Ridge Regression Revisited: Debiasing, Thresholding and Bootstrap

• URL: http://arxiv.org/abs/2009.08071v2
• Date: Thu, 22 Apr 2021 17:38:30 GMT
• Title: Ridge Regression Revisited: Debiasing, Thresholding and Bootstrap
• Authors: Yunyi Zhang and Dimitris N. Politis
• Abstract summary: ridge regression may be worth another look since -- after debiasing and thresholding -- it may offer some advantages over the Lasso. In this paper, we define a debiased and thresholded ridge regression method, and prove a consistency result and a Gaussian approximation theorem. In addition to estimation, we consider the problem of prediction, and present a novel, hybrid bootstrap algorithm tailored for prediction intervals.
• Score: 4.142720557665472
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, i.e., zeroing out regression coefficients that are not significant. By contrast, classical ridge regression can not reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the model selection. As a consequence, ridge regression may be worth another look since -- after debiasing and thresholding -- it may offer some advantages over the Lasso, e.g., it can be easily computed using a closed-form expression. % and it has similar performance to threshold Lasso. In this paper, we define a debiased and thresholded ridge regression method, and prove a consistency result and a Gaussian approximation theorem. We further introduce a wild bootstrap algorithm to construct confidence regions and perform hypothesis testing for a linear combination of parameters. In addition to estimation, we consider the problem of prediction, and present a novel, hybrid bootstrap algorithm tailored for prediction intervals. Extensive numerical simulations further show that the debiased and thresholded ridge regression has favorable finite sample performance and may be preferable in some settings.

Related papers

• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Engression: Extrapolation through the Lens of Distributional Regression [2.519266955671697]
  We propose a neural network-based distributional regression methodology called engression' An engression model is generative in the sense that we can sample from the fitted conditional distribution and is also suitable for high-dimensional outcomes. We show that engression can successfully perform extrapolation under some assumptions such as monotonicity, whereas traditional regression approaches such as least-squares or quantile regression fall short under the same assumptions.
  arXiv  Detail & Related papers  (2023-07-03T08:19:00Z)
• Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery [4.446017969073817]
  We show empirical success in terms of accuracy and robustness to noise with bootstrapping-based sequential thresholding least-squares estimator. We show that this bootstrapping-based ensembling technique can perform a provably correct variable selection procedure with an exponential convergence rate of the error rate.
  arXiv  Detail & Related papers  (2023-01-30T04:07:59Z)
• High-dimensional regression with potential prior information on variable importance [0.0]
  We propose a simple scheme involving fitting a sequence of models indicated by the ordering. We show that the computational cost for fitting all models when ridge regression is used is no more than for a single fit of ridge regression. We describe a strategy for Lasso regression that makes use of previous fits to greatly speed up fitting the entire sequence of models.
  arXiv  Detail & Related papers  (2021-09-23T10:34:37Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning [78.83598532168256]
  Marginal-likelihood based model-selection is rarely used in deep learning due to estimation difficulties. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable.
  arXiv  Detail & Related papers  (2021-04-11T09:50:24Z)
• Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression [91.3373131262391]
  Uncertainty is the only certainty there is. Traditionally, the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. How to model the uncertainty within the present-day technologies for regression remains an open issue.
  arXiv  Detail & Related papers  (2021-03-25T06:56:09Z)
• Path Sample-Analytic Gradient Estimators for Stochastic Binary Networks [78.76880041670904]
  In neural networks with binary activations and or binary weights the training by gradient descent is complicated. We propose a new method for this estimation problem combining sampling and analytic approximation steps. We experimentally show higher accuracy in gradient estimation and demonstrate a more stable and better performing training in deep convolutional models.
  arXiv  Detail & Related papers  (2020-06-04T21:51:21Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)
• The Reciprocal Bayesian LASSO [0.0]
  We consider a fully Bayesian formulation of the rLASSO problem, which is based on the observation that the rLASSO estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate. On simulated and real datasets, we show that the Bayesian formulation outperforms its classical cousin in estimation, prediction, and variable selection.
  arXiv  Detail & Related papers  (2020-01-23T01:21:59Z)
• On Low-rank Trace Regression under General Sampling Distribution [9.699586426043885]
  We show that cross-validated estimators satisfy near-optimal error bounds on general assumptions. We also show that the cross-validated estimator outperforms the theory-inspired approach of selecting the parameter.
  arXiv  Detail & Related papers  (2019-04-18T02:56:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.