Let's start with the definition of an Interior point method: an Interior point method is an algorithm that is used in solving both linear and nonlinear convex optimization problems that contain inequalities as constraints. The aim of this research is to implement the algorithm for a linear programming problem which it'll be discussed in the next section, the programming language used for this assignment is MATLAB.
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There are several ways in which it is possible to implement a non-linear regressor, but a backpropagation method seems what it is needed to solve this problem. Backpropagation needs for every possible entry tuple an exit value in order to compute the loss function. It is then minimized with a gradient-method as it’s shown in the least-squared approach. This is the basic idea behind neural network (NN). These kind of networks are able to optimally recognize various types of patterns, and they are used in different fields such as regression. However, it is necessary to tune several hyperparameters to obtain an adequate result. NN are essentially based on nodes:
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Input nodes, which are in finite number, that usually equals the number of inputs of the function. Our problem, for example, needs four nodes, because we have PM10, humidity, temperature and atmospheric pressure as inputs. The set of all input nodes constitutes the so-called input layer.
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Hidden nodes makem up that part of the NN that introduces a non-linearity into the model. They are organized in one or more layers. There are no fixed rules to select the correct number of hidden nodes or layers: only a "trial and error" approach can find an appropriate solution to problems (for our purpose, one hidden layer is enough but the problem of the number of nodes remains).
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Output node, which is one and only one for a regression task. NN can acquire more than 8 one output node, but in these cases they are used in other situations and fields which are not relevant in our situation.
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Written by MarcoChain.