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.
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…
Estimates high-dimensional distributions using tree tensor networks.
problem Estimating high-dimensional probability distributions from i.i.d. samples.
method Tree-based tensor formats, empirical risk minimization, L2 contrast, orthogonal bases.
result Effective approximation of classical probabilistic models like Gaussian and graphical models.
The paper tackles high-dimensional function approximation using tree-based tensor formats.
problem Approximating high-dimensional functions in statistical learning.
method Empirical risk minimization over tree-based tensor formats, exploiting multilinear models and sparsity.
result Numerical stability and reliability of the proposed algorithms for learning.
Tensorized random projections reduce high-dimensional tensor size efficiently.
problem Efficiently reducing the dimension of very high-dimensional tensors.
method Proposes two tensorized random projection maps using TT and CP decompositions.
result TT format offers superior performance in terms of required random projection size.
Low-bit training framework reduces energy consumption in CNNs.
problem Reducing energy consumption in convolutional neural networks.
method Low-bit training framework using MLS tensor format with dynamic quantization.
result Achieves superior trade-off between accuracy and bit-width.
Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.
problem Selecting optimal tree structure and ranks for high-dimensional function approximation.
method Proposes a complexity-based model selection method for tree tensor networks in empirical risk minimization.
result Demonstrates near-minimax adaptive performance across various smoothness classes.
Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
E2M optimizes tensor density estimation by relaxing α-divergence to KL-divergence.
problem Analytical challenges in traditional α-divergence optimization for tensor-based density estimation. method E2M algorithm: relaxes optimization to KL-divergence, then applies tensor many-body approximation. result Flexible modeling of various low-rank structures and their mixtures.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
problem Reducing the dimension of high-dimensional tensors for machine learning.
method Tensorized Rademacher random projections using Tensor Train decomposition.
result Tensorized Rademacher projections can replace Gaussian projections in tensor compression.
Efficiently price high-dimensional Bermudan options using tensor compression.
problem High-dimensional option pricing with computational complexity.
method Hierarchical tensor compression for Monte Carlo and dual martingale methods.
result Tensor compression alleviates the curse of dimensionality for Bermudan option pricing.
Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models all interactions of every order. The key idea is to represent an exponentially l…
MEI model improves knowledge graph completion by efficiently modeling interactions between embeddings.
problem Efficiently modeling interactions between knowledge graph embeddings to predict missing links.
method MEI divides embeddings into partitions and uses Tucker and block term formats to model interactions efficiently.
result Achieves state-of-the-art performance on link prediction tasks.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
Tensor trains simplify solving complex PDEs efficiently.
problem Solving high-dimensional parabolic PDEs using traditional methods is computationally infeasible.
method Reformulate PDEs as backward stochastic differential equations and use tensor train format for compression and efficient computation.
result Tensor train methods achieve a good balance between accuracy and computational efficiency.
Combines Koopman theory and tensor trains for high-dimensional dynamical systems.
problem Analyzing complex, high-dimensional dynamical systems.
method Tensor train (TT) format for low-rank approximation, Koopman operator theory for dynamics.
result Efficient algorithms for low-rank representation of evolution operators.
An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is contr…
Guaranteed convergence for tensor factorization using Riemannian gradient descent.
problem Recovering tensor train format from linear measurements.
method Optimization over left-orthogonal TT format using Riemannian gradient descent on Stiefel manifold.
result RGD converges linearly to the ground-truth tensor with polynomial error growth in tensor order.
Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neura…
The paper uses AI to analyze ECG data, revealing age-related changes and identifying key features.
problem Investigating age-related changes in ECG data to distinguish healthy from disease-related changes.
method Employed deep-learning and tree-based models on raw ECG signals and features from a diverse age group.
result Identified age-related declines in breathing rates and high SDANN values in elderly individuals.
Paper proposes efficient tensor completion method using Gaussian Process.
problem Tensor completion in high-dimensional data with unknown smooth functions.
method Gaussian Process Regression for initialization and TT-cross approximation for tensor rank selection.
result Improved reconstruction error compared to random initialization.
New method reduces high-dimensional financial problems using low-rank tensor approximation.
problem High-dimensional financial problems in pricing, calibration, and risk assessment.
method Low-rank tensor approximation for Chebyshev interpolation in tensor train (TT) format.
result Efficiently approximates interpolation coefficients using tensor completion.
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.
Tensor methods improve image classification performance.
problem Improving image classification accuracy using tensor-based machine learning.
method Two novel tensor-based approaches: MANDy kernel reformulation and alternating ridge regression in tensor-train format.
result Tensor-based methods are competitive with state-of-the-art neural networks.
Efficiently samples complex distributions using tensor train format.
problem Sampling from high-dimensional complex probability densities efficiently.
method Integrates tensor train format with backward stochastic differential equations (BSDEs) for fast, robust, and accurate sampling.
result Improved efficiency in sampling from challenging target distributions.
BFLOAT16 achieves SOTA results in deep learning training without hyper-parameter tuning.
problem Ensuring deep learning training achieves SOTA results without hyper-parameter tuning.
method Implemented a method to emulate BFLOAT16 operations in various frameworks.
result BFLOAT16 achieves SOTA results in deep learning training without hyper-parameter tuning.
A substantial progress in development of new and efficient tensor factorization techniques has led to an extensive research of their applicability in recommender systems field. Tensor-based recommender models push the boundaries of traditional collaborative filtering techniques by taking into account a multifaceted nat…
New method compresses random forest models for efficient storage.
problem Large storage requirements for ensemble models like random forests.
method Probabilistic modeling of trees followed by model clustering.
result High compression rates and perfect reconstruction of original ensembles.
TTRP method preserves distances in high-dimensional data with reduced storage and speed.
problem Preserving distances in high-dimensional datasets efficiently and accurately.
method Tensor train random projection (TTRP) using TT-ranks of one.
result TTRP is an expected isometric projection with bounded variance.
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed …
GrateTile optimizes CNN feature map storage for efficient data access.
problem Efficient storage and access of sparse CNN feature maps.
method Divides feature maps into uneven-sized subtensors, compresses and stores them in a compressed yet accessible format.
result Average 55% DRAM bandwidth reduction with minimal indexing overhead.
New trees-based models handle correlated data better.
problem Standard trees-based models ignore correlation structure.
method Explicitly accounts for correlation structure in splitting criterion, stopping rules, and fitted values.
result New approach superior to standard models in simulations and real data.
SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application based on MATALB. It provides a wide range of facilities for generating tensor data w…
Study reviews tree-based methods and introduces new ensemble strategies.
problem Improving the efficiency and performance of tree-based machine learning models.
method Review of tree-based methods, introduction of ISLE framework, ARM model combination strategy, and modified ISLEs.
result Performance evaluation of modified ISLEs on real data sets.
Causal deep learning tackles causal inference using tensor factor analysis.
problem Addressing causal questions in data using neural networks.
method Tensor factor analysis and neural network architectures (causal capsules, tensor transformer, multilinear projection algorithm).
result Derives deep neural networks for causal inference with tensor factor analysis.
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
New method improves feature selection in tree-based models.
problem Previous feature selection methods in tree-based models lack sufficient regularization and sub-optimal performance.
method Developed a new gain penalization approach for tree-based models that allows for flexible feature-specific importance weights.
result The new method improves out-of-sample performance, especially with correlated features.
Corrects bias in feature importance measures of tree-based methods.
problem Bias in feature importance measures of tree-based methods.
method Corrects bias by incorporating out-of-sample split-improvement.
result Better summaries and screening tools of feature importance.
Enhanced tree-based classifiers use derivatives and geometry for better function classification.
problem Improving classification of high-dimensional time series data.
method Integrates Functional Data Analysis with tree-based ensemble techniques, leveraging derivative and geometric features.
result Significant improvements over traditional approaches in function classification.
Tensor networks improve data privacy and robustness in convolutional neural networks.
problem Improving data privacy and robustness in convolutional neural networks.
method Tensor network decomposition for data partitioning and adversarial defense.
result Tensor networks can protect data privacy and resist adversarial attacks.
By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there i…
ENTED efficiently decomposes binary and count tensors using nonparametric Gaussian processes.
problem Handling high-dimensional and sparse binary and count data with traditional tensor decompositions.
method ENTED uses nonparametric Gaussian processes and sparse orthogonal variational inference to handle binary and count tensors.
result ENTED outperforms traditional methods in binary and count tensor completion tasks.
DOFEN improves DNN performance on tabular data benchmarks.
problem DOFEN tackles the performance gap between DNNs and tree-based models on tabular data.
method DOFEN uses a two-level rODT forest ensembling process inspired by oblivious decision trees.
result DOFEN achieves state-of-the-art results on the Tabular Benchmark.
Simulation study evaluates tree-based imputation methods for multi-level data.
problem Ignoring dependencies in hierarchical data can compromise imputation accuracy.
method Chained Random Forests and Extreme Gradient Boosting (mixgb) adapted for multi-level data.
result Adapted boosting methods outperform traditional MICE for Level-1 variables at higher missingness rates.
A new method estimates rare events using tensor trains.
problem Estimating rare event probabilities in high-dimensional problems.
method Approximating optimal importance distribution via tensor-train decompositions and compositions.
result Better variance reduction and efficient computation of rare event probabilities.
The paper introduces a method to control false splits in tree-based data aggregation.
problem Identifying the correct subgroups to treat as a single entity in tree-based data.
method Introduces the 'false split rate' and proposes a multiple hypothesis testing algorithm for tree-based aggregation.
result The proposed algorithm controls the false split rate, demonstrating its effectiveness on stock volatility and taxi fare data.
A new method uses CPD to efficiently model feature interactions in non-sequential data.
problem Efficiently modeling feature interactions in non-sequential data with high computational and memory costs.
method Implicitly represent model parameters as a tensor, factorize into a compact Tensor Train (TT) format, and use Canonical Polyadic (CP) Decomposition for invariance to feature ordering.
result The proposed CP-based predictor outperforms other TN-based predictors on sparse data and matches neural network performance on dense non-sequential tasks.
Tree-based models outperform deep learning on tabular data, especially for medium-sized datasets.
problem Understanding why tree-based models outperform deep learning on tabular data.
method Extensive benchmarks of tree-based and deep learning models on 45 datasets, accounting for hyperparameters.
result Tree-based models remain state-of-the-art on medium-sized tabular data, even without hyperparameter optimization.