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1. Latent deformation models for multivariate functional data and time‐warping separability

   https://doi.org/10.1111/biom.13851  

   Carroll, Cody; Müller, Hans‐Georg (April 2023, Biometrics)

   Abstract Multivariate functional data present theoretical and practical complications that are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are subject to mutual time warping. That is, the component processes exhibit a common shape but are subject to systematic phase variation across their domains in addition to subject‐specific time warping, where each subject has its own internal clock. This motivates a novel model for multivariate functional data that connect such mutual time warping to a latent‐deformation‐based framework by exploiting a novel time‐warping separability assumption. This separability assumption allows for meaningful interpretation and dimension reduction. The resulting latent deformation model is shown to be well suited to represent commonly encountered functional vector data. The proposed approach combines a random amplitude factor for each component with population‐based registration across the components of a multivariate functional data vector and includes a latent population function, which corresponds to a common underlying trajectory. We propose estimators for all components of the model, enabling implementation of the proposed data‐based representation for multivariate functional data and downstream analyses such as Fréchet regression. Rates of convergence are established when curves are fully observed or observed with measurement error. The usefulness of the model, interpretations, and practical aspects are illustrated in simulations and with application to multivariate human growth curves and multivariate environmental pollution data. 

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2. 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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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. 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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5. Equity in genetic newborn screening

   https://doi.org/10.1002/nav.21882  

   El_Hajj, Hussein; Bish, Douglas_R; Bish, Ebru_K (December 2019, Naval Research Logistics (NRL))

   Abstract State‐level newborn screening allows for early treatment of genetic disorders, which can substantially improve health outcomes for newborns. As the cost of genetic testing decreases, it is becoming an essential part of newborn screening. A genetic disorder can be caused by many mutation variants; therefore, an important decision is to determine which variants to search for (ie, thepaneldesign), under a testing budget. The frequency of variants that cause a disorder and the incidence of the disorder vary by racial/ethnic group. Consequently, it is important to consider equity issues in panel design, so as to reduce disparities among different groups. We study the panel design problem using cystic fibrosis (CF) as a model disorder, considering the trade‐offs between equity and accuracy, under a limited budget. Most states use a genetic test in their CF screening protocol, but panel designs vary, and, due to cost, no state's panel includes all CF‐causing variants. We develop models that design equitable genetic testing panels, and compare them with panels that maximize sensitivity in the general population. Our case study, based on realistic CF data, highlights the value of equitable panels and provides important insight for newborn screening practices. 

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