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. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived through the Rademacher complexity of neural networks, which may be of independent interest. We apply these approximation bounds to analyze the convergences of regression using norm constrained neural networks and distribution estimation by GANs. In particular, we obtain convergence rates for over-parameterized neural networks. It is also shown that GANs can achieve optimal rate of learning probability distributions, when the discriminator is a properly chosen norm constrained neural network.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionSimilar Papers 제목 키워드 기반
Optimal rates of approximation by shallow ReLU$^k$ neural networks and applications to nonparametric regression
We study the approximation capacity of some variation spaces corresponding to shallow ReLU$^k$ neural networks. It is shown that sufficiently smooth functions are contained in these spaces with finite variation norms. Fo…
regressionGuessing Efficiently for Constrained Subspace Approximation
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subsp…
ClusteringOff-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatme…
Causal InferenceActive Linear Regression for $\ell_p$ Norms and Beyond
We study active sampling algorithms for linear regression, which aim to query only a few entries of a target vector $b\in\mathbb R^n$ and output a near minimizer to $\min_{x\in\mathbb R^d} \|Ax-b\|$, for a design matrix …
Dimensionality ReductionOpen-Ended Question AnsweringregressionShallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization
This paper studies approximation by shallow ReLU$^s$ networks, $σ_s(t)=\max\{0,t\}^s$, together with their generalization behavior under $\ell_1$ path-norm control. For the $L^p$-type integral spaces $\widetilde{\mathcal…