Mr. Right Now By Theia Michaels
where \(\sigma (z)=1/\left( 1+\exp (-z\right)\) denotes the sigmoid activation function, and \(\beta\) is a scaling factor (which we set to \(\beta =2\)). In other words, \((\varvecU\varvecV^\intercal )_ij\) is scaled by 2\(\beta\) with a bias -\(\beta\), in order to predict the probability of the true interaction between the ith miRNA and the jth gene. The value of \(s_ij\) becomes nearer to 1 as the probability of the ith miRNA and the jth gene belonging to a common module increases, or equivalently, as the ith miRNA and the jth gene share an increasing number of modules in common. The tanh function is a scaled version of the sigmoid activation function, shifted vertically to adjust the range. The tanh activation can be rewritten as \(tanh(z) = 2\sigma (2z)-1\). By introducing a bias of of -\(\beta\), we shift the scaled activation horizontally. An advantage of the scaling factor, is that the gradient is larger than a regular sigmoid. Not only is this because of the multiplication by a 2\(\beta\) factor, but also because the function becomes more sensitive to a change in the input. In our case, these two effects combined lead to faster convergence, assuming that the learning rate does not cause exploding gradients.
Mr. Right Now by Theia Michaels
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