JSRT improves regression tree performance by incorporating global node information.
problem Regression tree performance relies on local node means, ignoring global node information.
method Proposes JSRT by integrating global mean information from different nodes.
result Demonstrates superior performance and efficiency compared to other regression tree methods.
New technique finds globally optimal symbolic equations.
problem Finding globally optimal mathematical expressions.
method Formulated a mixed integer non-linear program (MINLP).
result Guaranteed global optimality in symbolic regression.
Global convergence for robust regression problems via IRLS with enhancements.
problem Global convergence for robust regression problems.
method Augmentations to IRLS to ensure global recovery and improved robustness.
result Global recovery guarantees for robust regression problems, outperforming state-of-the-art algorithms.
Proposes a tool to contrast global vs personalized models in clinical prediction.
problem Balancing global vs personalized models in clinical prediction.
method Localized regression approach using autoencoder for dimension reduction.
result Identification of patient subgroups where global models fall short.
EM algorithm converges globally for two-component mixed linear regression.
problem Global convergence of EM algorithm for mixed linear regression.
method Developed new theoretical analysis for EM algorithm convergence in mixed linear regression.
result EM algorithm converges globally for two-component mixed linear regression.
Non-asymptotic uniform rates for k-NN regression are derived.
problem Estimating functions from noisy observations with unknown lower dimensionality.
method Derives high-probability finite-sample uniform rates of consistency for k-NN regression.
result k-NN regression rates are optimal up to logarithmic factors and adapt to unknown lower dimensions.
Tensor regression networks improve neural network compression and regularization.
problem Improving neural network compression and regularization with low-rank tensor approximations.
method Investigating various low-rank tensor approximations in tensor regression networks.
result Tensor regression networks with Global Average Pooling layer outperformed in deep CNNs, while shallow CNNs with tensor regression and dropout achieved lower test error.
A new method assesses regression models' global optimality.
problem Challenges in evaluating regression models without access to true data.
method Information Teacher framework based on Shannon mutual information.
result Demonstrates capability to detect global optimality.
RWR converges to global optimum in certain settings.
problem Proving convergence of RWR to optimal policy.
method Iterative learning with return-weighted log-likelihood.
result RWR converges to global optimum under certain conditions.
Study how optimization methods' choices affect the solutions they find.
problem Characterize the solutions found by optimization methods under different potentials and norms.
method Examined mirror descent, natural gradient descent, and steepest descent for underdetermined linear regression and separable linear classification.
result The specific global minimum reached by an algorithm can be characterized by the potential or norm of the optimization geometry, independent of hyperparameters.
New method uses MDL to infer causal direction between variables.
problem Inferring causal direction from observational data of two variables.
method Information theoretic approach based on Kolmogorov complexity and MDL principle.
result Proposes a compression scheme for encoding local and global functional relations.
Adaptive method improves prediction intervals with global coverage guarantees and local error distribution.
problem Global coverage guarantees of conformal regression are often violated by local error distributions.
method Adaptive Conformal Regression with Jackknife+ Rescaled Scores
result Improves local coverage without sacrificing global coverage, especially in low-data regimes.
The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice difficult, because it requires a global optimization of a complicated function,…
Optimal inference in distributed quantile regression without stringent scaling conditions.
problem Challenges in achieving optimal inference in distributed quantile regression due to the non-smooth nature of the QR loss function.
method Double-smoothing approach applied to local and global objective functions, with a trade-off between communication cost and statistical error.
result Established a finite-sample theoretical framework for distributed QR estimators, showing a trade-off between communication cost and statistical error.
New globally convergent Newton method tackles ill-conditioned generalized self-concordant losses.
problem Optimization of ill-conditioned generalized self-concordant losses in machine learning.
method Sequence of problems with decreasing regularization parameters, linear convergence with logarithmic condition number scaling.
result First large-scale algorithm with optimal generalization bounds for logistic and softmax regressions in non-parametric settings.
Paper studies optimal federated learning for nonparametric regression with privacy constraints.
problem Federated learning for nonparametric regression with heterogeneous differential privacy constraints.
method Proposes distributed privacy-preserving estimators and investigates their risk properties.
result Establishes matching minimax lower bounds for global and pointwise estimation.
New methods find eigenvectors faster than Lanczos's method.
problem Finding the leading eigenvector efficiently.
method Coordinate-wise methods combining shift-and-invert with linear regression.
result Global convergence with runtime guarantees better than Lanczos's method.
New algorithm solves ℓ0-norm constrained multilinear logistic regression for tensor data.
problem Non-convex and nonsmooth ℓ0-norm constraints in multilinear logistic regression. method APALM+ method for globally convergent optimization. result APALM+ ensures convergence to a first-order critical point. Gradient descent converges geometrically to optimal self-attention parameters.
problem Training softmax self-attention layers for linear regression.
method Structure-aware gradient descent with preconditioner and regularizer.
result Gradient descent converges geometrically to global minima.
Paper proposes robust tensor regression method for tensor data analysis.
problem Outliers in tensor data analysis can make existing methods sensitive.
method Nonconvex relaxation of tensor tubal rank in optimization framework.
result Global convergence of proposed estimation algorithm under mild assumptions.
Global optimization for hybrid system identification problems.
problem Switching linear regression and bounded-error estimation in hybrid systems.
method Branch-and-bound strategy with efficient lower bounds for continuous optimization.
result Global optimality is always guaranteed with scalable algorithms.
Agents learn locally, converge globally in online learning with kernels.
problem Multi-agent learning with limited data and communication.
method Local regression functions with consensus constraints, functional stochastic gradient descent, and greedy subspace projections.
result Agents' functions converge to a neighborhood of the globally optimal one as the penalty parameter increases.
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
Paper addresses online identification and clustering for mixed linear regression models.
problem Online identification and clustering of mixed linear regression models.
method Introduces two online identification algorithms based on the EM principle, proving global convergence without i.i.d. data assumptions.
result Global convergence of the proposed algorithms for mixed linear regression models.
Proposes φ-table for statistical SHAP explanations in regression models.
problem Lack of clear directional summaries, uncertainty, and fidelity in SHAP feature importance.
method SHAP importance selection, fitting a standardized linear surrogate, reporting coefficients, uncertainty, fidelity, and stability.
result Extends SHAP into a statistical global explanation with direction, uncertainty, fidelity, and stability.
Local control regression improves portfolio optimization accuracy.
problem Expensive and inaccurate global control regression for portfolio optimization.
method Introduced local control regression combined with adaptive grids.
result Choosing a coarse grid for local regression produces accurate results.
Deep learning models forecast multiple yield curves with improved accuracy.
problem Globalization of financial markets affects yield curves.
method Combines self-attention mechanism and nonparametric quantile regression.
result Effective point and interval forecasts of future yields.
Study uses APT and QR to identify risk factors affecting crude oil returns.
problem Determining the risk factors impacting crude oil returns.
method Employed Arbitrage Pricing Theory and Quantile Regression.
result Identified key risk factors: industrial production, inflation, energy prices, yield curve shape, and economic policy uncertainty.
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.
Paper addresses global convergence of MLR estimation under weak data conditions.
problem Learning mixed linear regression models with general data conditions.
method Two-step recursive identification algorithm using least squares and EM principles.
result Global convergence and optimal clustering performance established under general data conditions.
New method uses nearest neighbors quantile filter for probabilistic energy forecasting.
problem Creating accurate probabilistic energy forecasts using complex data mining techniques.
method Uses a new nearest neighbors quantile filter to create quantile regressions without a non-differentiable cost function.
result Demonstrates superior performance in Global Energy Forecasting Competition 2014.
A novel tree algorithm improves time series forecasting accuracy.
problem Improving accuracy in non-linear time series forecasting.
method Developed a hierarchical TAR model as a regression tree that trains globally across series, introducing a forecasting-specific tree algorithm with cross-series learning.
result Significantly higher accuracy than state-of-the-art tree-based algorithms and benchmarks across four metrics.
This paper analyzes local optimizers in Bayesian optimization for expensive functions.
problem Finding global optimizers in Bayesian optimization is challenging and time-consuming.
method The paper analyzes three acquisition functions (PI, EI, GP-UCB) and their local optimizers.
result Local optimizers can be used effectively in Bayesian optimization, reducing search time.
Method learns all edges and link parameters globally for binary pairwise Markov models.
problem Learning sparse Ising models with sparsity assumption.
method l1-regularized logistic regression for simultaneous estimation of all edges and link parameters.
result Numerical experiments show the advantage of the simultaneous estimation method.
Paper proposes a new method for robust modal regression.
problem Estimating the global mode of conditional density functions robustly.
method Directly approximates the gradient of modal regression risk using kernelized and neural-network-based log-density derivative estimators.
result Proposed methods achieve superior performance on various datasets.
This paper proposes a new method for GLM estimation using distance penalties to handle constraints.
problem Handling constraints in generalized linear models (GLM) is complicated.
method The approach uses distance penalties to optimize the log-likelihood, avoiding shrinkage.
result Distance penalties provide a flexible and non-shrinking alternative to traditional penalties.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Meta-analysis improves interpretation and efficiency across similar but non-identical datasets.
problem Meta-analysis of heterogeneous data in high dimensions.
method Integrative sparse regression with a global parameter for adaptability and anonymity.
result Superior identification of global parameter for high-dimensional linear models.
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We prove that the sparse estimator from such a method can retain all of the importa…
Proposes a framework to incorporate global sensitivity into local surrogate models.
problem Narrowing focus to local scale in surrogate modeling leads to re-learning global trends.
method Integrates global sensitivity analysis into local surrogate models through input warping.
result Local models become equally sensitive to all input directions, focusing on local dynamics.
FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.
problem Global optimization of non-convex objective functions over measure space.
method Introduces Fast Spawn\&Prune (FS\&P) combining CPGD with birth-death process.
result First theoretical guarantee of global convergence for discrete-time stochastic algorithms.
BOKE optimizes expensive functions with reduced computational costs.
problem High computational cost of Gaussian process-based Bayesian optimization.
method Kernel regression and density-based exploration integrated into confidence bounds.
result BOKE achieves global convergence and superior computational efficiency.
Kernel models learn low-dimensional predictive subspaces from input data.
problem Learning effective feature transformations in kernel models.
method Study of a compositional kernel ridge regression model.
result Global minimizers of the objective function identify the subspace with high probability.
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
problem Dimension reduction and regression are traditionally treated separately in multivariate data analysis.
method PLS-Lasso integrates dimension reduction directly into the regression process, presenting two formulations: PLS-Lasso-v1 and PLS-Lasso-v2.
result PLS-Lasso-v1 and PLS-Lasso-v2 outperform Lasso in financial index tracking.
Paper introduces a new sparse regression method using hard-thresholding penalties.
problem Sparse modeling in high-dimensional data.
method Sparse regression with hard-thresholding penalty.
result Oracle inequalities and shrinkage effects demonstrated for the proposed method.
Using open source data, we observe the fascinating dynamics of nighttime light. Following a global economic regime shift, the planetary center of light can be seen moving eastwards at a pace of about 60 km per year. Introducing spatial light Gini coefficients, we find a universal pattern of human settlements across dif…
New algorithm finds global minimum for TREX, controlling FDR.
problem Sparse high-dimensional regression with TREX's non-convex optimization.
method Polynomial-time algorithm for non-convex TREX optimization.
result Global minimum found for TREX, controlling FDR.
Improved Fréchet regression tackles noise and multicollinearity.
problem Addressing noise and multicollinearity in multi-label regression.
method Implicit regularization framework for explicit modeling of relationships.
result Effective modeling of complex dependencies without introducing biases.