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.
Study assesses drought and late-frost risks in Bavaria using vine copulas.
problem Assessing risks of late-frost and drought in Bavaria due to climate change.
method Used vine copula models for non-Gaussian and asymmetric dependencies, with univariate and bivariate regression analyses.
result Identified 'at-risk' regions for forest adaptation.
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.
Point forecasting of univariate time series is a challenging problem with extensive work having been conducted. However, nonparametric probabilistic forecasting of time series, such as in the form of quantiles or prediction intervals is an even more challenging problem. In an effort to expand the possible forecasting p…
Kolmogorov-Arnold Networks achieve optimal convergence rates in nonparametric regression.
problem Nonparametric function approximation in multivariate settings.
method Structured additive and multiplicative KANs using B-splines.
result Achieve minimax-optimal convergence rate O(n−2r/(2r+1)) for Sobolev space functions. Shallow neural networks can represent polynomials efficiently.
problem Representing polynomials using shallow neural networks.
method Using shallow neural networks of width 2(R+d)d to represent d-variate polynomials of degree R. result Derives minimax optimal convergence rate for shallow networks to unknown univariate regression functions.
Mirror flow in shallow neural networks shows similar implicit bias to gradient flow, with key differences in curvature penalties.
problem Analyzing implicit bias in shallow neural networks with mirror flow.
method Characterization through variational problems and scaled potentials.
result Mirror flow with scaled potentials induces a rich class of biases not captured by RKHS norms.
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient gradient computation that enables gradient-based optimization procedures, including…
We introduce a family of adaptive estimators on graphs, based on penalizing the ℓ1 norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate nonparametric regression, to graphs. Analogous to the univariate case, graph trend filteri…
New statistical methods improve explainability of boosting models.
problem Uncertainty quantification for boosting models is computationally intensive and hard to interpret.
method Derive methods for statistical inference using gradient boosting and Boulevard regularization.
result Achieve asymptotically normal predictions with theoretical guarantees and runtime independent of data size.
The paper develops a new method for estimating non-parametric regression functions with spatio-temporal dependencies.
problem Estimating non-parametric regression functions with spatio-temporal dependencies.
method Locally Adaptive Regression Splines (LARS) with ADMM algorithm.
result The method shows superior performance compared to existing techniques.
Constructs bivariate quantiles using vine copulas for multivariate analysis.
problem Need for research in multivariate quantiles, especially for bivariate responses.
method Constructs bivariate (conditional) quantiles using vine copula based bivariate regression model with a novel tree sequence graph structure.
result Avoids typical shortfalls of regression like transformations, interactions, collinearity, and quantile crossings.
We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…
Unified study of nine multi-output conformal methods with generalized scores.
problem Challenges in extending conformal prediction to multi-output problems.
method Nine conformal methods with generalized multi-output conformity scores.
result Generalized scores ensure asymptotic conditional coverage and exact finite-sample marginal coverage.
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…
Global models outperform univariate benchmarks in complex time series forecasting.
problem Comparing global forecasting models to univariate benchmarks in various challenging scenarios.
method Simulated datasets with controlled characteristics, including homogeneity, complexity, and series lengths. Global forecasting models (RNN, LGBM) compared to univariate techniques.
result Global models like RNN and LGBM are competitive in complex scenarios with short series lengths and heterogeneous data.
We develop Square Root Graphical Models (SQR), a novel class of parametric graphical models that provides multivariate generalizations of univariate exponential family distributions. Previous multivariate graphical models [Yang et al. 2015] did not allow positive dependencies for the exponential and Poisson generalizat…
This paper aims to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines und…
Multivariate boosted trees improve forecasting and control by capturing correlated predictions.
problem Capturing multivariate target cross-correlations and applying structured penalties to predictions.
method A computationally efficient algorithm for fitting multivariate boosted trees.
result Multivariate trees outperform univariate counterparts in correlated prediction scenarios.
DSPPs improve predictive distributions in scalable regression tasks.
problem Improving predictive distributions in scalable regression tasks.
method Inspired by DGPs, DSPPs use mini-batch training and kernel basis functions for uncertainty control.
result DSPPs provide significantly better calibrated predictive distributions than other methods.
MRI image quality affects statistical and predictive analysis of brain morphology.
problem Impact of MRI image quality on statistical and predictive analysis of brain morphology.
method Systematic testing of image quality on univariate statistics and machine learning classification using three large datasets.
result Low-quality MRI data significantly affects detecting significant sex/gender differences in smaller samples, but not in larger ones.
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.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are monotonically increasing. In this article, we present a new method for such regression …
Method estimates noise variance in Gaussian process regression.
problem Estimating noise variance in Gaussian process regression models.
method Reduces hyperparameter space, uses marginal likelihood function, derives bounds and asymptotes.
result Computational advantages and robustness compared to traditional methods.
G-GLN extends GLNs to multiple regression and density modeling.
problem Learning features in deep neural networks.
method G-GLN uses a distributed and local credit assignment mechanism based on optimizing a convex objective.
result G-GLN achieves competitive or state-of-the-art performance on regression benchmarks.
Modeling stock returns and volatility using a bivariate gamma generalized Laplace law.
problem Analyzing stock returns and volatility using a new statistical model.
method Maximum likelihood estimation for a bivariate generalized Laplace distribution, simplifying to linear regression.
result Explicit estimators derived with nonstandard convergence rates for certain parameter configurations.
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.
PEER tackles multi-response regression with incomplete outcomes efficiently.
problem Challenges in estimating, predicting, and computing with large-scale multi-response regression and incomplete outcomes.
method PEER converts multi-response regression into parallel univariate-response regressions.
result PEER achieves consistency in estimation, prediction, and variable selection.
We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both parsimonious and highly interpretable, as it implies that the outcome is related…
We consider the problem of learning a mixture of linear regressions (MLRs). An MLR is specified by k nonnegative mixing weights p1,…,pk summing to 1, and k unknown regressors w1,...,wk∈Rd. A sample from the MLR is drawn by sampling i with probability pi, then outputting (x,y) wh…
Study learns a projection and function in Gaussian models.
problem Learning a one-dimensional projection and a univariate function in high-dimensional Gaussian models.
method Gradient flow dynamics of alternating scheme, RKHS adaptation.
result Gradient flow dynamics converge with rate controlled by Gaussian regularity.
New theory shows large learning rates prevent overfitting in neural networks.
problem Generalization of two-layer ReLU neural networks in noisy regression problems.
method Gradient descent with constant learning rate converges to stable minima.
result Gradient descent with large learning rates finds smooth, sparse fits.
New method extracts aleatoric and epistemic uncertainties from regression-based neural networks.
problem Need for principled uncertainty reasoning in machine learning systems.
method Learning evidential distributions for aleatoric and epistemic uncertainties.
result Allows for the simultaneous extraction of both uncertainties without sampling or out-of-distribution data.
VEST automates feature engineering for time series forecasting.
problem Challenges in time series forecasting with improved performance.
method VEST combines auto-regression with statistical summarization of recent past dynamics.
result VEST significantly improves forecasting performance.
We present a novel k-way high-dimensional graphical model called the Generalized Root Model (GRM) that explicitly models dependencies between variable sets of size k > 2---where k = 2 is the standard pairwise graphical model. This model is based on taking the k-th root of the original sufficient statistics of any univa…
We consider the problem of nonparametric regression when the covariate is d-dimensional, where d≥1. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE and the constrained Hardy-Krause variation LSE. We show that these two LSEs are…
Proposed by Donoho (1997), Dyadic CART is a nonparametric regression method which computes a globally optimal dyadic decision tree and fits piecewise constant functions in two dimensions. In this article we define and study Dyadic CART and a closely related estimator, namely Optimal Regression Tree (ORT), in the contex…
Paper proposes a new GPR-HS framework for accurate VCV estimation in global equity indices.
problem Accurate forecasting of Volatility-Covariance Matrix (VCV) for regulatory processes.
method Hybrid Gaussian Process Regression-Historical Simulation (GPR-HS) framework.
result GPR-HS framework achieves regulatory compliance and outperforms static VaR benchmarks.
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.
The paper uses random matrix theory for multi-task regression, improving time series forecasting.
problem Improving time series forecasting using multi-task regression.
method Applying random matrix theory to multi-task regression problems, deriving closed-form solutions for optimization.
result Provides a robust foundation for hyperparameter optimization in multi-task regression scenarios.
This paper improves multi-label ranking by reweighting univariate losses, enhancing consistency and performance.
problem Improving multi-label ranking performance while maintaining consistency.
method Systematic study of consistency and generalization error bounds for learning algorithms, proposing a reweighted univariate loss.
result Inconsistent pairwise losses can lead to better performance than consistent univariate losses in practice.
Smart Bayes integrates generative and discriminative features for improved classification.
problem Improving classification performance by combining generative and discriminative modeling.
method Integrates generative likelihood-ratio features into a logistic-regression-style classifier.
result Often outperforms logistic regression and Naive Bayes in simulations and real data.
Unified probabilistic gradient boosting for entire conditional distribution modeling.
problem Creating accurate probabilistic forecasts from regression tasks.
method Unified probabilistic gradient boosting framework using XGBoost and LightGBM, modeling conditional moments or CDF via Normalizing Flows.
result Achieves state-of-the-art forecast accuracy.
Generative models often fail to preserve joint structure despite matching marginals.
problem Generative models fail to capture complex dependencies beyond univariate marginals.
method Introduced D_Sigma(P,Q) = ||Sigma_P - Sigma_Q||_F to measure covariance-level dependence fidelity.
result Covariance-level divergence can lead to structural instability in downstream inference.
New ensemble methods improve time series forecasting accuracy.
problem Global Forecasting Models (GFM) lack localisation for heterogeneous datasets.
method Ensemble techniques with clustering and varied GFM models.
result Significantly higher accuracy achieved compared to baseline models.
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 group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…