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一致稀疏深度学习：理论与计算AI 解读

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most O(n/ log (n)) connections and nice…

用于大规模贝叶斯变量选择的扩展随机梯度 MCMCAI 解读

Summary Stochastic gradient Markov chain Monte Carlo algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed dimension and the log-posterior density is differentiable with respect to the parameters. This paper proposes an extended stochastic gradient Markov chain Monte Carlo algorithm which, by introducing appropriate latent variables, can be…

对归一化常数难以计算的分布进行抽样的自适应交换算法AI 解读

Sampling from the posterior distribution for a model whose normalizing constant is intractable is a long-standing problem in statistical research. We propose a new algorithm, adaptive auxiliary variable exchange algorithm, or, in short, adaptive exchange (AEX) algorithm, to tackle this problem. The new algorithm can be viewed as a MCMC extension of the exchange algorithm, which generates auxiliary variables via an importance sampling procedure from a Markov chain running in…

超高维回归的拆分合并贝叶斯变量选择方法AI 解读

Summary We propose a Bayesian variable selection approach for ultrahigh dimensional linear regression based on the strategy of split and merge. The approach proposed consists of two stages: split the ultrahigh dimensional data set into a number of lower dimensional subsets and select relevant variables from each of the subsets, and aggregate the variables selected from each subset and then select relevant variables from the aggregated data set. Since the approach proposed…

基于倒数 L1 正则化的高维变量选择AI 解读

During the past decade, penalized likelihood methods have been widely used in variable selection problems, where the penalty functions are typically symmetric about 0, continuous and nondecreasing in (0, ∞). We propose a new penalized likelihood method, reciprocal Lasso (or in short, rLasso), based on a new class of penalty functions that are decreasing in (0, ∞), discontinuous at 0, and converge to infinity when the coefficients approach zero. The new penalty functions give…

高维高斯图模型中用于网络构建的等价偏相关度量AI 解读

Gaussian graphical models (GGMs) are frequently used to explore networks, such as gene regulatory networks, among a set of variables. Under the classical theory of GGMs, the construction of Gaussian graphical networks amounts to finding the pairs of variables with nonzero partial correlation coefficients. However, this is infeasible for high-dimensional problems for which the number of variables is larger than the sample size. In this article, we propose a new measure of…

高维广义线性模型的贝叶斯子集建模AI 解读

This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of…

大型地统计数据分析的重抽样随机逼近方法AI 解读

The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the…