Journal: The Annals of Statistics

Abbreviation

Ann. Statist.

Publisher

Institute of Mathematical Statistics

Journal Volumes

ISSN

0090-5364
2168-8966

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Publications 1 - 10 of 49
  • Doubly debiased lasso: High-dimensional inference under hidden confounding
    Item type: Journal Article
    Guo, Zijian; Ćevid, Domagoj; Bühlmann, Peter (2022)
    The Annals of Statistics
    Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the doubly debiased lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional parameters as well as the bias caused by the hidden confounding. We establish its asymptotic normality and also prove that it is efficient in the Gauss-Markov sense. The validity of our methodology relies on a dense confounding assumption, that is, that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application. The method is implemented by the DDL package available from CRAN.
  • The functional graphical lasso
    Item type: Journal Article
    Waghmare, Kartik G.; Masak, Tomas; Panaretos, Victor M. (2025)
    The Annals of Statistics
    We consider the problem of recovering conditional independence relationships between p jointly distributed Hilbertian random elements given n realizations thereof. We operate in the sparse high-dimensional regime, where n ≪ p and no element is related to more than d ≪ p other elements. In this context, we propose an infinite-dimensional generalization of the graphical lasso. We prove model selection consistency under natural assumptions and extend many classical results to infinite dimensions. In particular, we do not make additional structural assumptions. The plug-in nature of our method makes it applicable to heterogeneous data measured under any observational regime, whether sparse or dense, and indifferent to serial dependence between samples. In addition, it does not require dimensionality reduction by truncation. Importantly, our method can be understood as naturally arising from a coherent maximum likelihood philosophy.
  • On Statistical Learning of Simplices: Unmixing Problem Revisited
    Item type: Journal Article
    Najafi, Amir; Ilchi, Saeed; Saberi, Amir H.; et al. (2021)
    The Annals of Statistics
    We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of ϵ is O(K2/ϵ log K/ϵ), which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets demonstrate a comparable performance for our method on noiseless samples, while we outperform the state-of-the-art in noisy cases.
  • Square root penalty: Adaptation to the margin in classification and in edge estimation
    Item type: Journal Article
    Tsybakov, Alexandre B.; van de Geer, Sara (2005)
    The Annals of Statistics
  • CAM
    Item type: Journal Article
    Bühlmann, Peter; Peters, Jonas; Ernest, Jan (2014)
    The Annals of Statistics
  • Causal discovery in heavy-tailed models
    Item type: Journal Article
    Gnecco, Nicola; Meinshausen, Nicolai; Peters, Jonas; et al. (2021)
    The Annals of Statistics
    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 case, the causal tail coefficient is shown to reveal the causal structure if the distribution follows a linear structural causal model. This holds even in the presence of latent common causes that have the same tail index as the observed variables. Based on a consistent estimator of the causal tail coefficient, we propose a computationally highly efficient algorithm that estimates the causal structure. We prove that our method consistently recovers the causal order and we compare it to other well-established and nonextremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.
  • Boosting for high-dimensional linear models
    Item type: Journal Article
    Bühlmann, Peter (2006)
    The Annals of Statistics
  • Stable limits of martingale transforms with application to the estimation of Garch parameters
    Item type: Journal Article
    Mikosch, Thomas; Straumann, Daniel (2006)
    The Annals of Statistics
  • High-Dimensional Additive Modeling
    Item type: Journal Article
    Meier, Lukas; van de Geer, Sara; Bühlmann, Peter (2009)
    The Annals of Statistics
  • Recursive Monte Carlo filters
    Item type: Journal Article
    Künsch, Hans R. (2005)
    The Annals of Statistics
Publications 1 - 10 of 49