Abstract
We consider a set of data samples such that a fraction of the samples are arbitrary outliers, and the rest are the output samples of a single-layer neural network with rectified linear unit (ReLU) activation. Our goal is to estimate the parameters (weight matrix and bias vector) of the neural network, assuming the bias vector to be non-negative. We estimate the network parameters using the gradient descent algorithm combined with either the median- or trimmed mean-based filters to mitigate the effect of the arbitrary outliers. We then prove that $\tilde{O}( \frac{1}{p^2}+\frac{1}{\epsilon^2p})$ samples and $\tilde{O} ( \frac{d^2}{p^2}+ \frac{d^2}{\epsilon^2p})$ time are sufficient for our algorithm to estimate the neural network parameters within an error of $\epsilon$ when the outlier probability is $1-p$, {where $2/3< p \leq 1$} and the problem dimension is $d$ (with log factors being ignored here). Our theoretical and simulation results provide insights into the training complexity of ReLU neural networks in terms of the probability of outliers and problem dimension.
Original language | English |
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Title of host publication | 36th Conference on Neural Information Processing Systems 2022 |
Editors | S. Koyejo |
Number of pages | 11 |
ISBN (Electronic) | 9781713871088 |
Publication status | Published - 2022 |
Event | 36th Conference on Neural Information Processing Systems - Hybrid Conference, New Orleans, United States Duration: 28 Nov 2022 → 9 Dec 2022 Conference number: 36 |
Conference
Conference | 36th Conference on Neural Information Processing Systems |
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Abbreviated title | NeurIPS 2022 |
Country/Territory | United States |
City | New Orleans |
Period | 28/11/22 → 9/12/22 |