More Like this

1. Sure Independence Screening

   Fan, J.; Lv, J. (June 2018, Wiley StatsRef: Statistics Reference Online)

   Big data is ubiquitous in various fields of sciences, engineering, medicine, social sciences, and humanities. It is often accompanied by a large number of variables and features. While adding much greater flexibility to modeling with enriched feature space, ultra-high dimensional data analysis poses fundamental challenges to scalable learning and inference with good statistical efficiency. Sure independence screening is a simple and effective method to this endeavor. This framework of two-scale statistical learning, consisting of large-scale screening followed by moderate-scale variable selection introduced in Fan and Lv (2008), has been extensively investigated and extended to various model settings ranging from parametric to semiparametric and nonparametric for regression, classification, and survival analysis. This article provides an overview on the developments of sure independence screening over the past decade. These developments demonstrate the wide applicability of the sure independence screening based learning and inference for big data analysis with desired scalability and theoretical guarantees. 

   more » « less
2. SURE-tuned bridge regression

   https://doi.org/10.1007/s11222-023-10350-z  

   Loría, Jorge; Bhadra, Anindya (February 2024, Statistics and Computing)
3. Mathematics at the Airport? Why Sure!

   https://doi.org/10.1090/noti2451  

   Eisenbud, David; Mullen, Nicole; Stoll, Cliff (April 2022, Notices of the American Mathematical Society)
4. Reinforcement Learning with Almost Sure Constraints

   Castellano, Agustin; Min, Hancheng; Bazerque, Juan A.; Mallada, Enrique (June 2022, Proceedings of The 4th Annual Learning for Dynamics and Control Conference,)
5. Almost-Sure Termination by Guarded Refinement

   https://doi.org/10.1145/3674632  

   Gregersen, Simon Oddershede; Aguirre, Alejandro; Haselwarter, Philipp G; Tassarotti, Joseph; Birkedal, Lars (August 2024, Proceedings of the ACM on Programming Languages)

   Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs written in languages with specific syntactic patterns for looping. In this paper, we consider almost-sure termination for higher-order probabilistic programs with general references. This combination of features allows for recursion and looping to be encoded through a variety of patterns. Therefore, rather than developing proof rules for reasoning about particular recursion patterns, we instead propose an approach based on proving refinement between a higher-order program and a simpler probabilistic model, in such a way that the refinement preserves termination behavior. By proving a refinement, almost-sure termination behavior of the program can then be established by analyzing the simpler model. We present this approach in the form of Caliper, a higher-order separation logic for proving termination-preserving refinements. Caliper uses probabilistic couplings to carry out relational reasoning between a program and a model. To handle the range of recursion patterns found in higher-order programs, Caliper uses guarded recursion, in particular the principle of Löb induction. A technical novelty is that Caliper does not require the use of transfinite step indexing or other technical restrictions found in prior work on guarded recursion for termination-preservation refinement. We demonstrate the flexibility of this approach by proving almost-sure termination of several examples, including first-order loop constructs, a random list generator, treaps, and a sampler for Galton-Watson trees that uses higher-order store. All the results have been mechanized in the Coq proof assistant. 

   more » « less