# Forecasting Trade Direction and Size of Future Contracts Using Deep Belief Network

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2 quantities of trades allow market maker to properly gauge the supply and demand in the marketplace and thereby to modify their open orders. Deep Belief Network (DBN) Figure 3. Structure of our deep belief network. Consists of an input layer, 3 hidden layers of RBM and an output layer of RBM. Figure 4. Diagram of a restricted Boltzmann machine. Deep belief network is a probabilistic generative model proposed by Hinton [2]. It consists of an input layer, an output layer, and is composed of multiple layers of hidden variables stacked on top of each other. Using multiple hidden layers allows the network to learn higher order features. Hinton has developed an efficient, greedy layer-by-layer approach for learning the network weights. Each layer consists of a Restricted Boltzmann Machine (RBM). The deep belief network is trained in two steps, namely, the unsupervised pre-training and the supervised fine tuning. Unsupervised pre-training Traditionally, deep architectures is difficult to train because of their non-convex objective function. As a result, the parameters tend to converge at local optima. Performing unsupervised pre-training helps initialize the weights to better values and helps us find better local optima. [4] Unsupervised pre-training is performed by having each hidden layer greedily learns the identity function one at a time, using the output of the previous layer as the input. Supervised fine tuning Supervised fine tuning is performed after the unsupervised pre-training. The network is initialized using the weights from the pre-training. By performing unsupervised pre-training, we are able to find better local optima in the fine tuning phase than using randomly initialized weights. Restricted Boltzmann Machine Restricted Boltzmann Machines (RBMs) consist of visible and hidden units that form a bipartite graph (Figure 3). The visible and hidden units are conditionally independent given the other layer. The RBMs are then trained by maximizing the likelihood given by the following equation (Figure 5). RBM is trained using a method called contrastive divergence that is developed by Hinton. Further information can be found in Hinton s paper. [3] Figure 5. Log likelihood of the restricted Boltzmann machine. In this case, x(i) refers to the visible units. Dataset To ensure the relevancy of our results, we acquired tick-by-tick data of S&P equity index Futures (ES) from the

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