Proposes a new test for validating multivariate dynamic regression models.
problem Inadequate exogeneity conditions for conventional model specification tests in dynamic systems.
method Develops a generalized Durbin estimator for multiple-equation systems with dynamic dependencies, and constructs Wald tests.
result Bootstrap-based Wald tests improve finite-sample size control and validate the null hypothesis in multifactor models.
New framework for regression trees with multivariate response and dynamic mean vectors.
problem Characterizing and implementing regression trees for multivariate responses.
method High dimensional model with dynamic mean vectors over multi-dimensional change axes.
result Optimal rate of convergence and asymptotic valid confidence intervals for change points.
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite di…
We investigate the optimal structure of dynamic regression models used in multivariate time series prediction and propose a scheme to form the lagged variable structure called Backward-in-Time Selection (BTS) that takes into account feedback and multi-collinearity, often present in multivariate time series. We compare …
We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…
This paper reviews SDR methods for multivariate response regression.
problem Handling sufficient dimension reduction for multivariate response regression.
method Characterizes SDR estimators as inverse or forward regression methods.
result Pooled marginal, projective resampling, distance-based, ordinary least squares, partial least squares, and semiparametric SDR estimators are discussed.
Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
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.
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for constructing sparse estimates of the multivariate regression coefficient matrix that accoun…
The paper analyzes the generalizability of linear autoencoders and multivariate linear regression.
problem Limited theoretical understanding of linear autoencoders' performance.
method Proposes a PAC-Bayes bound for multivariate linear regression and shows LAEs as constrained models.
result The proposed PAC-Bayes bound is tight and correlates with practical metrics.
The paper introduces new estimators for multivariate functions using Fourier methods.
problem Estimating multivariate functions like densities and regression functions.
method Monte Carlo estimators based on the Fourier integral theorem.
result Established rates of convergence for new estimators, often superior to existing methods.
Paper proposes a joint quantile regression for VaR and ES forecasting.
problem Forecasting Value at Risk (VaR) and Expected Shortfall (ES) of multiple assets simultaneously.
method Multivariate quantile regression framework with time-varying process for VaR and ES.
result The proposed method outperforms other models in risk measure forecasts.
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
Bayesian neural network models improve uncertainty quantification in multivariate regression.
problem Uncertainty quantification in multivariate regression models with heteroscedastic noise.
method Proposes Bayesian Last Layer neural network models and EM algorithms for parameter learning.
result Capable of disentangling aleatoric and epistemic uncertainty.
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.
This study compares multivariate vs univariate machine learning for multi-output regression.
problem When to use multivariate ensemble techniques over separate univariate models.
method Comparative analysis of different multivariate approaches for multi-output regression.
result Multivariate ensemble techniques outperform separate univariate models in simulations.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
NGBoost boosts multivariate probabilistic regression.
problem Joint probabilistic regression for multivariate targets.
method Natural Gradient Boosting for nonparametric modeling.
result Competitive performance in oceanographic velocity prediction.
New method for multivariate distribution regression using NPT metric.
problem Regression with multivariate distributional responses and Euclidean predictors.
method Fréchet regression with nonparanormal transport (NPT) metric.
result Efficient estimation and granular interpretation of predictor effects.
We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly corrupted manifold-valued responses, a bottleneck issue commonly encountered in pr…
TSRGA scales multivariate linear regression for feature-distributed data.
problem Multivariate linear regression for feature-distributed data with high dimensions and many computing nodes.
method Two-stage relaxed greedy algorithm (TSRGA) for multivariate linear regression.
result TSRGA is highly scalable and can yield low-rank coefficient estimates.
Improved robustness in multivariate regression and classification with DRO under Wasserstein metric.
problem Outliers in covariates and responses.
method Distributionally Robust Optimization (DRO) with Wasserstein metric ambiguity set and regularization.
result Significant improvement in predictive error and robustness.
SMART combines decision trees and MARS for better regression modeling.
problem High variance in decision trees for continuous relationships, poor performance in MARS for discontinuities.
method SMART uses a decision tree to identify subsets with distinct continuous relationships, then applies MARS to fit these relationships independently.
result SMART improves regression performance over state-of-the-art methods in capturing discontinuities and continuous relationships.
Neural optimal transport improves multivariate conformal prediction.
problem Multivariate quantile regression challenges and existing methods ignore joint distribution geometry.
method Combines neural optimal transport with amortized optimization for efficient training and faster inference.
result Constructs tighter and more informative predictive regions for multivariate conformal prediction.
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.
Combines MCTM and NF for flexible multivariate density regression with interpretable marginals.
problem Difficult interpretation of flexible NF models and limitations of MCTM in flexibility.
method Hybrid approach combining MCTM for interpretable marginals and NF for complex joint distributions.
result Demonstrates versatility and improved performance compared to MCTM and other NF models.
SBAMDT uses adaptive soft splits to model complex decision boundaries.
problem Limited ability of standard decision trees to capture complex decision boundaries.
method Probabilistic additive decision tree model with adaptive soft multivariate splits.
result Demonstrated improved predictive performance on synthetic and real datasets.
This paper improves QoS metric prediction in DTNs using diffusion models.
problem Improving QoS metric prediction in Delay-Tolerant Networks (DTNs) to enhance network performance.
method Formulates QoS metric prediction as a probabilistic forecasting problem on multivariate time series, incorporating latent temporal dynamics.
result The proposed approach outperforms traditional methods in QoS metric prediction for DTNs.
Bayesian approach for multivariate density regression of complex data.
problem Regression of multivariate density-valued responses on predictors.
method Bayesian inference using sliced Wasserstein barycenter and SW distance.
result Accurate fits and reliable predictions for complex data.
We propose a calibrated multivariate regression method named CMR for fitting high dimensional multivariate regression models. Compared with existing methods, CMR calibrates regularization for each regression task with respect to its noise level so that it simultaneously attains improved finite-sample performance and tu…
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…
Improved local multivariable regression for better inference with limited data.
problem Limited sample size hampers local polynomial/multivariable regression.
method Prediction-Powered Inference (PPI) algorithm for local multivariable regression.
result Significantly reduces estimation variance without increasing error.
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
Proposes iVDFM for identifying latent factors in multivariate time series.
problem Identifying latent factors in multivariate time series with structural dynamics.
method Identifiable Variational Dynamic Factor Model (iVDFM) with iVAE-style conditioning.
result Identifiable latent factors up to permutation and component-wise affine transformations.
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying spar…
FineMorphs models smooth transformations for multivariate regression.
problem Efficiently modeling complex transformations for multivariate regression.
method Optimal control of affine and diffeomorphic transformations using smooth vector fields.
result FineMorphs can reduce dimensionality and adapt to large datasets.
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.
Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.
problem Functional predictor selection and estimation of smooth functional coefficients in high-dimensional multivariate functional data.
method Functional group-sparse regression methods in a generic Hilbert space of infinite dimension.
result Consistency of estimation and selection (oracle property) under infinite-dimensional Hilbert spaces.
In multivariate regression, a K-dimensional response vector is regressed upon a common set of p covariates, with a matrix B∗∈Rp×K of regression coefficients. We study the behavior of the multivariate group Lasso, in which block regularization based on the ℓ1/ℓ2 norm is used for supp…
Bayesian DDR models complex multivariate distributions.
problem Modeling relationships between multivariate distributions with differing dimensions.
method Generalized Bayesian framework using sliced Wasserstein distance and MALA for inference.
result Posterior consistency and robust fits demonstrated in simulations and real data.
Robust multivariate linear regression methods for online and offline use.
problem Estimating parameters of multivariate Gaussian linear regression models robustly.
method Robust versions of least-square criterion with online and offline algorithms.
result Asymptotic normality of robust estimates proved under weak assumptions.
In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a partial least squares solution and selects the most important variables for each facto…
Software helps teach latent variable methods in multivariate data analytics.
problem Challenges in understanding multivariate data analytics for students.
method Interactive software for comparing latent variable methods.
result Builds intuition on choosing methods and interpreting coefficients.
Model predicts individual insurance claim reserves using activation patterns.
problem Accurately predicting individual claim reserves in insurance contracts.
method Multinomial logistic regression to model claim activation and development.
result The model generates accurate predictions of total and per coverage reserves.
New method improves calibration in multi-output probabilistic models.
problem Challenges in achieving multivariate calibration in multi-output regression.
method General regularization framework to enforce multivariate calibration during training for arbitrary pre-rank functions.
result Significant improvement in calibration across all pre-rank functions without sacrificing predictive accuracy.
Proposes MinPEN framework for estimating relationships in multivariate models.
problem Estimating relationships between multivariate outcomes in statistical learning.
method MinPEN framework using minimum function penalty for non-convex optimization.
result Theoretical and practical validation of MinPEN framework for multivariate models.
The paper proposes a new auto-regressive model for multivariate distributional time series.
problem Statistical analysis of multivariate time series of probability measures.
method Wasserstein space, auto-regressive model, iterated random function systems.
result Consistent estimator for auto-regressive coefficients with sparse structure.
Improves MARS for nonparametric multivariate regression with dimension reduction.
problem High number of basis functions in MARS for high-order interactions.
method Linear combinations of covariates for dimension reduction, facilitating gradient calculation and eigen-analysis for estimation.
result Asymptotic theory and numerical studies show improved performance over MARS.