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Engression：从分布回归视角研究外推AI 解读

Abstract Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree ensemble based quantile regression. 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. Furthermore, we find that…

重尾模型中的因果发现AI 解读

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest themselves in extremes. This work aims to connect the two fields of causal inference and extreme value theory. We define the causal tail coefficient that captures asymmetries in the extremal dependence of two random variables. In the population…

锚回归：异质数据与因果性AI 解读

Abstract We consider the problem of predicting a response variable from a set of covariates on a data set that differs in distribution from the training data. Causal parameters are optimal in terms of predictive accuracy if in the new distribution either many variables are affected by interventions or only some variables are affected, but the perturbations are strong. If the training and test distributions differ by a shift, causal parameters might be too conservative to…

右奇异向量投影图：潜在混杂下的快速高维协方差估计AI 解读

Summary We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with…

因果 Dantzig：加性干预下含隐藏变量线性结构方程模型的快速推断AI 解读

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number of causal predictors. It was recently shown in Peters, Bühlmann and Meinshausen (2016) (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78 947–1012) that causal inference for the full model is possible when data from distinct observational…

利用不变预测进行因果推断：识别与置信区间AI 解读

Summary What is the difference between a prediction that is made with a causal model and that with a non-causal model? Suppose that we intervene on the predictor variables or change the whole environment. The predictions from a causal model will in general work as well under interventions as for observational data. In contrast, predictions from a non-causal model can potentially be very wrong if we actively intervene on variables. Here, we propose to exploit this invariance…

Group Bound：不对设计矩阵作假设的稀疏高维回归变量组置信区间AI 解读

Summary It is in general challenging to provide confidence intervals for individual variables in high dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a ‘group bound’ confidence interval can be derived without making any assumptions on the design matrix. The lower bound for the regression coefficient of individual variables can be derived via linear programming. The idea also generalizes naturally to groups of…

异质大规模数据中的最大最小效应AI 解读

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return…

讨论：通过凸优化选择潜变量图模型AI 解读

We want to congratulate the authors for a thought-provoking and very interesting paper.Sparse modeling of the concentration matrix has enjoyed popularity in recent years.It has been framed as a computationally convenient convex ℓ 1constrained estimation problem in Yuan and Lin (2007) and can be applied readily to higher-dimensional problems.The authors argue-we think correctly-that the sparsity of the concentration matrix is for many applications more plausible after the…

依赖下 Westfall–Young 多重检验置换程序的渐近最优性AI 解读

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We show that the Westfall–Young permutation method has asymptotically optimal power for a broad class of testing problems with a block-dependence and sparsity structure among the tests, when the number of tests tends to infinity.

高维回归中的 p 值AI 解读

Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder that splits the data into two parts. The number of variables is then reduced to a manageable size using the first split, while classical variable selection techniques can be applied to the remaining…

高维数据稀疏表示的Lasso型恢复AI 解读

The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables pn is potentially much larger than the number of samples n. However, it was recently discovered that the sparsity pattern of the Lasso estimator can only be asymptotically identical to the true sparsity pattern if the design matrix satisfies the so-called irrepresentable condition. The latter condition can easily be violated in the…

高维图与 Lasso 变量选择AI 解读

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from data. We show that neighborhood selection with the Lasso is a computationally attractive alternative to standard covariance selection for sparse high-dimensional graphs. Neighborhood selection estimates the conditional independence…

大量独立检验中错误原假设比例的估计AI 解读

We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower 100(1−α)% confidence bounds for this proportion, based on the empirical distribution of the p-values of the tests. Methods in this family are then compared in terms of ability to consistently…

一般依赖结构下多重关联检验中非真零假设数量的下界AI 解读

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false…