Search Results for author:
Found 48 papers, 6 papers with code
Deep Transfer Learning: Model Framework and Error Analysis
This paper presents a framework for deep transfer learning, which aims to leverage information from multi-domain upstream data with a large number of samples $n$ to a single-domain downstream task with a considerably smaller number of samples $m$, where $m \ll n$, in order to enhance performance on downstream task.
Approximation Bounds for Recurrent Neural Networks with Application to Regression
We derive upper bounds on the approximation error of RNNs for H\"older smooth functions, in the sense that the output at each time step of an RNN can approximate a H\"older function that depends only on past and current information, termed a past-dependent function.
Unsupervised Transfer Learning via Adversarial Contrastive Training
Learning a data representation for downstream supervised learning tasks under unlabeled scenario is both critical and challenging.
DRM Revisited: A Complete Error Analysis
In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision?
Quantum Compiling with Reinforcement Learning on a Superconducting Processor
To effectively implement quantum algorithms on noisy intermediate-scale quantum (NISQ) processors is a central task in modern quantum technology.
Model Free Prediction with Uncertainty Assessment
Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years.
Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Method
We present error bound in terms of the sample size $n$ and our work provides guidance on how to set the network depth, width, step size, and number of iterations for the projected gradient descent algorithm.
Characteristic Learning for Provable One Step Generation
We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models.
Latent Schr{ö}dinger Bridge Diffusion Model for Generative Learning
Our theoretical analysis encompasses the establishment of end-to-end error analysis for learning distributions via the latent Schr{\"o}dinger bridge diffusion model.
Convergence Analysis of Flow Matching in Latent Space with Transformers
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching.
Convergence of Continuous Normalizing Flows for Learning Probability Distributions
We establish non-asymptotic error bounds for the distribution estimator based on CNFs, in terms of the Wasserstein-2 distance.
Deep conditional distribution learning via conditional Föllmer flow
We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow.
Semi-Supervised Deep Sobolev Regression: Estimation, Variable Selection and Beyond
We propose SDORE, a semi-supervised deep Sobolev regressor, for the nonparametric estimation of the underlying regression function and its gradient.
Neural Network Approximation for Pessimistic Offline Reinforcement Learning
In this paper, we establish a non-asymptotic estimation error of pessimistic offline RL using general neural network approximation with $\mathcal{C}$-mixing data regarding the structure of networks, the dimension of datasets, and the concentrability of data coverage, under mild assumptions.
Gaussian Interpolation Flows
Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling.
Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits
Our results provide a theoretical foundation for designing practical PQCs and quantum neural networks for machine learning tasks that can be implemented on near-term quantum devices, paving the way for the advancement of quantum machine learning.
Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models
For the quadratic loss in nonparametric regression, we show that the adversarial excess risk bound can be improved over those for a general loss.
Current density impedance imaging with PINNs
In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization.
Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression
We establish error bounds for simultaneously approximating $C^s$ smooth functions and their derivatives using RePU-activated deep neural networks.
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs).
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
This paper analyzes the convergence rate of a deep Galerkin method for the weak solution (DGMW) of second-order elliptic partial differential equations on $\mathbb{R}^d$ with Dirichlet, Neumann, and Robin boundary conditions, respectively.
Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks
We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves.
Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning
We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets.
Approximation bounds for norm constrained neural networks with applications to regression and GANs
This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights.
Wasserstein Generative Learning of Conditional Distribution
The proposed approach uses a conditional generator to transform a known distribution to the target conditional distribution.
Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension
In this paper, we consider recovering $n$ dimensional signals from $m$ binary measurements corrupted by noises and sign flips under the assumption that the target signals have low generative intrinsic dimension, i. e., the target signals can be approximately generated via an $L$-Lipschitz generator $G: \mathbb{R}^k\rightarrow\mathbb{R}^{n}, k\ll n$.
A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis
In this work, we consider the algorithm to the (nonlinear) regression problems with $\ell_0$ penalty.
Non-Asymptotic Error Bounds for Bidirectional GANs
Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support.
Relative Entropy Gradient Sampler for Unnormalized Distributions
We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions.
Coordinate Descent for MCP/SCAD Penalized Least Squares Converges Linearly
Recovering sparse signals from observed data is an important topic in signal/imaging processing, statistics and machine learning.
Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity
Schr\"{o}dinger-F\"{o}llmer sampler (SFS) is a novel and efficient approach for sampling from possibly unnormalized distributions without ergodicity.
Deep Generative Learning via Schrödinger Bridge
At the sample level, we derive our Schr\"{o}dinger Bridge algorithm by plugging the drift term estimated by a deep score estimator and a deep density ratio estimator into the Euler-Maruyama method.
An error analysis of generative adversarial networks for learning distributions
This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples.
Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networks
To establish these results, we derive an upper bound for the covering number for the class of general convolutional neural networks with a bias term in each convolutional layer, and derive new results on the approximation power of CNNs for any uniformly-continuous target functions.
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class
In this paper, we construct neural networks with ReLU, sine and $2^x$ as activation functions.
Toward Understanding Supervised Representation Learning with RKHS and GAN
At the population level, we formulate the ideal representation learning task as that of finding a nonlinear map that minimizes the sum of losses characterizing conditional independence (with RKHS) and disentanglement (with GAN).
Ranked #4 on
Image Classification
on Kuzushiji-MNIST
Sufficient and Disentangled Representation Learning
We provide strong statistical guarantees for the learned representation by establishing an upper bound on the excess error of the objective function and show that it reaches the nonparametric minimax rate under mild conditions.
Generative Learning With Euler Particle Transport
The key task in training is the estimation of the density ratios or differences that determine the residual maps.
Deep Dimension Reduction for Supervised Representation Learning
We propose a deep dimension reduction approach to learning representations with these characteristics.
Learning Implicit Generative Models with Theoretical Guarantees
We then solve the McKean-Vlasov equation numerically using the forward Euler iteration, where the forward Euler map depends on the density ratio (density difference) between the distribution at current iteration and the underlying target distribution.
On Newton Screening
Based on this KKT system, a built-in working set with a relatively small size is first determined using the sum of primal and dual variables generated from the previous iteration, then the primal variable is updated by solving a least-squares problem on the working set and the dual variable updated based on a closed-form expression.
A Support Detection and Root Finding Approach for Learning High-dimensional Generalized Linear Models
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size.
A stochastic alternating minimizing method for sparse phase retrieval
Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention.
Wasserstein-Wasserstein Auto-Encoders
To address the challenges in learning deep generative models (e. g., the blurriness of variational auto-encoder and the instability of training generative adversarial networks, we propose a novel deep generative model, named Wasserstein-Wasserstein auto-encoders (WWAE).
Deep Generative Learning via Variational Gradient Flow
We propose a general framework to learn deep generative models via \textbf{V}ariational \textbf{Gr}adient Fl\textbf{ow} (VGrow) on probability spaces.
SNAP: A semismooth Newton algorithm for pathwise optimization with optimal local convergence rate and oracle properties
We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression.
A Primal Dual Active Set with Continuation Algorithm for the \ell^0-Regularized Optimization Problem
We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing.
A Unified Primal Dual Active Set Algorithm for Nonconvex Sparse Recovery
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations.
