Tag: topological
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Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval
Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval arXiv:2602.17779v1 Announce Type: new Abstract: We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signal $boldsymbol{theta}^star in mathbb{R}^d$ (where $d gg 1$) from a loss function $hat{R}(boldsymbol{theta})$…
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Colored Markov Random Fields for Probabilistic Topological Modeling
Colored Markov Random Fields for Probabilistic Topological Modeling arXiv:2512.03727v1 Announce Type: new Abstract: Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological…
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Prototype Selection Using Topological Data Analysis
Prototype Selection Using Topological Data Analysis arXiv:2511.04873v1 Announce Type: new Abstract: Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological Prototype Selector (TPS), for selecting representative subsets (prototypes) from large datasets. We demonstrate…
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Matched Topological Subspace Detector
Matched Topological Subspace Detector arXiv:2504.05892v1 Announce Type: new Abstract: Topological spaces, represented by simplicial complexes, capture richer relationships than graphs by modeling interactions not only between nodes but also among higher-order entities, such as edges or triangles. This motivates the representation of information defined in irregular domains as topological signals. By leveraging the spectral dualities…