Search Results for author: Puoya Tabaghi

Found 11 papers, 6 papers with code

Universal Representation of Permutation-Invariant Functions on Vectors and Tensors

no code implementations20 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.

Principal Component Analysis in Space Forms

1 code implementation6 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.

Dimensionality Reduction

Learning Ultrametric Trees for Optimal Transport Regression

1 code implementation21 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.

regression

HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering

1 code implementation19 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.

Clustering Denoising

Provably Accurate and Scalable Linear Classifiers in Hyperbolic Spaces

1 code implementation7 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.

Time Series Analysis

Highly Scalable and Provably Accurate Classification in Poincare Balls

1 code implementation8 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.

Classification Time Series Analysis

Linear Classifiers in Product Space Forms

1 code implementation19 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.

On Procrustes Analysis in Hyperbolic Space

no code implementations7 Feb 2021 Puoya Tabaghi, Ivan Dokmanic

Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation.

Translation

Geometry of Similarity Comparisons

no code implementations17 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.

Hyperbolic Distance Matrices

no code implementations18 May 2020 Puoya Tabaghi, Ivan Dokmanić

Hyperbolic space is a natural setting for mining and visualizing data with hierarchical structure.

Learning Schatten--von Neumann Operators

no code implementations29 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.

Learning Theory

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