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作者：Chen, Yuexin; Zhu, Lixing; Xu, Wangli
作者单位：Renmin University of China; Renmin University of China; Beijing Normal University
摘要：This article proposes a calibrated empirical likelihood test for ultra-high dimensional means that incorporates multiple projections. Under weak moment conditions on the distributions of data, we analyse all possible asymptotic distributions of the proposed test statistic in different scenarios. To determine the critical value and enhance test power, we employ the random symmetrization method based on the group of sign flips and use multiple selected projections. The test can still maintain th...
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作者：Javanmard, Adel; Shao, Simeng; Bien, Jacob
作者单位：University of Southern California; Amazon.com
摘要：Large datasets make it possible to build predictive models that can capture heterogenous relationships between the response variable and features. The mixture of high-dimensional linear experts model posits that observations come from a mixture of high-dimensional linear regression models, where the mixture weights are themselves feature-dependent. In this article, we show how to construct valid prediction sets for an & ell;1-penalized mixture of experts model in the high-dimensional setting. ...
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作者：Borgonovo, Emanuele; Figalli, Alessio; Ghosal, Promit; Plischke, Elmar; Savare, Giuseppe
作者单位：Bocconi University; Bocconi University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Chicago; Helmholtz Association; Helmholtz-Zentrum Dresden-Rossendorf (HZDR); Helmholtz Association; Helmholtz-Zentrum Dresden-Rossendorf (HZDR)
摘要：Recent investigations on the measures of statistical association highlight essential properties such as zero-independence (the measure is zero if and only if the random variables are independent), monotonicity under information refinement, and max-functionality (the measure of association is maximal if and only if we are in the presence of a deterministic (noiseless) dependence). An open question concerns the reasons why measures of statistical associations satisfy one or more of those propert...
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作者：Tan, Linda S. L.
作者单位：National University of Singapore
摘要：Natural gradients can improve convergence in stochastic variational inference significantly but inverting the Fisher information matrix is daunting in high dimensions. Moreover, in Gaussian variational approximation, natural gradient updates of the precision matrix do not ensure positive definiteness. To tackle this issue, we derive analytic natural gradient updates of the Cholesky factor of the covariance or precision matrix and consider sparsity constraints representing different posterior c...
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作者：Yan, Yuling; Su, Weijie J.; Fan, Jianqing
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Pennsylvania; Princeton University
摘要：In 2023, the International Conference on Machine Learning (ICML) required authors with multiple submissions to rank their papers by perceived quality. In this paper, we leverage these author-specified rankings to enhance peer review in machine learning and artificial intelligence conferences by extending the isotonic mechanism to exponential family distributions. This mechanism produces adjusted scores closely aligned with the original scores while strictly adhering to the author-specified ran...
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作者：Sood, Anav; Hastie, Trevor
作者单位：Stanford University
摘要：We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as column subset selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of principal variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum-likelihood estimation within a certain semi-par...
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作者：Yiu, Andrew; Fong, Edwin; Holmes, Chris; Rousseau, Judith
作者单位：University of Oxford; University of Hong Kong; University of Oxford; Centre National de la Recherche Scientifique (CNRS); Universite PSL; CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Dauphine
摘要：We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization, and predictive power of nonparametric Bayesian procedures to estimate low-dimensional functionals of interest without being restricted by the holistic Bayesian formalism. Starting from a conventional posterior on the whole data-generating distribution, we correct the marginal posterior for each functional of interest with the help of th...
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作者：Kiriliouk, Anna; Lee, Jeongjin; Segers, Johan
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作者：Singh, Rahul; Iliopoulos, George; Davidov, Ori
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi; University of Piraeus; University of Haifa
摘要：Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analysed. Novel, graph-based, necessary, and sufficient conditions that guarantee strong consistency, asymptotic normality, and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are provided. The methodology is em...
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作者：Fischer, Lasse; Ramdas, Aaditya
作者单位：University of Bremen; Carnegie Mellon University
摘要：In a Monte Carlo test, the observed dataset is fixed, and several resampled or permuted versions of the dataset are generated in order to test a null hypothesis that the original dataset is exchangeable with the resampled/permuted ones. Sequential Monte Carlo tests aim to save computational resources by generating these additional datasets sequentially one by one and potentially stopping early. While earlier tests yield valid inference at a particular prespecified stopping rule, our work devel...
