Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press a...

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference step of modern kernel methods that rely on embedding probability distributions in RKHSs. Given a finite sample, an empirical average has been used commonly as...

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an attractive method for variable selection since it promotes sparsity of the groups. We study the sensitivity of any group Lasso solution to the observations and provide its precise loca...

The problem of estimating the coeecients in a linear regression model is considered when some of the response values are missing. The conventional Yates procedure employing least squares predictions for missing values does not lead to any improvement over the least squares estimator using complete observations only. However, if we use Stein-rule predictions , it is demonstrated that some improv...

We analyze a hierarchical Bayes model which is related to the usual empirical Bayes formulation of James-Stein estimators. We consider running a Gibbs sampler on this model. Using previous results about convergence rates of Markov chains, we provide rigorous, numerical, reasonable bounds on the running time of the Gibbs sampler, for a suitable range of prior distributions. We apply these result...

SUMMARY In the presence of high-dimensional predictors, it is challenging to develop reliable regression models that can be used to accurately predict future outcomes. Further complications arise when the outcome of interest is an event time, which is often not fully observed due to censoring. In this article, we develop robust prediction models for event time outcomes by regularizing the Gehan...

among 2379 patients with upper urinary tract stones who underwent eswl (extracorporeal shock wave lithotripsy) at sina hospitál using the siemens lithostar, 638 developed stone street (steinstrasse). of these, 516 (81%) passed all of the stone fragments spontaneously and no treatment was required, 90 cases (14%) had more eswl sessions to complete the treatment, and 30 (4.7%) required further in...

The aim of this paper is to assess the performance of the Markowitz meanvariance framework over a thirty year time frame and address the question of; How should an investor optimally allocate their capital?. The effect of risk reduction by incorporating a Bayes-Stein estimator is also investigated. The performance of the framework is concluded by the out-ofsample performance of the mean-varianc...

This paper constructs a new estimator for large covariance matrices by drawing bridge between the classic (Stein (1975)) in finite samples and recent progress under large-dimensional asymptotics. The keeps eigenvectors of sample matrix applies shrinkage to inverse eigenvalues. corresponding formula is quadratic: it has two targets weighted quadratic functions concentration (that is, dimension d...

We study empirical Bayes estimation of the effect sizes N units from K noisy observations on each unit. show that it is possible to achieve near-Bayes optimal mean squared error, without any assumptions or knowledge about size distribution noise. The noise can be heteroscedastic and vary arbitrarily unit Our proposal, which we call Aurora, leverages replication inherent in per recasts problem a...