Related papers: Generalized persistence analysis based on stable r…
We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial…
Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are…
In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm,…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…
In this paper we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al.(2017) and Hallin et al.(2021). We study the characterization, computation and properties of…
In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the category of tame functors. We show how this pseudo-metric can be…
As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest…
In this paper, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of measure transportation. Unlike other existing proposals in…
A significant part of modern topological data analysis is concerned with the design and study of algebraic invariants of poset representations -- often referred to as multi-parameter persistence modules. One such invariant is the minimal…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…
Multidimensional persistence modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit…
Clinical trials often involve the assessment of multiple endpoints to comprehensively evaluate the efficacy and safety of interventions. In the work, we consider a global nonparametric testing procedure based on multivariate rank for the…
Feature selection, as a vital dimension reduction technique, reduces data dimension by identifying an essential subset of input features, which can facilitate interpretable insights into learning and inference processes. Algorithmic…
Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
The stability of topological persistence is one of the fundamental issues in topological data analysis. Numerous methods have been proposed to address the stability of persistent modules or persistence diagrams. Recently, the concept of…
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…