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1. Asymptotic distribution-free changepoint detection for data with repeated observations

   https://doi.org/10.1093/biomet/asab048  

   Song, Hoseung; Chen, Hao (September 2021, Biometrika)

   Summary A nonparametric framework for changepoint detection, based on scan statistics utilizing graphs that represent similarities among observations, is gaining attention owing to its flexibility and good performance for high-dimensional and non-Euclidean data sequences. However, this graph-based framework faces challenges when there are repeated observations in the sequence, which is often the case for discrete data such as network data. In this article we extend the graph-based framework to solve this problem by averaging or taking the union of all possible optimal graphs resulting from repeated observations. We consider both the single-changepoint alternative and the changed-interval alternative, and derive analytical formulas to control the Type I error for the new methods, making them readily applicable to large datasets. The extended methods are illustrated on an application in detecting changes in a sequence of dynamic networks over time. All proposed methods are implemented in an $$\texttt{R}$$ package $$\texttt{gSeg}$$ available on CRAN. 

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2. HyperTools: A Python toolbox for visualizing and manipulating high-dimensional data

   Heusser, Andrew C; Ziman, Kirsten; Owen, Lucy LW; Manning, Jeremy R (January 2017, arXiv.org)

   Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable over time as (x,y) coordinates on a graph), it is not always obvious how to visualize high-dimensional datasets in a similarly intuitive way. Here we present HypeTools, a Python toolbox for visualizing and manipulating large, high-dimensional datasets. Our primary approach is to use dimensionality reduction techniques (Pearson, 1901; Tipping & Bishop, 1999) to embed high-dimensional datasets in a lower-dimensional space, and plot the data using a simple (yet powerful) API with many options for data manipulation [e.g. hyperalignment (Haxby et al., 2011), clustering, normalizing, etc.] and plot styling. The toolbox is designed around the notion of data trajectories and point clouds. Just as the position of an object moving through space can be visualized as a 3D trajectory, HyperTools uses dimensionality reduction algorithms to create similar 2D and 3D trajectories for time series of high-dimensional observations. The trajectories may be plotted as interactive static plots or visualized as animations. These same dimensionality reduction and alignment algorithms can also reveal structure in static datasets (e.g. collections of observations or attributes). We present several examples showcasing how using our toolbox to explore data through trajectories and low-dimensional embeddings can reveal deep insights into datasets across a wide variety of domains. 

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3. Euclidean and complex geometries from real-time computations of gravitational Rényi entropies

   https://doi.org/10.1007/JHEP02(2025)136  

   Held, Jesse; Liu, Xiaoyi; Marolf, Donald; Wang, Zhencheng (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> Gravitational Rényi computations have traditionally been described in the language of Euclidean path integrals. In the semiclassical limit, such calculations are governed by Euclidean (or, more generally, complex) saddle-point geometries. We emphasize here that, at least in simple contexts, the Euclidean approach suggests an alternative formulation in terms of the bulk quantum wavefunction. Since this alternate formulation can be directly applied to the real-time quantum theory, it is insensitive to subtleties involved in defining the Euclidean path integral. In particular, it can be consistent with many different choices of integration contour. Despite the fact that self-adjoint operators in the associated real-time quantum theory have real eigenvalues, we note that the bulk wavefunction encodes the Euclidean (or complex) Rényi geometries that would arise in any Euclidean path integral. As a result, for any given quantum state, the appropriate real-time path integral yields both Rényi entropies and associated complex saddle-point geometries that agree with Euclidean methods. After brief explanations of these general points, we use JT gravity to illustrate the associated real-time computations in detail. 

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4. Sequential change‐point detection: Computation versus statistical performance

   https://doi.org/10.1002/wics.1628  

   Wang, Haoyun; Xie, Yao (July 2023, WIREs Computational Statistics)

   Abstract Change‐point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large‐scale, high‐dimensional, and complex streaming data call for computationally (memory) efficient sequential change‐point detection algorithms that are also statistically powerful. This gives rise to a computation versus statistical power trade‐off, an aspect less emphasized in the past in classic literature. This tutorial takes this new perspective and reviews several sequential change‐point detection procedures, ranging from classic sequential change‐point detection algorithms to more recent non‐parametric procedures that consider computation, memory efficiency, and model robustness in the algorithm design. Our survey also contains classic performance analysis, which provides useful techniques for analyzing new procedures. This article is categorized under:Statistical Models > Time Series ModelsAlgorithms and Computational Methods > AlgorithmsData: Types and Structure > Time Series, Stochastic Processes, and Functional Data 

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5. Neural embedding: learning the embedding of the manifold of physics data

   https://doi.org/10.1007/JHEP07(2023)108  

   Park, Sang Eon; Harris, Philip; Ostdiek, Bryan (July 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in the data analysis pipeline for many applications. Using progressively more realistic simulated collisions at the Large Hadron Collider, we show that this embedding approach learns the underlying latent structure. With the notion of volume in Euclidean spaces, we provide for the first time a viable solution to quantifying the true search capability of model agnostic search algorithms in collider physics (i.e. anomaly detection). Finally, we discuss how the ideas presented in this paper can be employed to solve many practical challenges that require the extraction of physically meaningful representations from information in complex high dimensional datasets. 

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