Paper studies quantized LRMR with random dithering for correlated tasks.
problem Estimating coefficient matrix in quantized multivariate regression.
method Uniform quantization with random dithering, constrained and regularized Lasso estimators.
result Achieves minimax optimal rate with dithering, slightly worsens quantization effect.
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Robustly estimates mean with quantized data and corruption.
problem Mean estimation under quantization and adversarial corruption.
method Constructs multivariate robust estimators in two settings.
result Optimal estimators up to logarithmic factors.
Study quantization effects on high-dimensional linear regression learning.
problem Understanding quantization's impact on learning high-dimensional linear regression models.
method Analyzes stochastic gradient descent for high-dimensional linear regression under various quantization targets.
result Establishes precise bounds on excess risk for different quantization schemes.
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.
A new method quantizes output space for multi-target regression.
problem Predicting multiple continuous targets using shared predictors.
method MRQ method that quantizes output space to model dependencies and scale.
result MRQ achieves high scalability and competitive accuracy.
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.
This work studies scaling laws for low-precision training in high-dimensional linear regression.
problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.
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.
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.
In this paper, we study the randomized distributed coordinate descent algorithm with quantized updates. In the literature, the iteration complexity of the randomized distributed coordinate descent algorithm has been characterized under the assumption that machines can exchange updates with an infinite precision. We con…
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.
A new method improves quantile regression for high-dimensional data.
problem Handling heteroscedastic, multimodal, or skewed data in quantile regression.
method Dynamic prototypes-based probability density estimation with conformalized high-density quantile regression.
result Enhanced prediction regions with valid coverage guarantees and scalability to higher dimensions.
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.
The multivariable Conway function is generalized to oriented framed trivalent graphs equipped with additional structure (coloring). This is done via refinements of Reshetikhin-Turaev functors based on irreducible representations of quantized gl(1|1) and sl(2). The corresponding face state sum models for the generalized…
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.
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.
Optimizes binary regression models with gradient ascent-descent methods.
problem Regression problems with binary weights in quantized learning and digital communication.
method Maximin optimization using gradient ascent-descent methods.
result The approach is optimal in linear regression with low noise and robust regression with few outliers.
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.
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.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
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.
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.
EP method speeds up Bayesian probit regression in high dimensions.
problem Computational challenges in high-dimensional Bayesian probit regression.
method Adapting EP approximation to multivariate Gaussian prior and skew-normal distribution.
result EP routine is computationally feasible in high-dimensional settings.
Optimizes minimum-volume prediction sets for multivariate regression.
problem Lack of efficient methods for multivariate conformal prediction.
method Optimization-driven framework for minimum-volume covering sets.
result Efficient and informative prediction sets with tight coverage.
The Morse-Smale complex of a function f decomposes the sample space into cells where f is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare multivariate functions. In this paper, we present some statistical results on es…