Auto-regressive models improve smoothing efficiency with exponentially tapered windows.
problem Improving time-series smoothing efficiency.
method An auto-regressive formulation for time-series smoothing.
result Auto-regressive models result in moving means with exponentially tapered windows.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We prove the existence of an optimal MAPE model and we show the universal consistency of Empirical Risk Minimization based on the MAPE. We also show that finding the best model under…
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
problem Finding local modes of regression functions and partitioning input space.
method Mean-shift-inspired algorithm for iterative gradient ascent.
result Proves convergence and rates of convergence for estimated local modes.
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…
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We show that universal consistency of Empirical Risk Minimiza…
Proposes a method for fair regression using RKHS.
problem Ensuring fairness in regression models with multiple sensitive attributes.
method Uses reproducing kernel Hilbert space (RKHS) to construct a functional space that satisfies MP fairness.
result Derives a closed-form solution for fair regression that is efficient and interpretable.
The paper proposes a method to produce well-calibrated predictions in regression tasks using maximum mean discrepancy.
problem The need for accurate uncertainty quantification in machine learning predictions.
method The method uses maximum mean discrepancy to minimize the kernel embedding measure and calibrate predictions.
result The method produces well-calibrated and sharp prediction intervals, outperforming state-of-the-art methods.
Huber regression assessed for robustness in statistical learning.
problem Understanding Huber regression in nonparametric statistical learning.
method Assessment from statistical learning perspective, focusing on risk consistency, adaptive tuning, and convergence rates.
result Huber regression can be asymptotically mean regression calibrated under (1+ε)-moment conditions, justifying its robustness. A fast method for LOOCV in k-NN regression reduces computation time.
problem Efficient computation of LOOCV for k-NN regression.
method Identical LOOCV estimate to (k+1)-NN MSE on training data.
result LOOCV computation can be done with (k+1)-NN regression once.
A new method for network regression using optimal transport.
problem How network topology changes with Euclidean covariates.
method Optimal transport approach based on Wasserstein metric.
result The method improves prediction accuracy in real-world data.
Improved heteroscedastic regression using neural networks with provably accurate mean estimates and calibrated variance.
problem Optimizing neural network parameters for heteroscedastic regression leads to suboptimal mean and variance estimates.
method Two simple modifications to optimization to retain accuracy of mean-only models and offer best-in-class variance calibration.
result Mean estimates from the proposed method are provably as accurate as those from a homoscedastic model.
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 tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.
problem Improving loss function for deep neural network based vector-to-vector regression.
method Presenting performance bounds and new properties of MAE, deriving generalized upper bounds, and interpreting MAE as a Laplacian distribution.
result MAE is a more suitable loss function than MSE for DNN based vector-to-vector regression, especially when errors follow a Laplacian distribution.
A new method for distribution regression using sliced Wasserstein distance.
problem Learning functions over spaces of probabilities.
method Proposes an OT-based estimator using the Sliced Wasserstein distance.
result Proves universal consistency and excess risk bounds for the proposed estimator.
Biased mean regression estimates factors exceeding expected loss or radiation release severity.
problem Estimating factors exceeding expected loss or radiation severity levels.
method Biased mean regression using superexpectation error minimization.
result Equivalent to quantile regression and CVaR optimization under specific conditions.
New insights into correntropy-based regression reveal robustness and unified approaches.
problem Learning robust regression functions under additive noise.
method Minimum distance estimation and conditional mean, mode, median functions.
result Unified approach to conditional mean, mode, and median functions.
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We also show that, under some asumptions, universal consisten…
Boosting trees can test necessary conditions for regression model calibration.
problem Testing calibration and auto-calibration in regression models.
method Using boosting trees to test calibration and auto-calibration.
result Boosting trees prove to be very powerful in testing calibration and auto-calibration in large insurance datasets.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n=ildeO(d/ε2) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
Simple methods improve regression transferability estimation.
problem Estimating how well regression models transfer between tasks.
method Two simple, computationally efficient approaches based on negative regularized mean squared error.
result Significantly outperform existing methods in accuracy and efficiency.
Cryptocurrency prices predicted using LSTM, SVM, and polynomial regression.
problem Uncertainty in crypto coin values.
method Long Short Term Memory, Support Vector Machine, Polynomial Regression models.
result Support Vector Machine with linear kernel had the smallest mean square error.
Paper introduces a medoid-based approach for efficient Fréchet regression.
problem Regression in metric spaces with random objects.
method Adapted random forest algorithm with medoid-based splitting rule.
result Asymptotic equivalence and consistency of the regression estimator.
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
Probit regression was first proposed by Bliss in 1934 to study mortality rates of insects. Since then, an extensive body of work has analyzed and used probit or related binary regression methods (such as logistic regression) in numerous applications and fields. This paper provides a fresh angle to such well-established…
The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression ->…
Neural networks simplify SDR in regression tasks.
problem Sufficient dimension reduction in regression problems.
method Applying neural networks with rank regularization to estimate the central mean subspace.
result Neural networks effectively perform SDR, consistent with theoretical estimations.
LALR adapts learning rate for faster convergence in regression and neural nets.
problem Finding optimal learning rates for faster convergence in regression and neural networks.
method Lipschitz continuity theory applied to Mean Absolute Error and Quantile loss functions.
result Adaptive learning rate policy enables up to 20x faster convergence.
The paper uses deep neural networks to estimate and infer ATE without needing to know the dimension of the data.
problem Estimating and inferring the average treatment effect (ATE) in complex data settings.
method The paper uses deep neural networks to estimate the mean regression function and then calculates the ATE. It establishes consistency and asymptotic normality of the estimators.
result The deep neural network estimates of ATE are consistent and asymptotically normal, providing dimension-free rates.
Regularization helps resolve ambiguity in mean-variance models, improving predictive uncertainty quantification.
problem Signal-to-noise ambiguity in overparameterized mean-variance models.
method Statistical field theory framework to explain phase transition.
result Regularization reduces variability and improves predictive uncertainty quantification.
Optimal nonparametric regression estimator adapts to unknown smoothness.
problem Nonparametric regression with unknown smoothness.
method Constructs an interpolating estimator that adapts to unknown smoothness.
result Minimax optimal rates achieved on Hölder classes.
Paper supports robust estimation in regression with heavy-tailed errors.
problem Support estimation in high-dimensional heteroscedastic mean regression.
method Use of Huber loss function and adaptive LASSO penalty for robust estimation.
result Sign-consistency and optimal rates of convergence in ℓ∞ norm. Ridge regression shows different behaviors in binary classification with noisy labels.
problem Binary classification with noisy labels and anisotropic cluster distributions.
method Investigation of ridge regression behavior in overparameterized settings with label noise.
result Ridge regression exhibits qualitatively different behavior based on the scale of cluster mean vectors and covariance matrices.
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.
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a…
A novel k-NN method estimates conditional mean and variance efficiently.
problem Joint estimation of conditional mean and variance.
method Integrates k-NN with automated variance selection.
result Achieves fast convergence rates and improved precision.
Network agents solve adaptive regression problems with compressed signals.
problem Solving regression problems in networks with communication constraints.
method ACTC diffusion strategy with randomized differential compression.
result Optimized resource allocation improves performance.
Bayesian model captures mean and variance of response variables.
problem Complex, predictor-dependent relationships and heteroscedastic patterns in data.
method Sum-of-tessellations for mean, product-of-tessellations for variance.
result Model captures nuanced variance structures and provides reliable predictive uncertainty.
Proposes CCME framework for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects in complex distributions.
method Embeds conditional distributions into RKHS, develops meta-estimators for CCME.
result Establishes finite-sample convergence rates and double robustness for CCME estimators.
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absol…
Flexible Bayesian approach for generalized linear models, especially for sparse logistic regression.
problem Sparse logistic regression challenges in machine learning.
method Empirical Bayes approach with mean-field variational inference, tuning-free and scalable.
result Superior predictive performance in sparse logistic regression compared to existing methods.
Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for this. In this technical report, we develop a new k-means variant called Augmented …
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
A new type of distributional regression tree uses soft split rules for better predictive performance.
problem Estimating complete conditional distributions in regression.
method Distributional adaptive soft regression trees using multivariate soft split rules.
result The method outperforms various benchmark methods, especially in complex non-linear interactions.