اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression
290
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. However, in moderately high-dimensional problems, where the number of features $d$ is a non-negligible fraction of the sample size $n$, the logistic regression maximum likelihood estimator (MLE), and statistical procedures based the large-sample approximation of its distribution, behave poorly. Recently, Sur and Cand`es (2019) showed that these issues can be corrected by applying a new approximation of the MLEs sampling distribution in this high-dimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of the emph{signal strength}, which is a function of the underlying parameters $beta$ of the logistic regression. To address this issue, we propose SLOE, a fast and straightforward approach to estimate the signal strength in logistic regression. The key insight of SLOE is that the Sur and Cand`es (2019) correction can be reparameterized in terms of the emph{corrupted signal strength}, which is only a function of the estimated parameters $widehat beta$. We propose an estimator for this quantity, prove that it is consistent in the relevant high-dimensional regime, and show that dimensionality correction using SLOE is accurate in finite samples. Compared to the existing ProbeFrontier heuristic, SLOE is conceptually simpler and orders of magnitude faster, making it suitable for routine use. We demonstrate the importance of routine dimensionality correction in the Heart Disease dataset from the UCI repository, and a genomics application using data from the UK Biobank. We provide an open source package for this method, available at url{https://github.com/google-research/sloe-logistic}.
قيم البحث
اقرأ أيضاً
Variational Bayes (VB) is a popular scalable alternative to Markov chain Monte Carlo for Bayesian inference. We study a mean-field spike and slab VB approximation of widely used Bayesian model selection priors in sparse high-dimensional logistic regr
ession. We provide non-asymptotic theoretical guarantees for the VB posterior in both $ell_2$ and prediction loss for a sparse truth, giving optimal (minimax) convergence rates. Since the VB algorithm does not depend on the unknown truth to achieve optimality, our results shed light on effective prior choices. We confirm the improved performance of our VB algorithm over common sparse VB approaches in a numerical study.
We propose a variational Bayesian (VB) procedure for high-dimensional linear model inferences with heavy tail shrinkage priors, such as student-t prior. Theoretically, we establish the consistency of the proposed VB method and prove that under the pr
oper choice of prior specifications, the contraction rate of the VB posterior is nearly optimal. It justifies the validity of VB inference as an alternative of Markov Chain Monte Carlo (MCMC) sampling. Meanwhile, comparing to conventional MCMC methods, the VB procedure achieves much higher computational efficiency, which greatly alleviates the computing burden for modern machine learning applications such as massive data analysis. Through numerical studies, we demonstrate that the proposed VB method leads to shorter computing time, higher estimation accuracy, and lower variable selection error than competitive sparse Bayesian methods.
This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the other class,
often called controls). We first derive the asymptotic distribution of the maximum likelihood estimator (MLE) of the unknown parameter, which shows that the asymptotic variance convergences to zero in a rate of the inverse of the number of the events instead of the inverse of the full data sample size. This indicates that the available information in rare events data is at the scale of the number of events instead of the full data sample size. Furthermore, we prove that under-sampling a small proportion of the nonevents, the resulting under-sampled estimator may have identical asymptotic distribution to the full data MLE. This demonstrates the advantage of under-sampling nonevents for rare events data, because this procedure may significantly reduce the computation and/or data collection costs. Another common practice in analyzing rare events data is to over-sample (replicate) the events, which has a higher computational cost. We show that this procedure may even result in efficiency loss in terms of parameter estimation.
Bootstrapping provides a flexible and effective approach for assessing the quality of batch reinforcement learning, yet its theoretical property is less understood. In this paper, we study the use of bootstrapping in off-policy evaluation (OPE), and
in particular, we focus on the fitted Q-evaluation (FQE) that is known to be minimax-optimal in the tabular and linear-model cases. We propose a bootstrapping FQE method for inferring the distribution of the policy evaluation error and show that this method is asymptotically efficient and distributionally consistent for off-policy statistical inference. To overcome the computation limit of bootstrapping, we further adapt a subsampling procedure that improves the runtime by an order of magnitude. We numerically evaluate the bootrapping method in classical RL environments for confidence interval estimation, estimating the variance of off-policy evaluator, and estimating the correlation between multiple off-policy evaluators.
Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and u
nstructured electronic health record data. A major hurdle currently is a lack of valid statistical inference methods for the case probability. In this paper, considering high-dimensional sparse logistic regression models for prediction, we propose a novel bias-corrected estimator for the case probability through the development of linearization and variance enhancement techniques. We establish asymptotic normality of the proposed estimator for any loading vector in high dimensions. We construct a confidence interval for the case probability and propose a hypothesis testing procedure for patient case-control labelling. We demonstrate the proposed method via extensive simulation studies and application to real-world electronic health record data.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
