no code implementations • 22 May 2024 • Yijin Ni, Xiaoming Huo
Maximum Mean Discrepancy (MMD) is a probability metric that has found numerous applications in machine learning.
no code implementations • 18 Mar 2024 • Tian-Yi Zhou, Namjoon Suh, Guang Cheng, Xiaoming Huo
Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i. e., functionals).
no code implementations • 27 Jan 2024 • Yiling Xie, Xiaoming Huo
Alternatively, a two-step procedure is proposed -- adaptive adversarial training, which could further improve the performance of adversarial training under $\ell_\infty$-perturbation.
no code implementations • 8 Jan 2024 • Hyunouk Ko, Xiaoming Huo
In this paper, we prove the universal consistency of wide and deep ReLU neural network classifiers trained on the logistic loss.
no code implementations • 26 Sep 2023 • Hyunouk Ko, Namjoon Suh, Xiaoming Huo
The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers.
no code implementations • 15 Aug 2023 • Tian-Yi Zhou, Xiaoming Huo
This paper studies the binary classification of unbounded data from ${\mathbb R}^d$ generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks.
1 code implementation • 11 Jul 2023 • Etash Kumar Guha, Eugene Ndiaye, Xiaoming Huo
Given a sequence of observable variables $\{(x_1, y_1), \ldots, (x_n, y_n)\}$, the conformal prediction method estimates a confidence set for $y_{n+1}$ given $x_{n+1}$ that is valid for any finite sample size by merely assuming that the joint distribution of the data is permutation invariant.
no code implementations • 30 May 2023 • Etash Kumar Guha, Prasanjit Dubey, Xiaoming Huo
In this paper, we derive a novel bound on the generalization error of Magnitude-Based pruning of overparameterized neural networks.
no code implementations • 27 Mar 2023 • Yiling Xie, Xiaoming Huo
We propose an adjusted Wasserstein distributionally robust estimator -- based on a nonlinear transformation of the Wasserstein distributionally robust (WDRO) estimator in statistical learning.
no code implementations • 7 Mar 2023 • Yujie Zhao, Xiaoming Huo
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization.
no code implementations • 23 Jan 2023 • Yiling Luo, Yiling Xie, Xiaoming Huo
To compare, we prove that the computational complexity of the Stochastic Sinkhorn algorithm is $\widetilde{{O}}({n^2}/{\epsilon^2})$, which is slower than our accelerated primal-dual stochastic mirror algorithm.
no code implementations • 2 Dec 2022 • Yiling Luo, Xiaoming Huo, Yajun Mei
Our second estimator is a Hessian-free estimator that overcomes the aforementioned limitation.
no code implementations • 29 Oct 2022 • Yiling Xie, Yiling Luo, Xiaoming Huo
Computing the empirical Wasserstein distance in the independence test requires solving this special type of OT problem, where $m=n^2$.
no code implementations • 25 Oct 2022 • Tian-Yi Zhou, Xiaoming Huo
It is frequently observed that overparameterized neural networks generalize well.
no code implementations • 29 Apr 2022 • Yiling Luo, Xiaoming Huo, Yajun Mei
In addition, the Gradient Descent (GD) with a moderate or small step-size converges along the direction that corresponds to the smallest eigenvalue.
no code implementations • 29 Apr 2022 • Yiling Luo, Xiaoming Huo, Yajun Mei
On the other hand, algorithms such as gradient descent and stochastic gradient descent have the implicit regularization property that leads to better performance in terms of the generalization errors.
1 code implementation • 2 Mar 2022 • Yiling Xie, Yiling Luo, Xiaoming Huo
A primal-dual accelerated stochastic gradient descent with variance reduction algorithm (PDASGD) is proposed to solve linear-constrained optimization problems.
no code implementations • ICLR 2022 • Namjoon Suh, Hyunouk Ko, Xiaoming Huo
We study the generalization properties of the overparameterized deep neural network (DNN) with Rectified Linear Unit (ReLU) activations.
no code implementations • 29 Sep 2021 • Yiling Luo, Xiaoming Huo, Yajun Mei
This paper studies the Stochastic Gradient Descent (SGD) algorithm in kernel regression.
no code implementations • 12 Mar 2021 • Yuchen He, Namjoon Suh, Xiaoming Huo, Sungha Kang, Yajun Mei
We provide a set of sufficient conditions which guarantee that, from a single trajectory data denoised by a Local-Polynomial filter, the support of $\mathbf{c}(\lambda)$ asymptotically converges to the true signed-support associated with the underlying PDE for sufficiently many data and a certain range of $\lambda$.
no code implementations • 26 Oct 2020 • Yujie Zhao, Xiaoming Huo
At the same time, each surrogate function is strictly convex, which enables a provable faster numerical rate of convergence.
no code implementations • 2 Dec 2019 • Namjoon Suh, Xiaoming Huo, Eric Heim, Lee Seversky
We propose a combined model, which integrates the latent factor model and the logistic regression model, for the citation network.
no code implementations • 4 Nov 2015 • Cheng Huang, Xiaoming Huo
A potential application of the one-step approach is that one can use multiple machines to speed up large scale statistical inference with little compromise in the quality of estimators.