no code implementations • 20 Oct 2023 • Puoya Tabaghi, Yusu Wang
Restricting the domain of the functions to finite multisets of $D$-dimensional vectors, Deep Sets also provides a \emph{universal approximation} that requires a latent space dimension of $O(N^D)$ -- where $N$ is an upper bound on the size of input multisets.
1 code implementation • 6 Jan 2023 • Puoya Tabaghi, Michael Khanzadeh, Yusu Wang, Sivash Mirarab
Finding a low-dimensional Riemannian affine subspace for a set of points in a space form amounts to dimensionality reduction because, as we show, any such affine subspace is isometric to a space form of the same dimension and curvature.
1 code implementation • 21 Oct 2022 • Samantha Chen, Puoya Tabaghi, Yusu Wang
For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the space.
1 code implementation • 19 May 2022 • Eli Chien, Puoya Tabaghi, Olgica Milenkovic
Furthermore, it is currently not known how to choose the most suitable approximation objective for noisy fitting.
1 code implementation • 7 Mar 2022 • Chao Pan, Eli Chien, Puoya Tabaghi, Jianhao Peng, Olgica Milenkovic
The excellent performance of the Poincar\'e second-order and strategic perceptrons shows that the proposed framework can be extended to general machine learning problems in hyperbolic spaces.
1 code implementation • 8 Sep 2021 • Eli Chien, Chao Pan, Puoya Tabaghi, Olgica Milenkovic
For hierarchical data, the space of choice is a hyperbolic space since it guarantees low-distortion embeddings for tree-like structures.
1 code implementation • 19 Feb 2021 • Puoya Tabaghi, Chao Pan, Eli Chien, Jianhao Peng, Olgica Milenkovic
The results show that classification in low-dimensional product space forms for scRNA-seq data offers, on average, a performance improvement of $\sim15\%$ when compared to that in Euclidean spaces of the same dimension.
no code implementations • 7 Feb 2021 • Puoya Tabaghi, Ivan Dokmanic
Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation.
no code implementations • 17 Jun 2020 • Puoya Tabaghi, Jianhao Peng, Olgica Milenkovic, Ivan Dokmanić
To study this question, we introduce the notions of the \textit{ordinal capacity} of a target space form and \emph{ordinal spread} of the similarity measurements.
no code implementations • 18 May 2020 • Puoya Tabaghi, Ivan Dokmanić
Hyperbolic space is a natural setting for mining and visualizing data with hierarchical structure.
no code implementations • 29 Jan 2019 • Puoya Tabaghi, Maarten de Hoop, Ivan Dokmanić
We study the learnability of a class of compact operators known as Schatten--von Neumann operators.