximation methods like matrix and tensor decompositions.
result These methods provide transparent and interpretable insights into patient phenotypes.
We solve the ANOVA decomposition for categorical inputs.
problem Lack of a closed-form expression for ANOVA decomposition with categorical dependent variables.
method Bridge functional analysis with discrete Fourier analysis to derive a closed-form decomposition.
result Closed-form decomposition for categorical inputs without assumptions.
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Proposes mWDN for interpreting time series analysis.
problem Lack of effective modeling for frequency information in time series analysis.
method Wavelet-based multilevel neural network structure (mWDN).
result Demonstrates excellent performance and interpretability of mWDN models.
The paper proves Hodge decompositions and partial bar partial lemmas for G2 and Calabi-Yau manifolds.
problem Proving Hodge decompositions and partial bar partial lemmas for G2 and Calabi-Yau manifolds.
method Defining cohomology spaces analogous to Bott-Chern cohomology and relating them to harmonic forms on the manifolds.
result Geometric interpretation of cohomology classes in terms of submanifolds and gerbes for G2 manifolds.
A new tensor decomposition method for fMRI data captures both spatial and temporal variability.
problem Challenges in modeling shared and subject-specific structure in multisubject spatiotemporal data, especially in neuroimaging.
method Introduces a spatiotemporal variational tensor decomposition (ST-VTD) framework combining tensor factorization with structured priors for flexible representation of spatial and temporal dynamics.
result Significantly improves latent factor recovery in fMRI data compared to classical and probabilistic decomposition benchmarks.
A new model decomposes market variability into interpretable components.
problem Understanding the factors driving market variability and predicting future movements.
method H-SGDLM framework with HAR-RV model for GPU-scalable multivariate volatility estimation.
result Superior performance in predicting large moves and longer-term market variability.
New method compresses deep learning layers using tensor decomposition.
problem Reduction of computation cost and interpretability for tensor data.
method CP-decomposition to compress convolutional layers in deep learning.
result Reduces model complexity and maintains prediction performance.
The paper explores geometric decompositions for Ricci tensors and their applications.
problem Understanding Ricci tensors on compact Riemannian manifolds.
method Utilizes Berger-Ebin and York L2-orthogonal decompositions. result New insights into Ricci almost solitons and harmonic maps.
Optimized DMD for fast atmospheric chemistry forecasting.
problem Forecasting global atmospheric chemistry dynamics efficiently.
method Optimized Dynamic Mode Decomposition (DMD) for reduced order modeling.
result Significant improvement in computational speed and interpretability.
CD interprets LSTM predictions by identifying word interactions.
problem LSTMs are black boxes; understanding their internal workings is difficult.
method Contextual decomposition (CD) to interpret LSTM predictions.
result CD reliably identifies word interactions and sentiment combinations.
TRIM improves interpretability of deep neural networks in cosmology.
problem Understanding which features a deep neural network uses in a transformed space.
method TRIM (Transformation IMportance) attributes importances to features in a transformed space.
result Combining TRIM with contextual decomposition helps identify physical features learned by DNNs.
Study shows how noise and distractions affect neural network explanations.
problem Lack of consideration for noise and distractions in neural network explanations.
method Examined the impact of noise and distracting elements on neural network interpretation models.
result Noise and distracting elements influence the results of neural network explanations.
Classifies collective motions in biological networks using graph dynamic mode decomposition.
problem Classifying complex collective motions in biological networks based on transient and complexly changing network properties.
method Data-driven spectral analysis (graph dynamic mode decomposition) to extract dynamical properties.
result Contextual node information and physical properties are crucial for classifying collective motions.
A new method purifies interaction effects in models to improve interpretability.
problem Interaction effects can be misinterpreted as separate main effects, complicating model interpretation.
method Proposes pure interaction effects and a Functional ANOVA decomposition algorithm to identify and isolate interaction effects.
result Identifies and separates interaction effects from main effects, showing large disparities in model interpretation.
Proposes using Dynamic Mode Decomposition with delays for short-term human motion anticipation.
problem Lack of interpretability and explainability in neural network-based motion anticipation methods.
method Dynamic Mode Decomposition with delays for motion representation and prediction.
result Anticipation errors comparable or better than recurrent neural networks for very short times.
Improved SVM classification with interpretable features from scattered data.
problem Classification of scattered data points in high-dimensional spaces.
method Truncated ANOVA decomposition for sparse feature selection; use of trigonometric or wavelet feature maps.
result Better classification accuracy and interpretability with ℓ1-norm regularization. VDA improves disentanglement of latent representations in complex signals.
problem Learning disentangled and interpretable representations in nonstationary, high-dimensional time-evolving signals.
method Variational decomposition autoencoding (VDA) framework, incorporating signal decomposition, contrastive self-supervised task, and variational prior approximation.
result DecVAEs surpass state-of-the-art VAE-based methods in disentanglement quality and generalization.
ED-VAE improves VAEs by explicitly including entropy components in ELBO.
problem Limitations of traditional VAEs with ELBO in generating high-quality samples and interpreting latent spaces.
method Introduces ED-VAE, a re-formulation of ELBO that includes entropy and cross-entropy components.
result Significantly enhances model flexibility and improves interpretability and generative performance.
We break down transformer embeddings into interpretable components revealing hidden geometric structures.
problem Understanding the hidden geometry and interpretability of transformer models.
method Decomposed transformer embeddings into position, context, and residual components.
result Pervasive mathematical structure in transformer embeddings, including position and context vectors.
t-PINE learns interpretable node embeddings from graph data.
problem Lack of interpretability and predictability in graph representation learning.
method t-PINE uses a multi-view graph, combining adjacency matrix and nearest neighbor adjacency, for CP decomposition.
result t-PINE significantly outperforms baseline methods in multi-label classification problems.
CoDA Nets improve interpretability in neural networks.
problem Improving interpretability in neural networks.
method Dynamic Alignment Units (DAUs) for input-dependent linear transformations.
result CoDA Nets achieve on par results with ResNet and VGG models on complex datasets.
We propose a framework for training GANs on composed data, improving model modularity and interpretability.
problem Training GANs on complex, composed data.
method Composition/decomposition framework for adversarially training GANs on composed data.
result Improves modularity, extensibility, and interpretability of GANs.
New method for interpreting complex ML models.
problem Interpreting complex black-box ML models.
method Functional decomposition of black-box predictions into simpler subfunctions.
result Main effects provide insights into feature contributions and interactions.
Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
Proposes ANOVA-TPNN for stable interpretation of complex functions.
problem Stability issues in estimating components of functional ANOVA models.
method Introduces ANOVA-TPNN based on tensor product basis expansion.
result ANOVA-TPNN provides stable estimation of components.
New symplectic caps and embeddings found in complex projective plane.
problem Embeddings of homology balls in complex projective plane.
method Handlebody construction of symplectic caps and embeddings.
result First examples of symplectic handlebody decompositions of a closed symplectic 4-manifold.
Geometrically describes hyperbolic structures on link complements using quantum groups.
problem Describing hyperbolic structures on link complements algebraically.
method Uses octahedral decomposition and Kashaev-Reshetikhin's braiding on quantum group Uξ(sl2). result Shows how to interpret geometrically the algebraic gluing equations for hyperbolic structures.
A new method adds pseudo-data to tensor decomposition to improve accuracy and enforce various regularizations.
problem No general method to regularize tensor decomposition methods.
method Supplement training data with pseudo-data to balance true data and desired regularization.
result Improves inference accuracy and enforces various regularizations on synthetic and real data.
We provide a unified view of additive explanations for dependent inputs.
problem Challenges in obtaining a tractable representation and estimating the decomposition for dependent inputs.
method Combining Hilbert space methods with generalized functional ANOVA, we build an explicit decomposition Riesz Basis.
result Proposed a simple yet powerful algorithm to estimate the decomposition from data.
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discr…
We give a direct interpretation of Neumann's combinatorial formula for the Chern-Simons invariant of a 3-manifold with a representation in PSL(2,C) whose restriction to the boundary takes values in upper triangular matrices. Our construction does not involve group homology or Bloch group but is based on the constructio…