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Related papers: Sparse Index Tracking via Topological Learning

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We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of…

Mathematical Finance · Quantitative Finance 2017-05-31 Tim Leung , Brian Ward

We develop a novel algorithm for feature extraction in time series data by leveraging tools from topological data analysis. Our algorithm provides a simple, efficient way to successfully harness topological features of the attractor of the…

Computational Geometry · Computer Science 2019-06-05 Kwangho Kim , Jisu Kim , Alessandro Rinaldo

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

Machine Learning · Computer Science 2020-11-11 Arnur Nigmetov , Aditi S. Krishnapriyan , Nicole Sanderson , Dmitriy Morozov

We introduce a financial portfolio optimization framework that allows us to automatically select the relevant assets and estimate their weights by relying on a sorted $\ell_1$-Norm penalization, henceforth SLOPE. Our approach is able to…

Portfolio Management · Quantitative Finance 2021-07-30 Philipp J. Kremer , Sangkyun Lee , Malgorzata Bogdan , Sandra Paterlini

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Methodology · Statistics 2020-03-17 Yu-Min Chung , William Cruse , Austin Lawson

In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…

Methodology · Statistics 2025-12-10 Cagatay Ayhan , Audrey N. Nash , Roberto Vincis , Martin Bauer , Richard Bertram , Tom Needham

Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the…

Computer Vision and Pattern Recognition · Computer Science 2021-02-15 Tegan Emerson , Sarah Tymochko , George Stantchev , Jason A. Edelberg , Michael Wilson , Colin C. Olson

Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…

Algebraic Topology · Mathematics 2024-04-19 Jian Liu , Dong Chen , Guo-Wei Wei

Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…

Machine Learning · Computer Science 2025-04-02 ZiXin Lin , Nur Fariha Syaqina Zulkepli

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any…

Social and Information Networks · Computer Science 2012-03-06 Animashree Anandkumar , Avinatan Hassidim , Jonathan Kelner

Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…

Mathematical Finance · Quantitative Finance 2023-07-11 Miguel A. Ruiz-Ortiz , José Carlos Gómez-Larrañaga , Jesús Rodríguez-Viorato

The Total Portfolio Approach and Strategic Asset Allocation are widely viewed as competing frameworks for institutional portfolio management. We argue they differ in a single governance parameter: the tracking error constraint. Using U.S.…

Portfolio Management · Quantitative Finance 2026-03-04 Ashwin Alankar , Allan Maymin , Philip Maymin , Myron Scholes , Sujiang Zhang

Asynchronous trading in high-frequency financial markets introduces significant biases into econometric analysis, distorting risk estimates and leading to suboptimal portfolio decisions. Existing synchronization methods, such as the…

Econometrics · Economics 2025-07-17 Xinbing Kong , Cheng Liu , Bin Wu

An actively managed portfolio almost never beats the market in the long term. Thus, many investors often resort to passively managed portfolios whose aim is to follow a certain financial index. The task of building such passive portfolios…

We propose a distributionally robust index tracking model with the conditional value-at-risk (CVaR) penalty. The model combines the idea of distributionally robust optimization for data uncertainty and the CVaR penalty to avoid large…

Optimization and Control · Mathematics 2023-09-12 Ruyu Wang , Yaozhong Hu , Chao Zhang

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…

Methodology · Statistics 2017-12-27 Chul Moon , Noah Giansiracusa , Nicole A. Lazar

We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying…

Portfolio Management · Quantitative Finance 2025-12-16 Travon Lucius , Christian Koch , Jacob Starling , Julia Zhu , Miguel Urena , Carrie Hu

In topological data analysis, a point cloud data P extracted from a metric space is often analyzed by computing the persistence diagram or barcodes of a sequence of Rips complexes built on $P$ indexed by a scale parameter. Unfortunately,…

Computational Geometry · Computer Science 2016-09-27 Tamal K. Dey , Dayu Shi , Yusu Wang

A methodology to perform topological regularization via information filtering network is introduced. This methodology can be directly applied to covariance selection problem providing an instrument for sparse probabilistic modeling with…

Machine Learning · Computer Science 2021-11-02 Tomaso Aste

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

Chaotic Dynamics · Physics 2020-01-28 Audun Myers , Elizabeth Munch , Firas A. Khasawneh