We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…
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48 results for “Hierarchical Tucker”
Paper compresses RNNs using HT decomposition for better performance.
problem Large model sizes of RNNs in sequence analysis.
method Hierarchical Tucker (HT) tensor decomposition for model compression.
result HT-LSTM achieves better compression and accuracy than state-of-the-art methods.
Extends geometrical description of tensor manifolds in tree-based formats.
problem Geometrical description of tensor manifolds in tree-based formats.
method Provided a new geometrical description of manifolds of tensors in tree-based format.
result Geometrical description compatible with Tucker format.
DinTucker: Scaling up Gaussian process models on multidimensional arrays with billions of elementscs.LG
Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear rel…
Paper characterizes optimization landscape of Tucker decomposition.
problem Finding exact Tucker decomposition is a nonconvex optimization problem.
method Characterized the optimization landscape and provided a local search algorithm.
result All local minima are globally optimal if tensor has an exact Tucker decomposition.
Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively straightforward but powerful linear model based on Tucker decomposi…
FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.
problem Handling continuous-indexed tensor data that doesn't fit traditional Tucker decomposition.
method FunBaT treats continuous-indexed data as interactions between a core tensor and a group of latent functions modeled by Gaussian processes (GP). It converts each GP into a state-space prior and uses advanced message-passing techniques for scalable inference.
result FunBaT effectively handles real-world data with continuous indexes, demonstrating its advantage in synthetic and real-world applications.
HOTCAKE compresses CNNs by decomposing kernels into smaller parts.
problem Compressing deep CNNs without significant accuracy loss.
method Input channel decomposition, guided Tucker rank selection, higher order Tucker decomposition, fine-tuning.
result HOTCAKE produces highly compressed CNN models with good accuracy.
A new tensor completion method using tensor networks with Tucker wrapper.
problem Low-rank tensor completion in various applications.
method Solving LRTC as a system of nonlinear equations using a two-level alternative least squares method.
result The method converges to the exact solution at a linear rate with high probability.
NACT improves tensor regression predictions with regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented regularization on Tucker decomposition.
result Achieves exact regularization on core tensor in linear and generalized linear tensor regression.
A new kernel improves tensor classification accuracy and reduces computation time.
problem Challenges in classifying high-dimensional tensor data.
method Proposes a weighted subspace exponential kernel based on Tucker decomposition.
result The new kernel outperforms existing methods in accuracy and computational efficiency.
A new diffusion model generates structured tensors for high-dimensional data.
problem Generating a structured tensor with a target distribution.
method Tucker diffusion model with Tucker-Unet architecture.
result Generated tensors converge to the true data distribution at a rate dependent on tensor mode dimensions.
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast empirical evidence supporting this belief, theoretical justifications to date are li…
A new probabilistic BTD method for tensor data.
problem Modeling higher-order tensors with robust inference.
method Probabilistic Block-Term Decomposition using variational Bayesian inference and von-Mises Fisher distribution.
result The proposed pBTD can quantify multi-linear structures robustly.
Sparse Tucker Decomposition and Graph Regularization for High-Dimensional Time Series Forecastingmath.ST
Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.
problem High-dimensional time series forecasting with over-parameterization issue.
method Sparse Tucker decomposition and graph regularization for tensor-based model.
result Non-asymptotic error bound and superior performance in numerical experiments.
Paper proposes BTuD for unsupervised feature selection.
problem Feature selection in unsupervised learning.
method Bayesian Tucker decomposition (BTuD) with Gaussian residual.
result Successfully applied to various datasets.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
Unified model for tensor completion using low-rank and sparse Tucker decomposition.
problem Estimating missing data from incomplete tensor measurements.
method Unified low-rank and sparse enhanced Tucker decomposition model with ADMM.
result Our model achieves higher recovery accuracy on various real-world data sets.
Unified framework for statistical inference of low-rank tensors.
problem Statistical inference for tensors in high-dimensional data.
method Unified framework using debiasing and tangent space projection.
result Achieves asymptotic normality and minimax-optimal confidence intervals.
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.
SDIFT generates full-field dynamics from sparse, irregular data.
problem Modeling and reconstructing physical dynamics from sparse, off-grid observations.
method SDIFT uses a functional Tucker model and sequential diffusion for generating full-field evolution from irregular sparse observations.
result Significant improvements in reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
A new method for traffic data imputation considering spatiotemporal correlations.
problem Traffic data imputation, especially for high-level missing scenarios.
method Spatiotemporal regularized Tucker decomposition approach.
result The proposed method outperforms existing methods on real-world traffic datasets.
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to solve the optimization problem. The convergence of the algorithm is given. We employ…
This work improves tensor decomposition methods, especially for large datasets.
problem Lack of efficient methods for estimating Tucker decompositions.
method Applies Johnson-Lindenstrauss type guarantees to Tucker decompositions with random embeddings.
result Effective dimension reduction with minimal error for large tensors.
Tucker and Ky Fan's lemma are combinatorial analogs of the Borsuk-Ulam theorem (BUT). In 1996, Yu. A. Shashkin proved a version of Fan's lemma, which is a combinatorial analog of the odd mapping theorem (OMT). We consider generalizations of these lemmas for BUT-manifolds, i.e. for manifolds that satisfy BUT. Proofs rel…
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
Gradient descent promotes low-rank solutions in tensor completion.
problem Implicit regularization in tensor factorization using gradient descent.
method Introduced deep Tucker and TensorTrain (TT) unconstrained factorization to address tensor completion.
result Gradient descent promotes solutions with low-rank.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.
problem Link prediction in incomplete knowledge graphs.
method Factorized bilinear pooling model with Tucker decomposition constraints.
result Efficient and parameter-efficient model with low-rank approximation.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
problem High-dimensional and incomplete tensor completion.
method Spectra-Guided Neural Tucker Factorization (SG-NTF) with Spatio-Temporal Co-Gating (STCG).
result Maintains competitive completion accuracy with parameter efficiency.
Estimates low-rank distributional matrices from incomplete samples.
problem Matrix completion for distributional entries with limited observed data.
method Kernel mean embeddings, Tucker rank, functional unfolding operators.
result Effective estimator for distributional matrix completion established.
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of data. However, as the data tensor often has multiple modes and is large-scale, exist…
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…
We introduce Bayesian Poisson Tucker decomposition (BPTD) for modeling country--country interaction event data. These data consist of interaction events of the form "country took action toward country at time ." BPTD discovers overlapping country--community memberships, including the number of latent com…
ALCORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with -norm constraint.
result ALCORE achieves similar results to full Tucker decomposition at a fraction of the cost.
New tensor model reduces GLM estimation error and sample complexity.
problem Estimating GLM coefficients with reduced sample complexity.
method Developed LSR tensor model and block coordinate descent algorithm.
result Minimax lower bound on estimation error, suggesting lower sample complexity.
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging problem is related to determination of model complexity (i.e., multilinear rank), e…
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.
Counterexamples to a conjecture on ribbon graph genus changes were found and proven.
problem A conjecture on genus changes in ribbon graphs was formulated and disproven.
method A family of counterexamples was found and proven.
result Essentially, the counterexamples found by Qi Yan and Xian'an Jin are the only ones.
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
problem Reducing dimensionality of tensor predictors for improved interpretation and accuracy.
method Developed two tensor dimension reduction methods using Tucker and CP decompositions.
result Substantial improvement in accuracy over existing methods in simulations and applications.
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our …
Minimizing the nuclear norm of a matrix has been shown to be very efficient in reconstructing a low-rank sampled matrix. Furthermore, minimizing the sum of nuclear norms of matricizations of a tensor has been shown to be very efficient in recovering a low-Tucker-rank sampled tensor. In this paper, we propose to recover…
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
problem Smoothness-based nonparametric density estimators are not optimal for all types of data.
method Incorporates a multi-view latent variable model into histogram-style estimators.
result A new histogram estimator converges faster to multi-view models in error.
Hierarchical Spatio-Channel Clustering for Efficient Model Compression in Medical Image Analysiscs.CV
This paper proposes a new method to compress CNNs for medical image analysis, improving efficiency and accuracy.
problem Large memory and computational requirements of CNNs in resource-constrained environments.
method Hierarchical spatio-channel low-rank compression framework that partitions feature maps into spatial regions and groups channels according to co-activation patterns within each region.
result The proposed method achieves significant FLOP reduction, inference speed-up, and improved classification accuracy compared to existing methods.
Paper learns meaningful state and action representations from MDP trajectories.
problem Learning good state and action representations from MDP trajectories.
method Tensor decomposition, kernelization, importance sampling, low-Tucker-rank approximation.
result The learned state/action abstractions provide accurate approximations to latent block structures.
LCBO tackles constrained optimization in high dimensions, offering a polynomial convergence rate.
problem Bayesian optimization for high-dimensional constrained problems.
method LCBO uses local descent and uncertainty-driven exploration, proving polynomial convergence rate.
result LCBO achieves a polynomial convergence rate for KKT residuals in high dimensions.
Paper proves -means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of -means on persistence diagram space.
result Performance of -means on persistence diagrams and measures is superior.