Related papers: Sparse Index Tracking via Topological Learning
The Vietoris-Rips filtration for an $n$-point metric space is a sequence of large simplicial complexes adding a topological structure to the otherwise disconnected space. The persistent homology is a key tool in topological data analysis…
Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a…
Recognizing that asset markets generally exhibit shared informational characteristics, we develop a portfolio strategy based on transfer learning that leverages cross-market information to enhance the investment performance in the market of…
Modern portfolio optimization is centered around creating a low-risk portfolio with extensive asset diversification. Following the seminal work of Markowitz, optimal asset allocation can be computed using a constrained optimization model…
Persistent homology is a central tool in topological data analysis, but its application to large and noisy datasets is often limited by computational cost and the presence of spurious topological features. Noise not only increases data size…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
Index funds are substantially preferred by investors nowadays, and market sensitivities are instrumental in managing index funds. An index fund is a mutual fund aiming to track the returns of a predefined market index (e.g., the S&P 500). A…
Three novel applications of computational topology in the field of fusion science are developed. A procedure for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using Vietoris-Rips…
Public databases of large-scale topology measures (e.g.RIPE Atlas) are very popular both in the research and in the practitioners communities. They are used, at least, for understanding the state of the Internet in real time, for outage…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…
A streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. Recently, several sophisticated frameworks for robustification of classical streaming algorithms have been…
Portfolio management is essential for any investment decision. Yet, traditional methods in the literature are ill-suited for the characteristics and dynamics of cryptocurrencies. This work presents a method to build an investment portfolio…
In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant…
Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One…
In the present work we address the problem of evaluating the historical performance of a trading strategy or a certain portfolio of assets. Common indicators such as the Sharpe ratio and the risk adjusted return have significant drawbacks.…
Modern visual trackers usually construct online learning models under the assumption that the feature response has a Gaussian distribution with target-centered peak response. Nevertheless, such an assumption is implausible when there is…
We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…
We propose a new regret minimization algorithm for episodic sparse linear Markov decision process (SMDP) where the state-transition distribution is a linear function of observed features. The only previously known algorithm for SMDP…