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In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
Speckle patterns produced by coherent X-ray have a close relationship with the internal structure of materials but quantitative inversion of the relationship to determine structure from speckle patterns is challenging. Here, we investigate…
Oriented object detection predicts orientation in addition to object location and bounding box. Precisely predicting orientation remains challenging due to angular periodicity, which introduces boundary discontinuity issues and symmetry…
We applied angular X-ray Cross-Correlation analysis (XCCA) to scattering images from a femtosecond resolution LCLS X-ray free-electron laser (XFEL) pump-probe experiment with solvated PtPOP ([Pt$_2$(P$_2$O$_5$H$_2$)$_4$]$^{4-}$) metal…
Multiplicity correlation measurements provide insight into the dynamics of high energy collisions. Models describing these collisions need these correlation measurements to tune the strengths of the underlying QCD processes which influence…
Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…
We consider constraint-based methods for causal structure learning, such as the PC-, FCI-, RFCI- and CCD- algorithms (Spirtes et al. (2000, 1993), Richardson (1996), Colombo et al. (2012), Claassen et al. (2013)). The first step of all…
Out-of-time-order correlators (OTOC), recently being the center of discussion on quantum chaos, are a tool to understand the information scrambling in different phases of quantum many-body systems. We propose a disordered ladder spin model,…
Causal Bayesian Networks provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established…
We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize…
In causal machine learning, the fitting and evaluation of nuisance models are often performed on separate partitions, or folds, of the observed data. This technique, called cross-fitting, eliminates bias introduced by the use of black-box…
We propose to identify directions invariant to a given classifier so that these directions can be controlled in tasks such as style transfer. While orthogonal decomposition is directly identifiable when the given classifier is linear, we…
We address the problem of predicting a target ordinal variable based on observable features consisting of functional profiles. This problem is crucial, especially in decision-making driven by sensor systems, when the goal is to assess an…
X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) are powerful probes of electronic structure owing to their chemical and orbital selectivity. For powder samples, however, interpreting RIXS spectral…
Canonical correlation analysis (CCA) is a technique to find statistical dependencies between a pair of multivariate data. However, its application to high dimensional data is limited due to the resulting time complexity. While the…
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…