Unified approach to linear regression using covariance fitting for optimal weights.
problem Finding optimal weights for linear regression models when weights are unknown.
method Covariance fitting SPICE-methodology to obtain data-adaptive weights.
result Tuned versions of known regularized estimators are unified under a common approach.
We analyze optimal weighted ridge regression in overparameterized linear models.
problem Optimal regularization in overparameterized linear regression models.
method Generalized ridge regression with weighted regularization.
result The optimal regularization parameter can be negative in overparameterized settings.
In this paper, we consider one dimensional (shallow) ReLU neural networks in which weights are chosen randomly and only the terminal layer is trained. First, we mathematically show that for such networks L2-regularized regression corresponds in function space to regularizing the estimate's second derivative for fairly …
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
We propose and analyze a variant of the classic Polyak-Ruppert averaging scheme, broadly used in stochastic gradient methods. Rather than a uniform average of the iterates, we consider a weighted average, with weights decaying in a geometric fashion. In the context of linear least squares regression, we show that this …
Regularized linear regression improves binary classification performance, especially with ridge and ℓ1 regularization.
problem Improving binary classification accuracy with noisy labels.
method Systematic study of regularization strengths on linear classifiers trained on noisy binary classification data.
result Ridge regression consistently improves classification error, while ℓ1 regularization can induce sparsity and ℓ∞ regularization can concentrate weights to two values. Many state-of-the-art machine learning models such as deep neural networks have recently shown to be vulnerable to adversarial perturbations, especially in classification tasks. Motivated by adversarial machine learning, in this paper we investigate the robustness of sparse regression models with strongly correlated co…
Corrects distribution shift in target shift scenarios using importance weighting.
problem Analyzes importance weighting for correcting distribution shift under target shift.
method Analyzed importance-weighted kernel ridge regression under target shift.
result Shows that importance weighting corrects the train-test mismatch without altering input-space complexity.
Study connects Gaussian processes and regularization for sequence-function mappings.
problem Understanding and interpreting sequence-function maps in biology.
method Relates Gaussian process priors, regularization, and gauge fixing in overparameterized weight space.
result Established the relationship between regularized regression and Gaussian processes in function space.
A new method improves flow matching by dynamically weighting density estimates.
problem High-dimensional integration inefficiency in flow matching.
method Density-weighted Dynamic Stein operators.
result Significant improvement in vector field smoothness and sampling efficiency.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
Improved RTM uses integer weights to reduce computation and increase interpretability.
problem Lack of interpretability in nonlinear regression models.
method Integer weighted RTM clauses, combined with a novel learning scheme.
result Significantly reduced computation cost with improved accuracy.
Improves prediction stability with model misspecification and distribution shift.
problem Inaccurate parameter estimation and instability of prediction in real-world applications.
method Proposes Decorrelated Weighting Regression (DWR) algorithm to optimize weights for samples and variables.
result Significantly improves accuracy of parameter estimation and prediction stability.
Unified framework for accurate coresets in latent variable models and regularized regression.
problem Efficiently training models on large datasets.
method Unified framework for constructing accurate coresets for latent variable models and ℓp-regularized regression. result Unified framework reduces coreset size for latent variable models and ℓp-regularized regression. Transformer learns context and regularization for ICL in inverse problems.
problem Learning context and effective regularization for transformer-based in-context learning (ICL) in inverse problems.
method Introduced a linear transformer to learn inverse mapping from contextual examples to weight vectors, addressing rank-deficient problems.
result Transformer implicitly learns a prior distribution and effective regularization strategy, outperforming traditional methods.
Improved generalization with iterative self-distillation using weighted ground-truth targets.
problem Improving generalization accuracy in neural networks.
method Iterative kernel regression with weighted ground-truth targets and ℓ2 regularization. result Closed-form solution for optimal weighting parameter and efficient estimation.
Bayes-optimal learning of deep random networks with Gaussian weights is studied.
problem Learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.
method Closed-form expressions for Bayes-optimal test error, ridge regression, kernel and random features regression are computed.
result Optimally regularized ridge regression and kernel regression achieve Bayes-optimal performances, while logistic loss yields a near-optimal test error for classification.
Novel method learns memory kernels in Langevin equations.
problem Estimating memory kernels in Langevin equations.
method Regularized Prony method for correlation functions, followed by regression over Sobolev norm-based loss function with RKHS regularization.
result Method outperforms other regression estimators in exponentially weighted L^2 space.
Novel characterization of augmented balancing weights combining outcome and weighting models.
problem Improving estimation accuracy in machine learning models with balancing weights.
method Characterization of augmented balancing weights as linear models, extending to ridge and lasso regression.
result Equivalence and closed-form expressions for specific model choices, providing insights into performance.
Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is critical to the interpretability of a learned model. Much of the current literature…
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
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…
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can comp…
Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years, tensor regression networks have been investigated from the perspective of their comp…
Interpretable machine-learning models can be unstable under multicollinearity, leading to oscillatory weights that do not reflect meaningful contributions.
problem Interpretable machine-learning models can be unstable under multicollinearity.
method Theoretical analysis of eigenmodes of the feature correlation matrix.
result Small-eigenvalue modes associated with multicollinearity amplify fluctuations in the weights and generate oscillatory patterns that do not necessarily reflect meaningful contributions.
Paper analyzes spectral algorithms under covariate shift, providing convergence rates.
problem Addressing distributional mismatch in regression models.
method Incorporates importance weights into spectral algorithms in RKHS.
result Establishes minimax-optimal convergence rates for misspecified cases.
New algorithm reduces ERM problem size while maintaining accuracy.
problem Empirical risk minimization problem size reduction.
method Adaptive Deterministic Uniform-Weight Trimming (ADUWT) algorithm.
result Uniform (1±ε) relative-error approximation for ERM objective. Optimizes pruning masks for neural networks using probabilistic fine-tuning and PAC-Bayes bounds.
problem Improving neural network performance through adaptive pruning of weights.
method Optimizes stochastic pruning masks by minimizing expected loss, considering data-adaptive regularization and feature alignment.
result Probabilistic fine-tuning leads to improved test error over baseline methods in neural networks.
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the weight normalization (WN) method [Salimans and Kingma, 2016] and a variant call…
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.
Optimal weighted random forests improve prediction accuracy.
problem Unequal prediction performance among random forest trees.
method Proposes 1-step and 2-step optimal weighting algorithms.
result Asymptotically optimal in terms of squared loss and risk.
New scalable algorithm for non-negative linear regression with entropy-regularized OT loss.
problem Generalizing task-specific linear models to broader applications.
method Sinkhorn-like scaling iterations for convex penalty and datafit terms.
result Simple multiplicative updates for various penalty and datafit terms.
This paper develops a new theory for ensemble learning beyond variance reduction.
problem Ensemble learning's effectiveness for stable estimators is not fully explained by variance reduction.
method Develops a general weighting theory for ensemble learning, formalizing ensembles as linear operators and introducing geometric and spectral constraints.
result Structured weights can outperform uniform averaging by reshaping approximation geometry and redistributing spectral complexity.
Kernel balancing weights are generalized as KRRR, providing better confidence intervals for treatment effects.
problem Lack of generalization error, correct feature specification, and limited to average effects.
method Interpreting kernel balancing weights as KRRR, relaxing feature specification, and extending Gaussian approximation.
result KRRR provides strong generalization properties and justifies confidence sets for causal functions.
Soft diamond regularizers improve deep learning performance and sparsity.
problem Improving deep learning performance and sparsity of trained weights.
method New soft diamond synaptic weight priors based on thick-tailed symmetric alpha stable probability curves.
result Soft diamond regularizers outperform state-of-the-art methods in deep learning tasks.
Gradient descent on ReLU networks with square loss implicitly favors balanced weights.
problem Understanding implicit regularization in nonlinear neural networks with regression losses.
method Analyzing gradient descent dynamics on ReLU networks with square loss.
result It is impossible to characterize the implicit regularization of ReLU networks with square loss by any explicit function of model parameters.
New algorithm reduces online logistic regression regret without exponential constant.
problem Improper learning in online logistic regression with logarithmic regret.
method Regularized empirical risk minimization with surrogate losses.
result Regret scaling as O(B log(Bn)) with low computational complexity.
Proposes a method to estimate causal effects of continuous treatments using instrumental variables.
problem Estimating causal effects of continuous treatments in the presence of unmeasured confounders.
method Introduces a novel framework using instrumental variables and a uniform regular weighting function to identify and estimate average dose-response functions.
result Establishes the asymptotic properties of the proposed methods for estimating average dose-response functions.
PIANO speeds up multinomial logistic regression solving.
problem Handling large datasets and many classes in logistic regression.
method Parallel iterative algorithm based on Majorization Minimization.
result PIANO converges to a stationary point of Multinomial and Sparse Multinomial Logistic Regression.
ReTaSA tackles continuous target shift in regression problems.
problem Continuous target shift in regression settings.
method Nonparametric regularized approach to estimate importance weight function.
result The method provides theoretical justification for the estimated importance weight function.
Oracle inequality for sparse neural nets adapts to unknown structure.
problem Sparse deep neural nets in nonparametric regression.
method Gibbs posterior distribution with Metropolis-adjusted Langevin algorithms and mixture of uniform priors.
result Oracle inequality showing adaptation to unknown regularity and structure, achieving minimax-optimal rate of convergence.
A new screening rule speeds up OWL regression solving.
problem High-dimensional sparse learning with OWL regression's computational cost and memory usage.
method Safe screening rule for OWL regression using iterative strategy.
result Significant computational gain without accuracy loss.
The paper reveals three mechanisms for weak-to-strong generalization.
problem Understanding the mechanisms behind weak-to-strong generalization in imperfect labeling scenarios.
method Theoretical analysis of simple models including ridge regression and weighted ridge regression, and a nonlinear multi-index setting.
result A student model can compensate for a teacher's under-regularization and achieve lower test error.
Unified framework for semi-supervised regression with misspecified models.
problem Estimating regression coefficients in conditional mean models with unlabeled data.
method Developed an augmented inverse probability weighted (AIPW) method using regularized calibrated estimators for PS and OR nuisance models.
result The proposed estimator is consistent, asymptotically normal, and provides valid confidence intervals even with misspecified OR models and high-dimensional data.
Stacked regressions improve predictive accuracy by combining estimators.
problem Improve predictive accuracy in regression models.
method Analogous to least-squares, learn combination weights by minimizing regularized empirical risk with nonnegativity constraint.
result The stacked estimator has strictly smaller population risk than the best single estimator, especially when signal-to-noise ratio is small.
Deep learning models can adaptively estimate functions with varying smoothness using regularization.
problem Estimating functions with heterogeneous smoothness in Besov or BV classes.
method Introduced a Parallel NN variant of deep ReLU networks with ℓ2 regularization equivalent to promoting ℓp-sparsity. result Achieves minimax rates for Besov and BV classes with exponentially closer performance as depth increases.
A new image interpolation model using sparse representation and nonlocal linear regression.
problem Image interpolation without blurring and noise.
method Sparse representation, nonlocal self-similarity, nonlocal linear regression, adaptive sub-dictionary learning, weighted encoding.
result Our method outperforms state-of-the-art methods in quantitative measures and visual quality.
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …