A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Persistently trained EBMs generate images and estimate complex densities.
CuMPerLay vectorizes CMP for deep learning, improving image analysis.
Improved persistence spheres map measures to functions, stable under partial transport.
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful re…
GeoTop resolves topological ambiguity in diagnostic imaging using geometric-topological analysis.
Paper shows equivalence between MM and PH for n-D Morse functions.
Obstructive sleep apnea is a serious condition causing a litany of health problems especially in the pediatric population. However, this chronic condition can be treated if diagnosis is possible. The gold standard for diagnosis is an overnight sleep study, which is often unobtainable by many potentially suffering from …
Survey on optimizing topological descriptors for machine learning.
Topology-based information retrieval improves query accuracy.
This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform no…
Topology-GS improves 3D GS for better structural and feature integrity.
Study forecasts U.S. bond index using deep learning, finding persistence is key.
New framework distinguishes lung cancer subtypes using MALDI mass spectrometry.
Z-GCNETs uses topological data to improve time series forecasting.
A novel topological method analyzes fMRI data over time.
Veterans with mild traumatic brain injury (mTBI) have reported auditory and visual dysfunction that persists beyond the acute incident. The etiology behind these symptoms is difficult to characterize with current clinical imaging. These functional deficits may be caused by shear injury or micro-bleeds, which can be det…
High-resolution nowcasting is an essential tool needed for effective adaptation to climate change, particularly for extreme weather. As Deep Learning (DL) techniques have shown dramatic promise in many domains, including the geosciences, we present an application of DL to the problem of precipitation nowcasting, i.e., …
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning…
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisi…
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We…
In multi-temporal SAR interferometry (MT-InSAR), persistent scatterer (PS) pixels are used to estimate geophysical parameters, essentially deformation. Conventionally, PS pixels are selected on the basis of the estimated noise present in the spatially uncorrelated phase component along with look-angle error in a tempor…
Approaches for approximating persistent homology for large datasets.
Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
Expands Bredon's trick for applications in geometry and topology.
Proposes deep graph persistence to address neural persistence issues in deep learning.
Paper proves -means clustering works on persistence diagrams.
Formula for interleaving distance of rectangle persistence modules.
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized exam…
New method for analyzing multiparameter persistence modules from smooth functions.
Develops robust persistence diagrams using kernel methods.
The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not useful for classification. We show that, to the contrary, near state-of-the-art clas…
This paper interprets critical scales in persistent homology for compact metric spaces.
MuRiT efficiently computes multi-parameter persistence barcodes.
Persistent homology can recognize knotting in curves.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of d…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a …
The choice of the control frequency of a system has a relevant impact on the ability of reinforcement learning algorithms to learn a highly performing policy. In this paper, we introduce the notion of action persistence that consists in the repetition of an action for a fixed number of decision steps, having the effect…
Given a compact geodesic space we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
A new method compares persistent cycles in topological data.
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …
This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide new methods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main result in this article i…
Paper uses TDA for automated Parkinson's disease classification and severity assessment.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
New lattice path method for statistical inference of persistent diagrams.