Keywords: [ ReLU ] [ Unsupervised Learning ] [ Truncated Gaussian ] [ Learning distribution ]

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 $\tilde{O}\left( \frac{1}{p^2}+\frac{1}{\epsilon^2p}\right)$ samples and $\tilde{O}\left( \frac{d^2}{p^2}+ \frac{d^2}{\epsilon^2p}\right)$ 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

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