The paper analyzes multivariate Hawkes processes and their induced population processes.
problem Analyzing the time-dependent joint probability distribution of multivariate Hawkes processes.
method Exact and asymptotic analysis of general multivariate Hawkes processes and their induced population processes.
result Full characterization of the time-dependent joint transform of the multivariate population process and its intensity process.
CA-NN uses neural networks to scale correspondence analysis.
problem Scaling correspondence analysis to large datasets.
method Reinterpreting CA as a functional optimization problem over finite variance functions, approximated by neural networks.
result CA-NN enables scalable correspondence analysis.
This paper improves PPCA robustness using t-distributions.
problem Improving robustness of probabilistic PCA.
method Using multivariate t-distributions and a hierarchical model. result Clarified the correct correspondence between the multivariate t-PPCA framework and the hierarchical model. Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
The paper tackles noisy functional data by exploring a multivariate perspective.
problem Noisy functional data measured on discrete points.
method Factor model and principal components analysis.
result The latent signal can be accurately estimated using multivariate methods.
PCA simplifies multivariate extreme data analysis.
problem Analyzing multivariate extreme values with high-dimensional data.
method Principal Component Analysis (PCA) for dimensionality reduction.
result PCA helps preserve essential information for extreme value analysis.
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
New methods estimate multivariate shortfall risk more efficiently.
problem Estimating multivariate shortfall risk is computationally challenging.
method Combines Fourier inversion and RQMC sampling in frequency domain.
result Fourier RQMC methods outperform existing benchmarks.
MFSSA improves reconstruction accuracy of multivariate functional time series.
problem Improving reconstruction accuracy of multivariate functional time series.
method Developed MFSSA, a functional extension of MSSA, for different dimensional domains.
result Better reconstruction accuracy of MFTS signals using MFSSA compared to other methods.
Proposes a multivariate regression model for better analysis of multiple datasets.
problem Insufficient performance of single-dataset analysis in integrative studies.
method Sparse estimation for variable and group selection, alternating direction method of multipliers algorithm.
result Demonstrated improved performance through simulations and real data analysis.
Study uses copulas and DCC-GARCH for multivariate risk analysis of VaR and CVaR.
problem Multivariate risk analysis for Value at Risk (VaR) and Conditional Value at Risk (CoVaR).
method Copulas and Dynamic Conditional Correlation (DCC)-GARCH models applied to historical financial data.
result Comparison of different copula families for goodness-of-fit and effectiveness.
Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and anomaly detection. One convenient (non-parametric) characterization of extremal de…
The paper examines stochastic ordering of Gini indexes for multivariate elliptical risks.
problem Stochastic ordering of Gini indexes for multivariate elliptical risks.
method Established conditions for monotonicity of Gini index in usual stochastic order.
result Suitable conditions for multivariate elliptical risks generalize those for multivariate normal risks.
New similarity index avoids limitations of CCA in neural networks.
problem Limitations of existing methods in measuring neural network representation similarity.
method Introducing a similarity index based on centered kernel alignment (CKA) to measure representational similarity matrices.
result CKA reliably identifies correspondences between representations in networks trained from different initializations.
Research uses deep learning and copulas to predict multivariate survival data.
problem Handling right-censored and correlated multivariate survival data.
method Integrates deep learning, copula functions, and survival analysis. Uses copula-based activation functions to model nonlinear dependencies.
result Enhanced prediction accuracy for multivariate survival responses.
New sampling strategy preserves relationships in multivariate scientific data.
problem Reducing storage and enabling efficient multivariate analyses on large scientific data.
method Uses principal component analysis for multivariate data and combines with existing univariate sampling algorithms.
result Efficacy demonstrated on real-world data sets, showing data reduction and multivariate analysis ease.
Meta algorithm solves multivariate optimization using univariate optimizers.
problem Multivariate global optimization problems.
method Meta algorithm combining univariate global optimizers.
result Meta algorithm provides robust regret guarantees.
Regularizes ML algorithms for robust multivariate analysis against distribution shifts.
problem Ensuring robustness of multivariate analysis algorithms against distribution shifts.
method Integrates a causal regularisation term into the loss function of multivariate analysis algorithms.
result Demonstrates improved out-of-distribution generalisation with reduced-rank regression and partial least squares.
A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample v…
Novel MCA-based rule mining speeds up psychiatric disorder screening.
problem High dimensionality and heterogeneity in clinical data.
method Developed a novel categorical rule mining method based on MCA.
result 100x faster than state-of-the-art methods for large datasets.
Unified derivation of stochastic order conditions for elliptical distributions.
problem Classifying multivariate elliptical distributions based on stochastic orders.
method Established an identity for comparing expectations of functions of elliptical vectors and used it to derive conditions for stochastic orders.
result Unified derivation of conditions for various stochastic orders in multivariate elliptical distributions.
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a multivariate generalized Gaussian process model, and derive Taylor and Laplace al…
Proposes a new model for non-linear regression of multivariate time series data.
problem Regression models for non-scalar variables, especially time series, have limitations.
method Develops a non-linear function-on-function model using neural networks.
result Demonstrates effectiveness through real-world applications.
Study invariant connections on multivariate Gaussian distributions.
problem Understanding statistical connections on multivariate Gaussian distributions.
method Investigate invariant connections on N0n with the Fisher metric. result Explicitly determined invariant connections and their moduli spaces.
Post-detection analysis identifies responsible coordinates for multivariate change-points.
problem Identifying which coordinates in multivariate time series change after a detected change-point.
method Two-sample testing procedures with nonparametric tests for Type I error control.
result Strong performance of proposed post hoc statistical procedures.
CDSA uses self-attention to impute missing values in multivariate, geo-tagged time series data.
problem Missing values in multivariate, geo-tagged time series data.
method Cross-Dimensional Self-Attention (CDSA) for sequence modeling across time, location, and sensor measurements.
result CDSA outperforms state-of-the-art methods in imputation and forecasting on real-world datasets.
New algorithm extracts shared latent space for cortico-muscular interactions.
problem Challenges of high dimensionality and limited sample sizes in multivariate cortico-muscular analysis.
method Structured and sparse partial least squares coherence (ssPLSC) algorithm.
result ssPLSC achieves competitive or better performance in scenarios with limited sample sizes and high noise levels.
A new method detects anomalies in multivariate streams without unit dependence.
problem Detect anomalies in multivariate streams without unit dependence.
method Proposes SigMahaKNN combining variance norm and path signature.
result SigMahaKNN detects anomalies better than existing methods.
A method for inferring graph from multivariate time series using ADMM.
problem Inferring conditional independence graph from multivariate Gaussian time series.
method Formulated as multi-attribute graph estimation, used ADMM to minimize penalized negative log-likelihood.
result Proposed method outperforms existing frequency-domain approaches in graph edge detection.
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
Graphical estimation of count time series dependencies.
problem Estimating dependencies between multivariate count time series.
method Parameter-driven generalized linear model with l1-type regularization and MCEM algorithm.
result Characterization of disease spread interdependence and sources/sinks in Greater Mumbai.
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market comp…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish …
Function trees simplify complex ML models for better understanding.
problem Understanding and interpreting machine learning model predictions.
method Representing a multivariate function as a tree of simpler functions.
result Function trees reveal the global internal structure of functions.
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
New method uses contours of segmented images for X-ray classification.
problem Classifying X-ray images of segmented radiography.
method Develops a new approach for image analysis of multivariate planar curves, addressing alignment issues.
result Demonstrates the robustness and appeal of the proposed method through detection of cardiomegaly and numerical experiments.
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the minimax error rate that is sharp up to logarithmic factors. We also analyze the p…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, F measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives…
New method for estimating functional Gaussian graphical models for multivariate data.
problem Challenges in extending Gaussian graphical models to multivariate functional data due to compact covariance operators.
method Introducing partial separability for multivariate functional data, leading to a novel Karhunen-Loève expansion and efficient estimation through the joint graphical lasso.
result A well-defined functional Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of identical fixed dimension.
Paper proposes copula-based models for analyzing multivariate zero-inflated continuous data.
problem Challenges in analyzing multivariate zero-inflated continuous data with mixed discreteness and continuity.
method Proposes two copula-based density estimation models and rectified Gaussian copula.
result Demonstrates superior performance compared to conventional methods.
This study improves estimation of the first principal component in multivariate functional data.
problem Estimating the first principal component of multivariate random processes.
method Defined covariance functions and operators, introduced LASSO optimization, and established minimax lower bounds.
result The method provides an optimal variance in the minimax sense for estimating eigenelements.
Researchers forecast VoIP traffic in mobile networks using multivariate time series analysis.
problem Predicting VoIP traffic behavior in real mobile networks for better resource allocation.
method Multivariate time series analysis, Vector Autoregressive models, machine learning techniques.
result Forecasting accuracy and insights into VoIP traffic dynamics.
This paper extends hypergraph construction to multivariate time series using signature transforms.
problem Constructing hypergraphs from collections of multivariate time series.
method Leveraging signature transforms to introduce controlled randomness and robustness.
result Validated on synthetic datasets, the method enhances robustness in hypergraph construction.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
problem Understanding minimal dependence among Bernoulli random vectors.
method Geometric and algebraic representations of multivariate symmetric Bernoulli distributions.
result Characterizes extremal negative dependence and builds minimal dependence copulas.
Extends online linear regression to handle multivariate data.
problem Hierarchical forecasting with multivariate responses.
method Introduces MultiVAW, extending Vovk-Azoury-Warmuth algorithm to multivariate setting.
result Achieves logarithmic regret in time for multivariate online linear regression.
A new method handles mismatched data in multivariate regression.
problem Handling mismatched data in multivariate linear regression.
method Two-stage approach: first stage estimates parameters, second stage estimates permutation.
result Permutation recovery conditions become less stringent with increasing number of responses.
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix map…