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bayesian_neural_networks_pymc4.ipynb

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"### Model definition\n",
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"To model the non-linear relationship between `x` and `y` in the dataset we use a ReLU neural network with two hidden layers, 5 neurons each. The weights of the neural network are random variables instead of deterministic variables. This is what makes a neural network a Bayesian neural network. Here, we assume that the weights follow a normal distribution and are independent. \n",
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"To model the non-linear relationship between `x` and `y` in the dataset we use a ReLU neural network with two hidden layers, 5 neurons each. The weights of the neural network are random variables instead of deterministic variables. This is what makes a neural network a Bayesian neural network. Here, we assume that the weights are independent random variables. \n",
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"The neural network defines a prior over the mean `loc` of the data likelihood `obs` which is represented by a normal distribution. For simplicity, the aleatoric uncertainty (`noise`) in the data is assumed to be known. Thanks to PyMC4's model composition support, priors can be defined layer-wise using the `layer` generator function and composed to a neural network as shown in function `model`. During inference, a posterior distribution over the neural network weights is obtained. "
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