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no code implementations • 27 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.

no code implementations • 12 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, including those in machine learning, statistics, bioinformatics, economics, and medicine.

no code implementations • 5 May 2023 • Huy Nguyen, TrungTin Nguyen, Nhat Ho

Understanding parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature.

no code implementations • 30 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.

no code implementations • 26 Apr 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.

1 code implementation • 12 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.

1 code implementation • 10 Jan 2023 • Khai Nguyen, Tongzheng Ren, Nhat Ho

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

1 code implementation • 1 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.

no code implementations • 4 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.

1 code implementation • 28 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.

no code implementations • 24 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.

no code implementations • 19 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.

no code implementations • 11 Oct 2022 • Xing Han, Tongzheng Ren, Tan Minh Nguyen, Khai Nguyen, Joydeep Ghosh, Nhat Ho

Recent work by Nguyen et al., (2022) has shown that the self-attention mechanism, which is the center of the Transformer architecture, can be viewed as a non-parametric estimator based on kernel density estimation (KDE).

no code implementations • 29 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.

1 code implementation • 27 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.

1 code implementation • 4 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.

no code implementations • 1 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.

no code implementations • 27 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.

no code implementations • 25 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.

no code implementations • 23 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.

no code implementations • 16 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.

2 code implementations • 4 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.

1 code implementation • 25 Mar 2022 • Khai Nguyen, Nhat Ho

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

1 code implementation • 1 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).

1 code implementation • 17 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.

no code implementations • 15 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.

no code implementations • 9 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.

no code implementations • 5 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.

no code implementations • 10 Jan 2022 • Nhat Ho, Stephen G. Walker

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

no code implementations • 29 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.

no code implementations • 29 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.

1 code implementation • 16 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.

no code implementations • 15 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.

no code implementations • 24 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.

2 code implementations • 22 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.

no code implementations • 18 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.

no code implementations • 22 Jul 2021 • Nhat Ho, Stephen G. Walker

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

no code implementations • 11 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.

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.

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.

2 code implementations • 11 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.

no code implementations • 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.

no code implementations • 27 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.

no code implementations • 28 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).

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.

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.

1 code implementation • 11 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.

Methodology

no code implementations • 4 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.

1 code implementation • 1 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.

no code implementations • 22 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.

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.

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 $n$.

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.

no code implementations • 11 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.

no code implementations • 10 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.

1 code implementation • 10 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.

no code implementations • 30 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 $m = 2$.

1 code implementation • 19 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.

no code implementations • 9 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.

no code implementations • 1 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 $\phi$.

no code implementations • 23 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.

no code implementations • 23 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.

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).

no code implementations • 16 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.

no code implementations • 1 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.

no code implementations • 19 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

no code implementations • 15 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.

no code implementations • 1 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).

no code implementations • 29 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.

no code implementations • 1 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.

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.

no code implementations • 9 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.

no code implementations • 11 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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