1. Use proper initialize method to avoid gradient vanish or exploded. For example: layer=[3,5,1], when initialize the second layer, W[2]=np.random.rand(5,3)*sqrt(1/5) It avoid the initial weight too big or to small. we can short the training time significantly by this way 2. Use regularization to reduce the variance (overfitting). L2 regularization: add lambda/(2*m) *sigma( all weights) to the cost function. We need to change the backward propagation formula if we use this regularization. drop out: inverted drop out: generate a matrix in this way: mask[l] = np.random.rand( W[l].shape[0], W[l].shape[0] ) mask[l] = (mask<keep_prob). astype(int) When forward propagation, use W[l]*mask[l]/keep_prob instead of W[l]; When backward propagation, use dW[l]*mask[l]/keep_prob instead of W[l]. 3. Use different optimize method to reduce the cost decay time. Batch gradient descent: traditional way. Mini_batch gradient descent: choose a mini-batch number such as...
Estimating VaR of portfolio by conditional copula-GARCH method C ontents 1. Introduction .. 1 2. Theory of copula .. 1 2.1 Introduction to copula .. 1 2.2 Copula family .. 2 2.3 Estimation method .. 3 2.4 Estimation of VaR .. 3 3. Empirical results .. 3 3.1 The data and the marginal distribution .. 3 3.2 Copula modeling .. 5 3.3 Estimation of VaR .. 5 4. Conclusion .. 7 References .. 8 1. Introduction Value at Risk (VaR) has become the standard measure used by financial institutions to quantify the market risk of an asset or a portfolio. Estimating VaR with one asset is not difficult, but it becomes complex when the portfolio contains ...