Search Results for author: Pratik Jawanpuria

Found 22 papers, 10 papers with code

Generalized Bures-Wasserstein Geometry for Positive Definite Matrices

1 code implementation20 Oct 2021 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

This paper proposes a generalized Bures-Wasserstein (BW) Riemannian geometry for the manifold of symmetric positive definite matrices.

On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry

1 code implementation1 Jun 2021 Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao

We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices.

Riemannian optimization

Light-weight Document Image Cleanup using Perceptual Loss

1 code implementation19 May 2021 Soumyadeep Dey, Pratik Jawanpuria

Smartphones have enabled effortless capturing and sharing of documents in digital form.

Transfer Learning

SPOT: A framework for selection of prototypes using optimal transport

no code implementations18 Mar 2021 Karthik S. Gurumoorthy, Pratik Jawanpuria, Bamdev Mishra

In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset.

Decision Making Prototype Selection

Manifold optimization for non-linear optimal transport problems

1 code implementation1 Mar 2021 Bamdev Mishra, N T V Satyadev, Hiroyuki Kasai, Pratik Jawanpuria

In this work, we discuss how to computationally approach general non-linear OT problems within the framework of Riemannian manifold optimization.

Integral Probability Metric based Regularization for Optimal Transport

no code implementations10 Nov 2020 Piyushi Manupriya, J. Saketha Nath, Pratik Jawanpuria

Also, in the special case where the regularization is squared maximum mean discrepancy based, the proposed OT variant, as well as the corresponding Barycenter formulation, turn out to be those of minimizing a convex quadratic subject to non-negativity/simplex constraints and hence can be solved efficiently.

Efficient Robust Optimal Transport with Application to Multi-Label Classification

2 code implementations22 Oct 2020 Pratik Jawanpuria, N T V Satyadev, Bamdev Mishra

Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications.

Classification Multi-class Classification +1

Learning Geometric Word Meta-Embeddings

no code implementations WS 2020 Pratik Jawanpuria, N T V Satya Dev, Anoop Kunchukuttan, Bamdev Mishra

We propose a geometric framework for learning meta-embeddings of words from different embedding sources.

Word Similarity

A Simple Approach to Learning Unsupervised Multilingual Embeddings

no code implementations EMNLP 2020 Pratik Jawanpuria, Mayank Meghwanshi, Bamdev Mishra

Recent progress on unsupervised learning of cross-lingual embeddings in bilingual setting has given impetus to learning a shared embedding space for several languages without any supervision.

Bilingual Lexicon Induction Dependency Parsing +3

Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings

no code implementations ACL 2020 Pratik Jawanpuria, Mayank Meghwanshi, Bamdev Mishra

We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages.

Bilingual Lexicon Induction Domain Adaptation +1

Statistical Optimal Transport posed as Learning Kernel Embedding

no code implementations NeurIPS 2020 J. Saketha Nath, Pratik Jawanpuria

This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings.

Riemannian optimization on the simplex of positive definite matrices

no code implementations25 Jun 2019 Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria

In this work, we generalize the probability simplex constraint to matrices, i. e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where $\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size $n\times n$ for all $i = \{1,\ldots, K \}$.

Riemannian optimization

Low-rank approximations of hyperbolic embeddings

no code implementations18 Mar 2019 Pratik Jawanpuria, Mayank Meghwanshi, Bamdev Mishra

While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately due to its usefulness in modeling continuous hierarchies.

Riemannian adaptive stochastic gradient algorithms on matrix manifolds

1 code implementation4 Feb 2019 Hiroyuki Kasai, Pratik Jawanpuria, Bamdev Mishra

We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column subspaces of gradients.

McTorch, a manifold optimization library for deep learning

1 code implementation3 Oct 2018 Mayank Meghwanshi, Pratik Jawanpuria, Anoop Kunchukuttan, Hiroyuki Kasai, Bamdev Mishra

In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.

Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach

2 code implementations TACL 2019 Pratik Jawanpuria, Arjun Balgovind, Anoop Kunchukuttan, Bamdev Mishra

Our approach decouples learning the transformation from the source language to the target language into (a) learning rotations for language-specific embeddings to align them to a common space, and (b) learning a similarity metric in the common space to model similarities between the embeddings.

Bilingual Lexicon Induction Multilingual Word Embeddings +2

A Unified Framework for Structured Low-rank Matrix Learning

1 code implementation ICML 2018 Pratik Jawanpuria, Bamdev Mishra

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.

Matrix Completion Multi-Task Learning

Low-rank geometric mean metric learning

1 code implementation14 Jun 2018 Mukul Bhutani, Pratik Jawanpuria, Hiroyuki Kasai, Bamdev Mishra

We propose a low-rank approach to learning a Mahalanobis metric from data.

Metric Learning

A dual framework for low-rank tensor completion

no code implementations NeurIPS 2018 Madhav Nimishakavi, Pratik Jawanpuria, Bamdev Mishra

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization.

Riemannian optimization

A Riemannian gossip approach to subspace learning on Grassmann manifold

no code implementations1 May 2017 Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria, Atul Saroop

Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others.

Low-Rank Matrix Completion

Structured low-rank matrix learning: algorithms and applications

no code implementations24 Apr 2017 Pratik Jawanpuria, Bamdev Mishra

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.

Matrix Completion Multi-Task Learning

Efficient Output Kernel Learning for Multiple Tasks

no code implementations NeurIPS 2015 Pratik Jawanpuria, Maksim Lapin, Matthias Hein, Bernt Schiele

The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other.

Multi-Task Learning

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