Neural networks improve nonparametric regression with measurement errors.
problem Nonparametric regression with measurement errors.
method Proposes a neural network design using FNN, normalizing flow, and inference network.
result Neural network approach is more flexible and superior or comparable to classical methods.
New method uses sparse deep neural networks for high-dimensional regression with improved parameter estimation.
problem Improving parameter estimation in high-dimensional sparse regression models.
method Proposes nonparametric estimation of partial derivatives in sparse deep neural networks.
result Established convergence rate of nonparametric estimation of partial derivatives as O(n−1/4). Deep neural networks with adversarial training achieve sup-norm convergence for nonparametric regression.
problem Achieving sup-norm convergence for deep neural network estimators in nonparametric regression.
method Developed an adversarial training scheme to address the sup-norm convergence issue.
result Deep neural network estimators achieve optimal sup-norm convergence with the proposed adversarial training.
The paper tightens bounds on covering numbers for deep ReLU networks.
problem Characterizing the capacity and performance of deep ReLU networks.
method Derives tight lower and upper bounds on metric entropy of ReLU networks.
result Establishes optimality in nonparametric regression via deep networks.
DNCF framework recovers real scenes from imperfect images robustly.
problem Recovering real scenes from imperfect images.
method Nonparametric deep network that learns physical image formation equations.
result DNCF framework robustly defends against adversarial attacks.
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
Deep Heaviside networks are limited but can be improved with connections or linear neurons.
problem Limited expressivity of deep Heaviside networks.
method Including skip connections or linear activation neurons improves expressivity.
result Lower and upper bounds for VC dimensions and approximation rates are derived.
Deep neural networks improve mean function estimation for functional data.
problem Estimating mean functions of functional data.
method Deep neural networks with ReLU activation, sparsely connected.
result Achieves optimal nonparametric convergence rate in empirical norm.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
Proposes a deep learning method for effective data representation.
problem Constructing effective data representations for prediction.
method A deep dimension reduction approach to learning representations with sufficiency, low dimensionality, and disentanglement.
result The proposed deep nonparametric representation is consistent and performs better than existing methods.
DF2M uses deep neural networks within a factor model for high-dimensional functional time series forecasting.
problem Forecasting high-dimensional functional time series with explainability and accuracy.
method Bayesian nonparametric model based on Indian Buffet Process and multi-task Gaussian Process, incorporating a deep kernel function.
result DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models.
Transfer learning using deep neural networks as feature extractors has become increasingly popular over the past few years. It allows to obtain state-of-the-art accuracy on datasets too small to train a deep neural network on its own, and it provides cutting edge descriptors that, combined with nonparametric learning m…
Deep neural network is a state-of-art method in modern science and technology. Much statistical literature have been devoted to understanding its performance in nonparametric estimation, whereas the results are suboptimal due to a redundant logarithmic sacrifice. In this paper, we show that such log-factors are not nec…
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
problem Nonparametric regression and classification under weak dependence.
method Sparse-penalized deep neural networks with oracle inequalities and convergence rates established.
result The proposed estimators outperform non-penalized ones in simulations.
This paper examines how noise affects deep neural networks and improves their performance.
problem The impact of noise on the stability of deep ReLU neural networks for nonparametric regression.
method Investigates the optimal rate of convergence for deep ReLU neural networks under Huber loss, considering the p-th moment of noise and the smoothness of the function.
result The optimal rate of convergence cannot be achieved by ordinary least squares but can be by Huber loss with a properly chosen parameter.
Paper provides label complexity guarantees for deep active learning.
problem Lack of rigorous label complexity guarantees for deep active learning.
method Studied deep active learning from nonparametric classification perspective.
result Proved near-optimal label complexity guarantees for deep active learning.
New theory shows deep networks adapt to data's intrinsic dimensionality even when data isn't on a low-dimensional manifold.
problem Existing theories on deep nonparametric regression assume data lie on a low-dimensional manifold, which is often not the case in real-world applications.
method Introduces effective Minkowski dimension to characterize the intrinsic dimension of data subsets and proves sample complexity depends on this new complexity notation.
result Deep neural networks can adapt to the effective Minkowski dimension of data, circumventing the curse of dimensionality for moderate sample sizes.
Deep neural networks with specific parameter sets can approximate smooth functions efficiently.
problem Approximating smooth functions with deep neural networks.
method Deep neural networks with ReLU activation and specific parameter sets {0,±21,±1,2} are used to approximate Cβ-smooth functions. result The constructed networks can approximate Cβ-smooth functions with parameters {0,±21,±1,2} efficiently, achieving the same convergence rate as sparse networks with parameters in [−1,1]. NTK neural networks are robust to adversarial attacks in nonparametric regression.
problem Adversarial robustness of neural networks in nonparametric regression.
method Gradient flow with early stopping for NTK neural networks, proving robustness in Sobolev spaces.
result NTK neural networks achieve optimal adversarial robustness rates in Sobolev spaces.
SDORE uses neural networks to estimate regression functions and their gradients, even with limited labeled data.
problem Nonparametric estimation of regression functions and their gradients.
method Semi-supervised deep ReQU neural networks with gradient norm regularization.
result Achieves minimax optimal convergence rates in L2-norm and plug-in gradient estimator convergence. Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to logn-factors) under a general composition assumption on the re…
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
Proposes inference for DNNs in GNRMs, addressing non-independence issues.
problem Inference for DNN-estimated means in GNRMs under non-independence.
method Develops a DNN estimator and ESM for variance estimation and confidence intervals.
result Demonstrates feasibility of inference under GNRMs with ESM.
Deep neural networks can learn smooth functions without parameters.
problem Learning smooth functions from shallow ReLU neural networks.
method Using over-parameterized shallow ReLU neural networks with norm constraints.
result Least squares estimators based on shallow neural networks are minimax optimal.
ICP models flexible DAG structures using Bayesian nonparametrics.
problem Learning the structure of complex neural networks.
method Bayesian nonparametric prior on DAGs and orders controlled by a latent Beta Process.
result ICP supports every possible DAG structure.
Deep neural networks tackle high-dimensional nonparametric interaction models.
problem Estimating structured regression functions in high-dimensional data.
method Analyze kth order nonparametric interaction models in growing and high dimensions, introducing debiasing techniques. result Debiased deep neural networks achieve optimal rates of convergence in both growing and high dimensions.
Paper derives convergence rates for NPMLE in Hellinger distance using deep neural networks.
problem Difficulty in proving convergence of excess risk in nonparametric logistic regression.
method Unified approach for analyzing NPMLE, deriving convergence rates in Hellinger distance.
result Derives nearly optimal convergence rates for NPMLE with deep neural networks.
Wide neural networks can degrade performance, contrary to conventional wisdom.
problem Understanding the limitations of increasing network width in neural networks.
method Using Deep Gaussian Processes to decouple capacity and width, analyzing their effects on representational power and non-Gaussianity.
result Wide neural networks can become less adaptable and more Gaussian, leading to performance degradation.
The paper tackles deep learning from dependent data, achieving optimal performance.
problem Deep learning from strongly mixing observations, especially with regularization and optimality.
method Sparse-penalized regularization for deep neural networks, oracle inequality for expected excess risk.
result Deep neural network estimator achieves minimax optimal rate for nonparametric autoregression.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
Deep learning method improves regression accuracy.
problem Nonparametric regression challenges.
method Over-parametrized deep neural networks with logistic activation, gradient descent, special topology, random initialization, and data-dependent learning rate.
result Theoretical bound on L2 error and improved finite sample performance. Paper analyzes deep neural networks with dependent data, establishing convergence rates and error bounds.
problem Statistical analysis of deep neural networks under dependent data.
method Establishes rates of convergence and L2-error bounds for nonparametric sieve estimators of DNNs. result Non-asymptotic probability bounds on L2-errors for DNN estimators under stationary β-mixing data. EEGNN improves graph neural networks by enhancing graph structure.
problem Mis-simplification of graphs by removing self-loops and unweighted edges reduces GNN performance.
method Proposes EEGNN framework using DMPGM for better graph structural information.
result EEGNN achieves significant performance improvement over baselines.
Deep P-Spline automates DNN structure selection for complex regression problems.
problem Challenges in selecting optimal network structures for DNNs.
method Linking neuron selection to knot placement in basis expansion techniques, introducing a difference penalty for automated knot selection.
result Deep P-Spline extends model class and forms a latent variable modeling framework with theoretical guarantees.
Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of Hölder functions on low-dimensional manifolds using deep ReLU networks. Suppose n training data are sampled from a Hölder function in $\mathc…
Deep neural networks enforce non-crossing quantile regression curves.
problem Estimating quantile regression curves without crossing.
method Penalized deep ReQU neural networks with a non-crossing penalty.
result Established non-asymptotic risk and error bounds for the estimated QRP.
Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single…
The aim of this work is to enable inference of deep networks that retain high accuracy for the least possible model complexity, with the latter deduced from the data during inference. To this end, we revisit deep networks that comprise competing linear units, as opposed to nonlinear units that do not entail any form of…
Deep neural nets estimate operators between infinite-dimensional spaces with fast rates.
problem Estimating operators between infinite-dimensional spaces.
method Deep neural networks for nonparametric estimation of Lipschitz operators.
result Error bounds decay with fast rates depending on intrinsic dimension.
Deep learning models can adaptively estimate functions with varying smoothness using regularization.
problem Estimating functions with heterogeneous smoothness in Besov or BV classes.
method Introduced a Parallel NN variant of deep ReLU networks with ℓ2 regularization equivalent to promoting ℓp-sparsity. result Achieves minimax rates for Besov and BV classes with exponentially closer performance as depth increases.
Bayesian deep learning with heavy-tailed weights achieves near-optimal performance.
problem Deep neural networks with heavy-tailed weights achieve near-optimal performance in various contexts.
method Introduced a Bayesian deep learning prior based on heavy-tailed weights and ReLU activation, showing near-optimal minimax contraction rates.
result Posterior distribution achieves near-optimal minimax contraction rates, adaptive to smoothness and intrinsic dimension.
Bayesian approach models neurodegenerative diseases without clinical labels.
problem Personalized, predictive modeling of neurodegenerative diseases.
method Probabilistic programmed deep kernel learning combining Gaussian processes and neural networks.
result Surpasses deep learning in accuracy and timeliness of predicting neurodegeneration.
The paper uses deep neural networks to estimate economic models without separability restrictions.
problem Estimating economic models with complex interaction effects and non-separable restrictions.
method Uses deep neural networks as a nonparametric sieve to approximate regression functions from nonlinear latent variable models.
result Economic shape, sparsity, or separability restrictions are imposed more straightforwardly when a flexible latent variable model is used.
Study on deep learning for speckle noise reduction in imaging modalities.
problem Multiplicative speckle noise challenges conventional deep learning methods for speckle denoising.
method Likelihood-based deep neural network (DNN) estimators for nonparametric regression under speckle noise.
result Established minimax rates for speckle denoising, matching those for additive Gaussian noise alone.
Develops a deep learning framework for various data types.
problem Handling nonparametric regression and classification across different data types.
method Introduces a general framework with two estimators: NPDNN and SPDNN, based on data satisfying generalized Bernstein-type inequalities.
result Both NPDNN and SPDNN estimators are minimax optimal in many classical settings.
We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical Lp losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the …
A new method for learning conditional distributions using ODEs and neural networks.
problem Learning conditional distributions efficiently and accurately.
method Conditional Föllmer Flow, discretized with Euler's method, using nonparametric velocity estimation.
result Effective approximation of target conditional distributions, with convergence results for Wasserstein-2 distance.
DFIV uses deep features for IV regression, achieving optimal rates.
problem Optimal IV regression with deep features for complex target functions.
method Two-stage approach: deep feature learning followed by IV regression.
result DFIV achieves minimax optimal learning rate under certain conditions.