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1. Lower Bounds for Testing Complete Positivity and Quantum Separability

   https://doi.org/10.1007/978-3-030-61792-9_30  

   Bădescu, Costin; O'Donnell, Ryan (December 2020, LATIN 2020: Theoretical Informatics)

   Kohayakawa, Y.; Miyazawa, F.K. (Ed.)

   In this work we are interested in the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given n copies of an unknown mixed quantum state ϱ on Cd⊗Cd , and one wants to test whether ϱ is separable or ϵ -far from all separable states in trace distance. We prove that n=Ω(d2/ϵ2) copies are necessary to test separability, assuming ϵ is not too small, viz. ϵ=Ω(1/d−−√) . We also study completely positive distributions on the grid [d]×[d] , as a classical analogue of separable states. We analogously prove that Ω(d/ϵ2) samples from an unknown distribution p are necessary to decide whether p is completely positive or ϵ -far from all completely positive distributions in total variation distance. 

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2. Partial separability and functional graphical models for multivariate Gaussian processes

   https://doi.org/10.1093/biomet/asab046  

   Zapata, J; Oh, S Y; Petersen, A (October 2021, Biometrika)

   Summary The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting challenging. For example, Gaussian graphical models have recently been extended to the setting of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. However, compared with multivariate data, a key difficulty is that the covariance operator is compact and thus not invertible. This paper addresses the general problem of covariance modelling for multivariate functional data, and functional Gaussian graphical models in particular. As a first step, a new notion of separability for the covariance operator of multivariate functional data is proposed, termed partial separability, leading to a novel Karhunen–Loève-type expansion for such data. Next, the partial separability structure is shown to be particularly useful in providing a well-defined functional Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of identical fixed dimension. This motivates a simple and efficient estimation procedure through application of the joint graphical lasso. Empirical performance of the proposed method for graphical model estimation is assessed through simulation and analysis of functional brain connectivity during a motor task. 

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3. What can we learn from unlearnable datasets?

   Sandoval-Segura, P; Singla, V; Geiping, J; Goldblum, M; Goldstein, T (February 2024, Advances in Neural Information Processing Systems)

   In an era of widespread web scraping, unlearnable dataset methods have the potential to protect data privacy by preventing deep neural networks from generalizing. But in addition to a number of practical limitations that make their use unlikely, we make a number of findings that call into question their ability to safeguard data. First, it is widely believed that neural networks trained on unlearnable datasets only learn shortcuts, simpler rules that are not useful for generalization. In contrast, we find that networks actually can learn useful features that can be reweighed for high test performance, suggesting that image protection is not assured. Unlearnable datasets are also believed to induce learning shortcuts through linear separability of added perturbations. We provide a counterexample, demonstrating that linear separability of perturbations is not a necessary condition. To emphasize why linearly separable perturbations should not be relied upon, we propose an orthogonal projection attack which allows learning from unlearnable datasets published in ICML 2021 and ICLR 2023. Our proposed attack is significantly less complex than recently proposed techniques. 

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4. A fast exact functional test for directional association and cancer biology applications

   https://doi.org/10.1109/TCBB.2018.2809743  

   Zhong, Hua; Song, Mingzhou (February 2018, IEEE/ACM Transactions on Computational Biology and Bioinformatics)

   Directional association measured by functional dependency can answer important questions on relationships between variables, for example, in discovery of molecular interactions in biological systems. However, when one has no prior information about the functional form of a directional association, there is not a widely established statistical procedure to detect such an association. To address this issue, here we introduce an exact functional test for directional association by examining the strength of functional dependency. It is effective in promoting functional patterns by reducing statistical power on dependent non-functional patterns. We designed an algorithm to carry out the test using a fast branch-and-bound strategy, which achieved a substantial speedup over brute-force enumeration. On data from an epidemiological study of liver cancer, the test identified the hepatitis status of a subject as the most influential risk factor among others for the cancer phenotype. On human lung cancer transcriptome data, the test selected 1068 transcription start sites of putative noncoding RNAs directionally associated with the presence or absence of lung cancer, stronger than 95 percent transcription start sites of 694 curated cancer genes. These predictions include non-monotonic interaction patterns, to which other routine tests were insensitive. Complementing symmetric (non-directional) association methods such as Fisher’s exact test, the exact functional test is a unique exact statistical test for evaluating evidence for causal relationships. 

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5. Reclassification and Multilingual Learners' Science Achievement

   https://doi.org/10.1002/tesq.3270  

   Pacheco, Mark B; Curran, F Chris; Boza, Lelydeyvis; Deig, Amber W; Harris, Katharine T; Tan, Tiffany S (November 2023, TESOL Quarterly)

   This study contributes to a growing body of scholarship at the intersection of bilingual education and education policy and examines reclassification, or the transition out of formal English language services in schools, as one potential lever in accelerating or decelerating multilingual learners’ science learning. More specifically, it traces multilingual learners’ science academic achievement vis‐à‐vis science test scores over a six‐year period using the nationally‐representative Early Childhood Longitudinal Study of 2010–11 (ECLS‐K:2011) data set. We use regression analyses with panel data to explore the relationship of reclassification with MLs’ science achievement at a national scale, and then, how variation in contextual factors (including family, school, and individual characteristics) shapes this relationship. Results show that, after controlling for covariates and prior test scores, reclassification is not significantly associated with differential science test scores when compared to students that retain their EL status. Results further show that reclassification is associated with higher science achievement for MLs who were previously in a dual‐language program but lower scores for those with higher prior achievement. We conclude with implications for the reclassification process, as well as directions for future research on reclassification, multilingual learners, and academic achievement. 

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