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"# Probability and Generalization\n",
"\n",
"We have introduced a sequence of steps to create a model using a dataset:\n",
"\n",
"1. Select a model.\n",
"2. Select a loss function.\n",
"3. Fit the model by minimizing the loss on the dataset.\n",
"\n",
"Thus far, we have introduced the constant model (1), a set of loss functions (2), and gradient descent as a general method of minimizing the loss (3). Following these steps will often generate a model that makes accurate predictions on the dataset it was trained on.\n",
"\n",
"Unfortunately, a model that only performs well on its training data has little real-world utility. We care about the model's ability to **generalize**. Our model should make accurate predictions about the population, not just the training data. This problem seems challenging to answerâ€”how might we reason about data we haven't seen yet?\n",
"\n",
"Here we turn to the inferential power of statistics. We first introduce some mathematical tools: random variables, expectation, and variance. Using these tools, we draw conclusions about our model's long-term performance on data from our population, even data that we did not use to train the model!"
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