The study analyzes XRP transaction networks to understand market dynamics.
problem Understanding market dynamics of XRP through transaction data.
method Weekly weighted directed networks are embedded into a vector space using network embedding techniques. A correlation tensor is calculated and analyzed using singular value decomposition.
result The correlation tensor provides insights into the system's behavior and dependence on model parameters.
Study shows XRP price correlates with transaction network metrics.
problem Understanding the relationship between cryptoasset price and network metrics.
method Analysis of correlation tensor spectra, random matrix theory comparison, singular values investigation.
result Distinct correlation between XRP price and singular values during bubble and non-bubble periods.
Biological neurons learn tensor decompositions of higher-order correlations using nonlinear Hebbian plasticity.
problem Learning higher-order correlations in biological neurons.
method Introduce and study generalized nonlinear Hebbian learning rules.
result Neurons can learn tensor eigenvectors of higher-order input correlation tensors.
Study examines how crypto arbitrage affects XRP price and network correlation.
problem Impact of crypto arbitrage on XRP price and network correlation.
method Examined XRP price fluctuations and correlation tensor spectra of transaction networks across crypto exchanges.
result Arbitrage opportunities across crypto exchanges anti-correlate with XRP price during bubble periods.
New model improves portfolio selection by analyzing tensor data.
problem Improving portfolio selection through better analysis of style returns.
method Introducing a tensor dynamic conditional correlation (TDCC) model with trace-normalization and dimension-normalization.
result The TDCC model enhances portfolio selection across multiple markets.
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
problem Learning complex nonlinear transformations of multiple data views.
method Maximizes high-order canonical correlation by jointly learning transformations of each view using a reformulated tensor decomposition.
result DTCCA efficiently handles high-dimensional and large number of views, overcoming scalability issues.
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
problem Missing structure in pairwise Fisher graphs for multi-observable radiation patterns.
method Higher-order Fisher tensors and natural exponential-family coordinates.
result Exact triality of Fisher tensors, cumulants, and hypergraphs.
Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.
problem Recovering multiple high-dimensional signals from correlated modalities.
method Bayesian Approximate Message Passing and Sequential Curriculum Learning.
result Sequential learning strategy optimally recovers weak signals in multi-modal settings.
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.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
problem Handling higher-order structures in multi-block data analysis.
method Tensor Generalized Canonical Correlation Analysis (TGCCA) with orthogonal rank-R CP decomposition.
result TGCCA outperforms state-of-the-art methods on simulated and real data.
SGD recovers multiple signal vectors in noisy tensor PCA.
problem Estimating multiple signal vectors from noisy tensor observations.
method Online stochastic gradient descent (SGD) in high dimensions with detailed analysis of correlations.
result Sequential elimination of correlations allows recovery of all spikes from Np−2 samples. This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same…
Derives stress-energy identities in Liouville theory on compact surfaces.
problem Stress-energy tensor correlation functions on compact Riemann surfaces.
method Varying correlation functions with respect to background metric, treating different types of variations separately.
result Stress-energy correlation functions expressed as differential operators acting on primary field correlation functions.
There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result of imperfect modalities, missing entries or noise corruption. To address these c…
Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…
Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while i…
New algorithm detects tensor dependence structure alterations efficiently.
problem Detecting alterations in tensor dependence structures.
method Tensor-normal distributions, decorrelation, centralization, SERA (Sparsity-Exploited Reranking Algorithm).
result The proposed SERA algorithm controls false discovery rates effectively.
Neural networks learn faster with correlated latent variables.
problem Efficiently learning from higher-order correlations in neural networks.
method Analytical derivation and simulations of two-layer neural networks.
result Correlations between latent variables speed up learning from higher-order correlations.
Enhances labels from unlabeled data using sample correlations.
problem Lack of label distributions in real-world applications.
method Proposes LESC and gLESC methods to enhance label distributions.
result Improves performance of label enhancement through sample correlations.
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, diff…
New method improves tensor completion by selectively preserving important elements.
problem Recovering corrupted high-dimensional tensor data with missing entries and noise.
method Tensor weighted correlated total variation (TWCTV) regularizer with ADMM algorithm.
result Superior performance in image completion, denoising, and background subtraction tasks.
In many real-world applications, data are often unlabeled and comprised of different representations/views which often provide information complementary to each other. Although several multi-view clustering methods have been proposed, most of them routinely assume one weight for one view of features, and thus inter-vie…
A new tensor network method for image classification reduces computation cost.
problem Efficiently classifying images in high-dimensional spaces.
method Proposes a multi-layered tensor network (MLTN) that performs one MPS operation per layer, reducing computation cost.
result Reduces computation cost without degrading performance.
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of correlation in MPS restricts its representation power heavily for modeling complex…
Traditional stock market prediction approaches commonly utilize the historical price-related data of the stocks to forecast their future trends. As the Web information grows, recently some works try to explore financial news to improve the prediction. Effective indicators, e.g., the events related to the stocks and the…
Proposes a method to reveal nonlinearities in tensor data.
problem Capturing nonlinear relationships in high-dimensional tensor data.
method Linear tensor projection method to maximize prediction accuracy.
result Effective in revealing nonlinear relationships in tensor data.
New model fills in missing traffic data efficiently.
problem Missing data in large-scale spatiotemporal traffic data.
method Developed scalable tensor learning model LSTC-Tubal for imputation.
result LSTC-Tubal achieves high accuracy with lower computational cost.
DEMOTE uses neural diffusion-reaction processes to capture temporal dynamics in sparse tensor data.
problem Sparse and temporally associated tensor data with limited structural knowledge.
method Develops a neural diffusion-reaction process to estimate dynamic embeddings for tensor modes.
result Captures both commonalities and personalities in evolving tensor entries.
New method uses tensor networks to price multi-asset options efficiently.
problem Pricing multi-asset options via classical full-grid solvers is computationally infeasible due to the curse of dimensionality.
method Quantized tensor trains (QTT) transform the d-asset Black-Scholes PDE into a tractable high-dimensional problem.
result Full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions can be computed with high accuracy.
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and vector spaces in the edges, called tensor network. Such tensor networks have been …
GLSKF improves tensor completion by capturing both global and local variations.
problem Tensor completion with missing entries, especially in data with spatial or temporal side information.
method Integrates smoothness-constrained low-rank factorization with a locally correlated residual process.
result GLSKF achieves superior performance and scalability on real-world datasets.
Paper optimizes tensor deflation for non-orthogonal signals.
problem Recovering low-rank signals from noisy tensors with correlated components.
method Developed an asymptotic analysis and optimized deflation procedure using random tensor theory.
result Proposed an efficient tensor deflation algorithm that optimizes a parameter introduced in the deflation mechanism.
Study recovers spike order in noisy tensor estimation without SNR assumptions.
problem Estimating multiple signal vectors from noisy tensor observations.
method Gradient flow optimization of a nonconvex function.
result Determines sample complexity for efficient permutation recovery.
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …
Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. …
New method tackles non-smooth tensor data for better recovery.
problem Non-smooth changes in tensor data degrade traditional t-SVD methods.
method Learnable tensor nuclear norm, Alternating Proximal Multiplier Method (APMM), multi-objective tensor recovery framework.
result The proposed method effectively recovers tensor data with non-smooth changes.
Proposes a method to enhance multi-view learning by maximizing higher order correlations.
problem Losing intrinsic interconnections among multiple views in pairwise correlation maximization.
method Formulates multi-view data as a low rank approximation problem using higher order correlation tensor and solves it with the generating polynomial method.
result Consistently outperforms prior methods on real multi-view data.
This work generalizes transformer attention to capture higher-order correlations efficiently.
problem Detecting triple-wise connections that were impossible for transformers.
method Developed a generalized attention scheme using Kronecker computation, showing near-linear time algorithms for bounded entries.
result A near-linear time algorithm for generalized attention computation in the bounded-entry setting.
The paper analyzes deflation for estimating a low-rank spike in large tensors with noise.
problem Estimating a low-rank symmetric spike in large tensors with additive Gaussian noise.
method Characterization of deflation performance in terms of vector alignments and weights.
result Understanding deflation mechanism in noisy conditions and designing more efficient methods.
We propose a novel multilinear dynamical system (MLDS) in a transform domain, named L-MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal slices are built, and thus resulting in the computational independence in the tra…
Learning from spatio-temporal data has numerous applications such as human-behavior analysis, object tracking, video compression, and physics simulation.However, existing methods still perform poorly on challenging video tasks such as long-term forecasting. This is because these kinds of challenging tasks require learn…
New estimator for tensor weights with improved bias.
problem Estimating tensor weights from noisy data.
method Random matrix theory and KKT conditions.
result Asymptotically unbiased estimator for tensor rank.
Spatio-temporal data compression method reduces memory usage.
problem Efficiently storing and analyzing large spatio-temporal datasets.
method Adaptive sampling of tensor slices to compress and preserve structure.
result SkeTenSmooth outperforms other sampling methods in retaining patterns.
In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this paper, we study convergence and statistical properties of two-dimensional canoni…
Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Tensor latent factor models can describe higher-order correlations for spatial data. However, they are computationally expensive to train and are sensitive to initialization, leading to spatially incoher…
Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.
problem Estimating factors and loadings in high-dimensional panel data with non-negligible correlations.
method Tensor Principal Component Analysis (TPCA) for estimating factors and loadings in a tensor factor model.
result Simple TPCA is optimal for strong factors and can be improved for weak factors with alternating least-squares iterations.