We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
Novel bounds for logistic regression coreset construction and feature selection.
problem Efficiently summarize and reduce logistic regression inputs.
method Feature space sketching for logistic regression.
result Tight bounds for coreset construction and feature selection.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
DFIV uses deep neural nets to learn nonlinear features in IV regression.
problem Learning causal relationships from observational data with nonlinear interactions.
method DFIV trains deep neural nets to define nonlinear features on instruments and treatments, alternating training to compose stages 1 and 2.
result DFIV outperforms state-of-the-art methods on IV benchmarks and off-policy policy evaluation.
Method learns feature map between source and target domains for high-dimensional regression with missing features.
problem High-dimensional regression with differing feature sets in target and source domains.
method First learns a feature map between missing and observed features using source data, then imputes missing features in target domain, and performs two-step transfer learning for penalized regression.
result Developed upper bounds on estimation and prediction errors for HTL, showing dependence on model complexity, sample size, feature map quality, and domain differences.
A new method for linear regression using feature graphs and hierarchical shrinkage.
problem Estimating robust parameters for linear regression models.
method Hierarchical Feature Regression (HFR) estimator that constructs a supervised feature graph to shrink parameters towards group targets.
result Demonstrates good predictive accuracy and versatility compared to other regularization techniques.
DFIV uses deep features for IV regression, achieving optimal rates.
problem Optimal IV regression with deep features for complex target functions.
method Two-stage approach: deep feature learning followed by IV regression.
result DFIV achieves minimax optimal learning rate under certain conditions.
This paper extends neural collapse to regression problems, revealing key features and structures.
problem Understanding the structure learned by deep neural networks in regression tasks.
method Established Neural Regression Collapse (NRC) across different models, analyzing feature and weight alignments.
result Deep neural regression models exhibit a collapsed feature space, aligning with target dimensions and covariances.
The presence of data corruption in user-generated streaming data, such as social media, motivates a new fundamental problem that learns reliable regression coefficient when features are not accessible entirely at one time. Until now, several important challenges still cannot be handled concurrently: 1) corrupted data e…
Incorporating feature selection into a classification or regression method often carries a number of advantages. In this paper we formalize feature selection specifically from a discriminative perspective of improving classification/regression accuracy. The feature selection method is developed as an extension to the r…
DRE combines DNN with random feature regression for efficient neural network design.
problem Designing and training deep neural networks (DNN) efficiently and effectively.
method DRE architecture with two-layer neural networks, randomly drawn input and output weights trained with linear ridge regression.
result DRE outperforms state-of-the-art DNN in many data sets with lower computational cost.
Securely trains fair models using homomorphic encryption.
problem Protecting sensitive features while testing model fairness.
method Fully homomorphic encryption for training and testing.
result Practical application to adult income data set.
CIRCE measures conditional independence for learning invariant features.
problem Learning invariant features while being conditionally independent of a distractor.
method CIRCE is a measure of conditional independence applied as a regularizer in feature learning.
result CIRCE provides a zero value if and only if features are conditionally independent of the distractor given the target.
New method provides calibrated feature importance explanations for regression models.
problem Lack of uncertainty quantification in existing local explanation methods.
method Extension of Calibrated Explanations method to support regression and probabilistic regression.
result Calibrated Explanations for regression provides quantified uncertainty and robust explanations.
One-class classification (OCC) deals with the classification problem in which the training data has data points belonging only to target class. In this paper, we study a one-class classification algorithm, One-Class Classification by Ensembles of Regression models (OCCER), that uses regression methods to address OCC pr…
Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel ridge regression can sometimes perform poorly. We propose weighting the features wit…
Improved kernel ridge regression for large datasets using weighted random binning.
problem Efficiently approximating kernel matrices for large-scale datasets.
method Introduced weighted random binning features for locality sensitive hashing.
result Weighted random binning features generate Gaussian processes of any desired smoothness.
The choice of normalization affects the coefficients in regularized regression models.
problem The impact of normalization on the coefficients of regularized regression models.
method Investigated lasso, ridge, and elastic net regression with different normalization methods for binary and mixed features.
result Normalization affects the coefficients of regularized regression models, and specific scaling methods can mitigate this effect.
We introduce single-set spectral sparsification as a deterministic sampling based feature selection technique for regularized least squares classification, which is the classification analogue to ridge regression. The method is unsupervised and gives worst-case guarantees of the generalization power of the classificati…
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.
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
Strategic feature manipulation helps learners identify meaningful variables in online regression settings.
problem Strategic feature manipulation poses a challenge for learners in online regression settings.
method Investigates how strategic feature manipulation by individuals can help learners recover meaningful features.
result Simple learner behavior can help accurately recover meaningful features and incentivize feature improvement.
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.
Machine learning finds new natural laws from noisy data.
problem Discovery of natural laws relies on human inspiration.
method Recursive-LASSO-based symbolic regression (RLS) method.
result Data-driven formulation of natural laws from noisy data.
We find a deterministic equivalent for random feature regression's test error, independent of feature map dimension.
problem Understanding the generalization performance of random feature ridge regression.
method We derive a deterministic equivalent for the test error of RFRR under a concentration property, showing it can be approximated by a closed-form expression dependent on feature map eigenvalues.
result Our approximation guarantee is non-asymptotic, multiplicative, and independent of the feature map dimension, providing a tight result for the smallest number of features achieving optimal minimax error rate.
This study improves stock price prediction for Apple Inc. using feature selection and regression models with technical indicators.
problem Improving stock price prediction accuracy for Apple Inc. using technical indicators.
method Evaluation of 123 technical indicators and 10 regression models on 13 years of Apple Inc. data.
result Combining feature selection with regression models significantly improves prediction accuracy.
This paper presents Correlated Nystrom Views (XNV), a fast semi-supervised algorithm for regression and classification. The algorithm draws on two main ideas. First, it generates two views consisting of computationally inexpensive random features. Second, XNV applies multiview regression using Canonical Correlation Ana…
Unified framework for sparse logistic regression with nonconvex regularization.
problem Sparse logistic regression with nonconvex regularization.
method Unified framework, line search criteria for nonconvex terms.
result Effective classification and feature selection at lower computational cost.
While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were train…
Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the n…
In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via fair feature embedding (FKR-F2E) in kernel space. Motivated by prior works on…
Aggregates predictions from multiple regression models using random projections and kernel methods.
problem Combining predictions from multiple regression models to improve accuracy.
method Random projection of high-dimensional feature space, followed by kernel-based consensual aggregation.
result The aggregation scheme performs similarly to using the original high-dimensional features, with high probability.
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
Safe screening rules reduce computation time in logistic regression with ℓ0−ℓ2 regularization.
problem Efficiently solving logistic regression with many features and regularization.
method Screening rules based on Fenchel dual lower bounds of strong conic relaxations.
result A high percentage of features can be safely removed before solving, leading to substantial speed-up.
HARFE approximates sparse additive functions using random features and ridge regression.
problem Approximating high-dimensional sparse additive functions.
method Hard-ridge random feature expansion with sparse ridge regression and hard-thresholding pursuit.
result HARFE method converges with a given error bound and achieves lower error than other algorithms.
Neural networks perform differently when regression is treated as classification.
problem Understanding why neural networks perform better when regression is treated as classification.
method Analyzing two-layer ReLU networks and their feature spaces, focusing on the cross entropy loss vs. square loss.
result The support of the measure induced by the square loss differs from that of the cross entropy loss, indicating optimization difficulties.
Rank regression from pairwise comparisons requires many comparisons to accurately learn model parameters.
problem Learning model parameters for rank regression from noisy pairwise comparisons.
method Uniform random pairwise comparisons to estimate model parameters with a given accuracy.
result Learning model parameters requires a number of comparisons proportional to dNlog3N/ε2. Analyzes neural networks using linear models to understand their behavior.
problem Understanding multi-layer neural networks through linear models.
method Recalls and reviews four models: linear regression with concentrated features, kernel ridge regression, random feature model, and neural tangent model.
result Highlights limitations of linear theory and discusses approaches to overcome them.
Efficiently predict LLM benchmarks using feature selection and regression.
problem Predicting full benchmark scores with minimal question subsets.
method Multiple regression with feature selection, using kernel ridge regression and mRMR.
result Improved prediction accuracy and ranking correlation across various benchmarks.
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the uncertainty in these selection procedures. In this paper, we propose a new method for inf…
New decentralized KRR algorithm adapts to node-specific data.
problem Consistent node-specific data in decentralized KRR.
method Data-dependent random features for adaptive RF generation.
result Average regression accuracy improved by 25.5% across six datasets.
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a response variable. This helps in solving the prediction problem with a low-dimensional…
The study identifies spurious correlations in high-dimensional regression and quantifies their impact.
problem Spurious correlations in high-dimensional regression models.
method Statistical characterization of spurious correlations, quantifying their amount via ridge regularization.
result The value of regularization strength that minimizes test loss is in an interval where spurious correlations increase.
SLEIPNIR improves Gaussian process regression with derivatives, scaling up efficiently and accurately.
problem Scaling Gaussian process regression with derivatives for large datasets.
method Quadrature Fourier features for feature expansion, proving error bounds.
result Deterministic, non-asymptotic, exponentially fast decaying error bounds for approximated kernel and posterior.
ERM performs well in feature learning with minimal feature maps.
problem Empirical risk minimization in feature learning with square loss.
method Asymptotic and non-asymptotic analysis of ERM performance.
result Excess risk quantiles of ERM match those of oracle procedure under certain conditions.
Distributed sensors compress and send features to a fusion center for linear regression.
problem Efficiently compress and transmit features from distributed sensors to a fusion center under varying communication constraints.
method Designs a distributed and adaptive feature compression scheme using optimal quantizers and simple adaptive strategies.
result Demonstrates improved inference performance through simulated experiments.
This paper uses quantum computing to solve sparse linear regression problems efficiently.
problem Sparse linear regression to identify important features from a large set of variables.
method Formulates the ℓ0 optimization problem as a QUBO problem and solves it using the D-Wave adiabatic quantum computer. result The QUBO solution matches the optimal solution for a wide range of sparsity penalty values across datasets.