Search Results for author: Nhat Ho

Found 88 papers, 27 papers with code

Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning

no code implementations4 Mar 2024 Tung Le, Khai Nguyen, Shanlin Sun, Nhat Ho, Xiaohui Xie

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis.

Object Tracking valid

On Parameter Estimation in Deviated Gaussian Mixture of Experts

no code implementations7 Feb 2024 Huy Nguyen, Khai Nguyen, Nhat Ho

We consider the parameter estimation problem in the deviated Gaussian mixture of experts in which the data are generated from $(1 - \lambda^{\ast}) g_0(Y| X)+ \lambda^{\ast} \sum_{i = 1}^{k_{\ast}} p_{i}^{\ast} f(Y|(a_{i}^{\ast})^{\top}X+b_i^{\ast},\sigma_{i}^{\ast})$, where $X, Y$ are respectively a covariate vector and a response variable, $g_{0}(Y|X)$ is a known function, $\lambda^{\ast} \in [0, 1]$ is true but unknown mixing proportion, and $(p_{i}^{\ast}, a_{i}^{\ast}, b_{i}^{\ast}, \sigma_{i}^{\ast})$ for $1 \leq i \leq k^{\ast}$ are unknown parameters of the Gaussian mixture of experts.

FuseMoE: Mixture-of-Experts Transformers for Fleximodal Fusion

no code implementations5 Feb 2024 Xing Han, Huy Nguyen, Carl Harris, Nhat Ho, Suchi Saria

As machine learning models in critical fields increasingly grapple with multimodal data, they face the dual challenges of handling a wide array of modalities, often incomplete due to missing elements, and the temporal irregularity and sparsity of collected samples.

Missing Elements

On Least Squares Estimation in Softmax Gating Mixture of Experts

no code implementations5 Feb 2024 Huy Nguyen, Nhat Ho, Alessandro Rinaldo

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model.

CompeteSMoE - Effective Training of Sparse Mixture of Experts via Competition

no code implementations4 Feb 2024 Quang Pham, Giang Do, Huy Nguyen, TrungTin Nguyen, Chenghao Liu, Mina Sartipi, Binh T. Nguyen, Savitha Ramasamy, XiaoLi Li, Steven Hoi, Nhat Ho

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width.

Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks

no code implementations3 Feb 2024 Duy M. H. Nguyen, Nina Lukashina, Tai Nguyen, An T. Le, TrungTin Nguyen, Nhat Ho, Jan Peters, Daniel Sonntag, Viktor Zaverkin, Mathias Niepert

Contrary to prior work, we propose a novel 2D--3D aggregation mechanism based on a differentiable solver for the \emph{Fused Gromov-Wasserstein Barycenter} problem and the use of an efficient online conformer generation method based on distance geometry.

Molecular Property Prediction Property Prediction

Sliced Wasserstein with Random-Path Projecting Directions

no code implementations29 Jan 2024 Khai Nguyen, Shujian Zhang, Tam Le, Nhat Ho

From the RPD, we derive the random-path slicing distribution (RPSD) and two variants of sliced Wasserstein, i. e., the Random-Path Projection Sliced Wasserstein (RPSW) and the Importance Weighted Random-Path Projection Sliced Wasserstein (IWRPSW).


Bayesian Nonparametrics Meets Data-Driven Robust Optimization

no code implementations28 Jan 2024 Nicola Bariletto, Nhat Ho

Training machine learning and statistical models often involves optimizing a data-driven risk criterion.

Binary Classification

Is Temperature Sample Efficient for Softmax Gaussian Mixture of Experts?

no code implementations25 Jan 2024 Huy Nguyen, Pedram Akbarian, Nhat Ho

We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as $\mathcal{O}(1/\log(n))$, where $n$ denotes the sample size.

Neural Collapse for Cross-entropy Class-Imbalanced Learning with Unconstrained ReLU Feature Model

no code implementations4 Jan 2024 Hien Dang, Tho Tran, Tan Nguyen, Nhat Ho

However, when the training dataset is class-imbalanced, some NC properties will no longer be true.

A General Theory for Softmax Gating Multinomial Logistic Mixture of Experts

no code implementations22 Oct 2023 Huy Nguyen, Pedram Akbarian, TrungTin Nguyen, Nhat Ho

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications.

Density Estimation regression

Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts

no code implementations25 Sep 2023 Huy Nguyen, Pedram Akbarian, Fanqi Yan, Nhat Ho

When the true number of experts $k_{\ast}$ is known, we demonstrate that the convergence rates of density and parameter estimations are both parametric on the sample size.

Density Estimation

Quasi-Monte Carlo for 3D Sliced Wasserstein

1 code implementation21 Sep 2023 Khai Nguyen, Nicola Bariletto, Nhat Ho

Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation.

Stochastic Optimization Style Transfer

LVM-Med: Learning Large-Scale Self-Supervised Vision Models for Medical Imaging via Second-order Graph Matching

1 code implementation NeurIPS 2023 Duy M. H. Nguyen, Hoang Nguyen, Nghiem T. Diep, Tan N. Pham, Tri Cao, Binh T. Nguyen, Paul Swoboda, Nhat Ho, Shadi Albarqouni, Pengtao Xie, Daniel Sonntag, Mathias Niepert

While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images.

Contrastive Learning Diabetic Retinopathy Grading +3

Privacy Preserving Bayesian Federated Learning in Heterogeneous Settings

no code implementations13 Jun 2023 Disha Makhija, Joydeep Ghosh, Nhat Ho

Moreover, the need for uncertainty quantification and data privacy constraints are often particularly amplified for clients that have limited local data.

Federated Learning Privacy Preserving +1

Beyond Vanilla Variational Autoencoders: Detecting Posterior Collapse in Conditional and Hierarchical Variational Autoencoders

no code implementations8 Jun 2023 Hien Dang, Tho Tran, Tan Nguyen, Nhat Ho

Specifically, via a non-trivial theoretical analysis of linear conditional VAE and hierarchical VAE with two levels of latent, we prove that the cause of posterior collapses in these models includes the correlation between the input and output of the conditional VAE and the effect of learnable encoder variance in the hierarchical VAE.

Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction

no code implementations27 May 2023 Tung Le, Khai Nguyen, Shanlin Sun, Kun Han, Nhat Ho, Xiaohui Xie

The metric is defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach.

Surface Reconstruction

Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts

1 code implementation12 May 2023 Huy Nguyen, TrungTin Nguyen, Khai Nguyen, Nhat Ho

Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several applications of machine learning and statistics.

Ensemble Learning

Sliced Wasserstein Estimation with Control Variates

1 code implementation30 Apr 2023 Khai Nguyen, Nhat Ho

To bridge the literature on variance reduction and the literature on the SW distance, we propose computationally efficient control variates to reduce the variance of the empirical estimation of the SW distance.

Energy-Based Sliced Wasserstein Distance

1 code implementation NeurIPS 2023 Khai Nguyen, Nhat Ho

The second approach is optimizing for the best distribution which belongs to a parametric family of distributions and can maximize the expected distance.

Point cloud reconstruction

Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstruction

1 code implementation12 Jan 2023 Khai Nguyen, Dang Nguyen, Nhat Ho

Despite being efficient, Max-SW and its amortized version cannot guarantee metricity property due to the sub-optimality of the projected gradient ascent and the amortization gap.

Point cloud reconstruction

Markovian Sliced Wasserstein Distances: Beyond Independent Projections

1 code implementation NeurIPS 2023 Khai Nguyen, Tongzheng Ren, Nhat Ho

Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions.

Neural Collapse in Deep Linear Networks: From Balanced to Imbalanced Data

2 code implementations1 Jan 2023 Hien Dang, Tho Tran, Stanley Osher, Hung Tran-The, Nhat Ho, Tan Nguyen

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing.

Image Classification

Joint Self-Supervised Image-Volume Representation Learning with Intra-Inter Contrastive Clustering

no code implementations4 Dec 2022 Duy M. H. Nguyen, Hoang Nguyen, Mai T. N. Truong, Tri Cao, Binh T. Nguyen, Nhat Ho, Paul Swoboda, Shadi Albarqouni, Pengtao Xie, Daniel Sonntag

Recent breakthroughs in self-supervised learning (SSL) offer the ability to overcome the lack of labeled training samples by learning feature representations from unlabeled data.

Brain Segmentation Clustering +3

Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature

1 code implementation28 Nov 2022 Khang Nguyen, Hieu Nong, Vinh Nguyen, Nhat Ho, Stanley Osher, Tan Nguyen

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing.

Improving Multi-task Learning via Seeking Task-based Flat Regions

no code implementations24 Nov 2022 Hoang Phan, Lam Tran, Ngoc N. Tran, Nhat Ho, Dinh Phung, Trung Le

Multi-Task Learning (MTL) is a widely-used and powerful learning paradigm for training deep neural networks that allows learning more than one objective by a single backbone.

Multi-Task Learning speech-recognition +1

Fast Approximation of the Generalized Sliced-Wasserstein Distance

no code implementations19 Oct 2022 Dung Le, Huy Nguyen, Khai Nguyen, Trang Nguyen, Nhat Ho

Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability distributions.

Improving Generative Flow Networks with Path Regularization

no code implementations29 Sep 2022 Anh Do, Duy Dinh, Tan Nguyen, Khuong Nguyen, Stanley Osher, Nhat Ho

Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function.

Active Learning

Hierarchical Sliced Wasserstein Distance

1 code implementation27 Sep 2022 Khai Nguyen, Tongzheng Ren, Huy Nguyen, Litu Rout, Tan Nguyen, Nhat Ho

We explain the usage of these projections by introducing Hierarchical Radon Transform (HRT) which is constructed by applying Radon Transform variants recursively.

Stochastic Multiple Target Sampling Gradient Descent

1 code implementation4 Jun 2022 Hoang Phan, Ngoc Tran, Trung Le, Toan Tran, Nhat Ho, Dinh Phung

Furthermore, when analysing its asymptotic properties, SVGD reduces exactly to a single-objective optimization problem and can be viewed as a probabilistic version of this single-objective optimization problem.

Multi-Task Learning

Transformer with Fourier Integral Attentions

no code implementations1 Jun 2022 Tan Nguyen, Minh Pham, Tam Nguyen, Khai Nguyen, Stanley J. Osher, Nhat Ho

Multi-head attention empowers the recent success of transformers, the state-of-the-art models that have achieved remarkable success in sequence modeling and beyond.

Image Classification Language Modelling +1

Efficient Forecasting of Large Scale Hierarchical Time Series via Multilevel Clustering

no code implementations27 May 2022 Xing Han, Tongzheng Ren, Jing Hu, Joydeep Ghosh, Nhat Ho

To attain this goal, each time series is first assigned the forecast for its cluster representative, which can be considered as a "shrinkage prior" for the set of time series it represents.

Clustering Time Series +1

Federated Self-supervised Learning for Heterogeneous Clients

no code implementations25 May 2022 Disha Makhija, Nhat Ho, Joydeep Ghosh

As the field advances, two key challenges that still remain to be addressed are: (1) system heterogeneity - variability in the compute and/or data resources present on each client, and (2) lack of labeled data in certain federated settings.

Federated Learning Representation Learning +1

Beyond EM Algorithm on Over-specified Two-Component Location-Scale Gaussian Mixtures

no code implementations23 May 2022 Tongzheng Ren, Fuheng Cui, Sujay Sanghavi, Nhat Ho

However, when the models are over-specified, namely, the chosen number of components to fit the data is larger than the unknown true number of components, EM needs a polynomial number of iterations in terms of the sample size to reach the final statistical radius; this is computationally expensive in practice.

Open-Ended Question Answering

An Exponentially Increasing Step-size for Parameter Estimation in Statistical Models

no code implementations16 May 2022 Nhat Ho, Tongzheng Ren, Sujay Sanghavi, Purnamrita Sarkar, Rachel Ward

Therefore, the total computational complexity of the EGD algorithm is \emph{optimal} and exponentially cheaper than that of the GD for solving parameter estimation in non-regular statistical models while being comparable to that of the GD in regular statistical settings.

Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution

2 code implementations4 Apr 2022 Khai Nguyen, Nhat Ho

Finally, we demonstrate the favorable performance of CSW over the conventional sliced Wasserstein in comparing probability measures over images and in training deep generative modeling on images.

Amortized Projection Optimization for Sliced Wasserstein Generative Models

1 code implementation25 Mar 2022 Khai Nguyen, Nhat Ho

Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications.

Global-Local Regularization Via Distributional Robustness

1 code implementation1 Mar 2022 Hoang Phan, Trung Le, Trung Phung, Tuan Anh Bui, Nhat Ho, Dinh Phung

First, they purely focus on local regularization to strengthen model robustness, missing a global regularization effect which is useful in many real-world applications (e. g., domain adaptation, domain generalization, and adversarial machine learning).

Domain Generalization

Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models

1 code implementation17 Feb 2022 Tudor Manole, Nhat Ho

These new loss functions accurately capture the heterogeneity in convergence rates of fitted mixture components, and we use them to sharpen existing pointwise and uniform convergence rates in various classes of mixture models.

Architecture Agnostic Federated Learning for Neural Networks

no code implementations15 Feb 2022 Disha Makhija, Xing Han, Nhat Ho, Joydeep Ghosh

With growing concerns regarding data privacy and rapid increase in data volume, Federated Learning(FL) has become an important learning paradigm.

Federated Learning

Improving Computational Complexity in Statistical Models with Second-Order Information

no code implementations9 Feb 2022 Tongzheng Ren, Jiacheng Zhuo, Sujay Sanghavi, Nhat Ho

This computational complexity is cheaper than that of the fixed step-size gradient descent algorithm, which is of the order $\mathcal{O}(n^{\tau})$ for some $\tau > 1$, to reach the same statistical radius.

Beyond Black Box Densities: Parameter Learning for the Deviated Components

no code implementations5 Feb 2022 Dat Do, Nhat Ho, XuanLong Nguyen

As we collect additional samples from a data population for which a known density function estimate may have been previously obtained by a black box method, the increased complexity of the data set may result in the true density being deviated from the known estimate by a mixture distribution.

Bayesian Consistency with the Supremum Metric

no code implementations10 Jan 2022 Nhat Ho, Stephen G. Walker

We present simple conditions for Bayesian consistency in the supremum metric.

On Cross-Layer Alignment for Model Fusion of Heterogeneous Neural Networks

no code implementations29 Oct 2021 Dang Nguyen, Trang Nguyen, Khai Nguyen, Dinh Phung, Hung Bui, Nhat Ho

To address this issue, we propose a novel model fusion framework, named CLAFusion, to fuse neural networks with a different number of layers, which we refer to as heterogeneous neural networks, via cross-layer alignment.

Knowledge Distillation Model Compression

On Label Shift in Domain Adaptation via Wasserstein Distance

no code implementations29 Oct 2021 Trung Le, Dat Do, Tuan Nguyen, Huy Nguyen, Hung Bui, Nhat Ho, Dinh Phung

We study the label shift problem between the source and target domains in general domain adaptation (DA) settings.

Domain Adaptation

Improving Transformers with Probabilistic Attention Keys

1 code implementation16 Oct 2021 Tam Nguyen, Tan M. Nguyen, Dung D. Le, Duy Khuong Nguyen, Viet-Anh Tran, Richard G. Baraniuk, Nhat Ho, Stanley J. Osher

Inspired by this observation, we propose Transformer with a Mixture of Gaussian Keys (Transformer-MGK), a novel transformer architecture that replaces redundant heads in transformers with a mixture of keys at each head.

Language Modelling

Towards Statistical and Computational Complexities of Polyak Step Size Gradient Descent

no code implementations15 Oct 2021 Tongzheng Ren, Fuheng Cui, Alexia Atsidakou, Sujay Sanghavi, Nhat Ho

We study the statistical and computational complexities of the Polyak step size gradient descent algorithm under generalized smoothness and Lojasiewicz conditions of the population loss function, namely, the limit of the empirical loss function when the sample size goes to infinity, and the stability between the gradients of the empirical and population loss functions, namely, the polynomial growth on the concentration bound between the gradients of sample and population loss functions.

Entropic Gromov-Wasserstein between Gaussian Distributions

no code implementations24 Aug 2021 Khang Le, Dung Le, Huy Nguyen, Dat Do, Tung Pham, Nhat Ho

When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions.

Improving Mini-batch Optimal Transport via Partial Transportation

2 code implementations22 Aug 2021 Khai Nguyen, Dang Nguyen, The-Anh Vu-Le, Tung Pham, Nhat Ho

Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications.

Partial Domain Adaptation

On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexity

no code implementations18 Aug 2021 Khang Le, Huy Nguyen, Tung Pham, Nhat Ho

We demonstrate that the ApproxMPOT algorithm can approximate the optimal value of multimarginal POT problem with a computational complexity upper bound of the order $\tilde{\mathcal{O}}(m^3(n+1)^{m}/ \varepsilon^2)$ where $\varepsilon > 0$ stands for the desired tolerance.

On Integral Theorems and their Statistical Properties

no code implementations22 Jul 2021 Nhat Ho, Stephen G. Walker

We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals.

Statistical Analysis from the Fourier Integral Theorem

no code implementations11 Jun 2021 Nhat Ho, Stephen G. Walker

Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions.

Structured Dropout Variational Inference for Bayesian Neural Networks

no code implementations NeurIPS 2021 Son Nguyen, Duong Nguyen, Khai Nguyen, Khoat Than, Hung Bui, Nhat Ho

Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability.

Bayesian Inference Computational Efficiency +2

On Robust Optimal Transport: Computational Complexity and Barycenter Computation

no code implementations NeurIPS 2021 Khang Le, Huy Nguyen, Quang Nguyen, Tung Pham, Hung Bui, Nhat Ho

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence.

On Transportation of Mini-batches: A Hierarchical Approach

2 code implementations11 Feb 2021 Khai Nguyen, Dang Nguyen, Quoc Nguyen, Tung Pham, Hung Bui, Dinh Phung, Trung Le, Nhat Ho

To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures.

Domain Adaptation

Point-set Distances for Learning Representations of 3D Point Clouds

1 code implementation ICCV 2021 Trung Nguyen, Quang-Hieu Pham, Tam Le, Tung Pham, Nhat Ho, Binh-Son Hua

From this study, we propose to use sliced Wasserstein distance and its variants for learning representations of 3D point clouds.

Point Cloud Registration Transfer Learning

On the computational and statistical complexity of over-parameterized matrix sensing

no code implementations27 Jan 2021 Jiacheng Zhuo, Jeongyeol Kwon, Nhat Ho, Constantine Caramanis

We consider solving the low rank matrix sensing problem with Factorized Gradient Descend (FGD) method when the true rank is unknown and over-specified, which we refer to as over-parameterized matrix sensing.

Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel

no code implementations28 Dec 2020 Nhat Ho, Stephen G. Walker

Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and the search for modes of multivariate density functions (modal regression).


Improving Relational Regularized Autoencoders with Spherical Sliced Fused Gromov Wasserstein

2 code implementations ICLR 2021 Khai Nguyen, Son Nguyen, Nhat Ho, Tung Pham, Hung Bui

To improve the discrepancy and consequently the relational regularization, we propose a new relational discrepancy, named spherical sliced fused Gromov Wasserstein (SSFG), that can find an important area of projections characterized by a von Mises-Fisher distribution.

Image Generation

Projection Robust Wasserstein Distance and Riemannian Optimization

no code implementations NeurIPS 2020 Tianyi Lin, Chenyou Fan, Nhat Ho, Marco Cuturi, Michael. I. Jordan

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance.

Riemannian optimization

Probabilistic Best Subset Selection via Gradient-Based Optimization

1 code implementation11 Jun 2020 Mingzhang Yin, Nhat Ho, Bowei Yan, Xiaoning Qian, Mingyuan Zhou

This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is also known as the best subset selection.


On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regression

no code implementations4 Jun 2020 Jeongyeol Kwon, Nhat Ho, Constantine Caramanis

In the low SNR regime where the SNR is below $\mathcal{O}((d/n)^{1/4})$, we show that EM converges to a $\mathcal{O}((d/n)^{1/4})$ neighborhood of the true parameters, after $\mathcal{O}((n/d)^{1/2})$ iterations.


Uniform Convergence Rates for Maximum Likelihood Estimation under Two-Component Gaussian Mixture Models

1 code implementation1 Jun 2020 Tudor Manole, Nhat Ho

We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances.

Instability, Computational Efficiency and Statistical Accuracy

no code implementations22 May 2020 Nhat Ho, Koulik Khamaru, Raaz Dwivedi, Martin J. Wainwright, Michael. I. Jordan, Bin Yu

Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case.

Computational Efficiency

Distributional Sliced-Wasserstein and Applications to Generative Modeling

1 code implementation ICLR 2021 Khai Nguyen, Nhat Ho, Tung Pham, Hung Bui

Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high dimensional space.


Fixed-Support Wasserstein Barycenters: Computational Hardness and Fast Algorithm

no code implementations NeurIPS 2020 Tianyi Lin, Nhat Ho, Xi Chen, Marco Cuturi, Michael. I. Jordan

We study the fixed-support Wasserstein barycenter problem (FS-WBP), which consists in computing the Wasserstein barycenter of $m$ discrete probability measures supported on a finite metric space of size $n$.

Open-Ended Question Answering

On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithm

1 code implementation ICML 2020 Khiem Pham, Khang Le, Nhat Ho, Tung Pham, Hung Bui

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components.

Sampling for Bayesian Mixture Models: MCMC with Polynomial-Time Mixing

no code implementations11 Dec 2019 Wenlong Mou, Nhat Ho, Martin J. Wainwright, Peter L. Bartlett, Michael. I. Jordan

We study the problem of sampling from the power posterior distribution in Bayesian Gaussian mixture models, a robust version of the classical posterior.

Flow-based Alignment Approaches for Probability Measures in Different Spaces

1 code implementation10 Oct 2019 Tam Le, Nhat Ho, Makoto Yamada

By leveraging a tree structure, we propose to align \textit{flows} from a root to each support instead of pair-wise tree metrics of supports, i. e., flows from a support to another, in GW.

Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes

no code implementations10 Oct 2019 Tam Le, Viet Huynh, Nhat Ho, Dinh Phung, Makoto Yamada

We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance.


On the Complexity of Approximating Multimarginal Optimal Transport

no code implementations30 Sep 2019 Tianyi Lin, Nhat Ho, Marco Cuturi, Michael. I. Jordan

This provides a first \textit{near-linear time} complexity bound guarantee for approximating the MOT problem and matches the best known complexity bound for the Sinkhorn algorithm in the classical OT setting when $m = 2$.

On Efficient Multilevel Clustering via Wasserstein Distances

1 code implementation19 Sep 2019 Viet Huynh, Nhat Ho, Nhan Dam, XuanLong Nguyen, Mikhail Yurochkin, Hung Bui, and Dinh Phung

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data.


Convergence Rates for Gaussian Mixtures of Experts

no code implementations9 Jul 2019 Nhat Ho, Chiao-Yu Yang, Michael. I. Jordan

We provide a theoretical treatment of over-specified Gaussian mixtures of experts with covariate-free gating networks.

On the Efficiency of Entropic Regularized Algorithms for Optimal Transport

no code implementations1 Jun 2019 Tianyi Lin, Nhat Ho, Michael. I. Jordan

We prove that APDAMD achieves the complexity bound of $\widetilde{O}(n^2\sqrt{\delta}\varepsilon^{-1})$ in which $\delta>0$ stands for the regularity of $\phi$.

Posterior Distribution for the Number of Clusters in Dirichlet Process Mixture Models

no code implementations23 May 2019 Chiao-Yu Yang, Eric Xia, Nhat Ho, Michael I. Jordan

In this work, we provide a rigorous study for the posterior distribution of the number of clusters in DPMM under different prior distributions on the parameters and constraints on the distributions of the data.


Fast Algorithms for Computational Optimal Transport and Wasserstein Barycenter

no code implementations23 May 2019 Wenshuo Guo, Nhat Ho, Michael. I. Jordan

First, we introduce the \emph{accelerated primal-dual randomized coordinate descent} (APDRCD) algorithm for computing the OT distance.

Neural Rendering Model: Joint Generation and Prediction for Semi-Supervised Learning

no code implementations ICLR 2019 Nhat Ho, Tan Nguyen, Ankit B. Patel, Anima Anandkumar, Michael. I. Jordan, Richard G. Baraniuk

The conjugate prior yields a new regularizer for learning based on the paths rendered in the generative model for training CNNs–the Rendering Path Normalization (RPN).

Neural Rendering

On Structured Filtering-Clustering: Global Error Bound and Optimal First-Order Algorithms

no code implementations16 Apr 2019 Nhat Ho, Tianyi Lin, Michael. I. Jordan

We also conduct experiments on real datasets and the numerical results demonstrate the effectiveness of our algorithms.


Sharp Analysis of Expectation-Maximization for Weakly Identifiable Models

no code implementations1 Feb 2019 Raaz Dwivedi, Nhat Ho, Koulik Khamaru, Martin J. Wainwright, Michael. I. Jordan, Bin Yu

We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i. i. d.

On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms

no code implementations19 Jan 2019 Tianyi Lin, Nhat Ho, Michael. I. Jordan

We show that a greedy variant of the classical Sinkhorn algorithm, known as the \emph{Greenkhorn algorithm}, can be improved to $\widetilde{\mathcal{O}}(n^2\varepsilon^{-2})$, improving on the best known complexity bound of $\widetilde{\mathcal{O}}(n^2\varepsilon^{-3})$.

Data Structures and Algorithms

On Deep Domain Adaptation: Some Theoretical Understandings

no code implementations15 Nov 2018 Trung Le, Khanh Nguyen, Nhat Ho, Hung Bui, Dinh Phung

The underlying idea of deep domain adaptation is to bridge the gap between source and target domains in a joint space so that a supervised classifier trained on labeled source data can be nicely transferred to the target domain.

Domain Adaptation Transfer Learning

A Bayesian Perspective of Convolutional Neural Networks through a Deconvolutional Generative Model

no code implementations1 Nov 2018 Tan Nguyen, Nhat Ho, Ankit Patel, Anima Anandkumar, Michael. I. Jordan, Richard G. Baraniuk

This conjugate prior yields a new regularizer based on paths rendered in the generative model for training CNNs-the Rendering Path Normalization (RPN).

Probabilistic Multilevel Clustering via Composite Transportation Distance

no code implementations29 Oct 2018 Nhat Ho, Viet Huynh, Dinh Phung, Michael. I. Jordan

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence.


Singularity, Misspecification, and the Convergence Rate of EM

no code implementations1 Oct 2018 Raaz Dwivedi, Nhat Ho, Koulik Khamaru, Michael. I. Jordan, Martin J. Wainwright, Bin Yu

A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument.

Multilevel Clustering via Wasserstein Means

1 code implementation ICML 2017 Nhat Ho, XuanLong Nguyen, Mikhail Yurochkin, Hung Hai Bui, Viet Huynh, Dinh Phung

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data.


Singularity structures and impacts on parameter estimation in finite mixtures of distributions

no code implementations9 Sep 2016 Nhat Ho, XuanLong Nguyen

Our study makes explicit the deep links between model singularities, parameter estimation convergence rates and minimax lower bounds, and the algebraic geometry of the parameter space for mixtures of continuous distributions.

Identifiability and optimal rates of convergence for parameters of multiple types in finite mixtures

no code implementations11 Jan 2015 Nhat Ho, XuanLong Nguyen

This paper studies identifiability and convergence behaviors for parameters of multiple types in finite mixtures, and the effects of model fitting with extra mixing components.

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