{"id":3261,"date":"2021-02-23T14:00:14","date_gmt":"2021-02-23T14:00:14","guid":{"rendered":"https:\/\/thenextweb.com\/?p=1340172"},"modified":"2021-02-23T14:00:14","modified_gmt":"2021-02-23T14:00:14","slug":"how-to-turn-your-dogs-nap-time-into-a-regularized-linear-model","status":"publish","type":"post","link":"https:\/\/www.londonchiropracter.com\/?p=3261","title":{"rendered":"How to turn your dog\u2019s nap time into a regularized linear model"},"content":{"rendered":"\n

Looking at this nap duration model, <\/span>Beta 0<\/em> <\/span>is the <\/span>intercept<\/strong>, the value the target takes when all features are equal to zero.<\/p>\n

The remaining betas are the unknown <\/span>coefficients<\/strong> <\/span>which, along with the intercept, are the missing pieces of the model. You can observe the outcome of the combination of the different features, but you don\u2019t know all the details about how each feature impacts the target.<\/p>\n

Once you determine the value for each coefficient you know the direction, either positive or negative, and the magnitude of the impact each feature has in target.<\/p>\n

With a linear model, you\u2019re assuming all features are independent of each other so, for instance, the fact that you got a delivery doesn\u2019t have any impact on how many treats your dog gets in a day.<\/p>\n

Additionally, you think there\u2019s a linear relationship between the features and the target.<\/p>\n

So, on the days you get to play more with your dog they\u2019ll get more tired and will want to nap for longer. Or, on days when there are no squirrels outside your dog won\u2019t need to nap as much, because they didn\u2019t spend as much energy staying alert and keeping an eye on the squirrels\u2019 every move.<\/p>\n

For how long will your dog nap tomorrow?<\/h2>\n

With the general idea of the model in your mind, you collected data for a few days. Now you have real observations of the features and the target of your model.<\/p>\n

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<\/i><\/a>A few days\u2019 worth of observations of features and targets for your dog\u2019s nap duration.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/figure>\n

But there are still a few critical pieces missing, the coefficient values and the intercept.<\/p>\n

One of the most popular methods to find the coefficients of a linear model is <\/span>Ordinary Least Squares<\/a>.<\/p>\n

The premise of Ordinary Least Squares (OLS) is that you\u2019ll pick the coefficients that minimize the <\/span>residual sum of squares<\/strong><\/a>, i.e., the total squared difference between your predictions and the observed data[1].<\/p>\n

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With the residual sum of squares, not all residuals are treated equally. You want to make an example of the times when the model generated predictions too far off from the observed values.<\/p>\n

It\u2019s not so much about the prediction being too far off above or below the observed value, but the magnitude of the error. You square the residuals and penalize the predictions that are too far off while making sure you\u2019re only dealing with positive values.<\/p>\n

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With residual sum of squares, it\u2019s not so much about the prediction being too far above or below the observed value, but the magnitude of that error.<\/p>\n<\/blockquote>\n

This way when RSS is zero it really means prediction and observed values are equal, and it\u2019s not just the bi-product of arithmetic.<\/p>\n

In python, you can use <\/span>ScikitLearn<\/a> <\/span>to fit a linear model to the data using Ordinary Least Squares.<\/p>\n

Since you want to test the model with data it was not trained on, you want to hold out a percentage of your original dataset, into a test set. In this case, the test dataset sets aside 20% of the original dataset at random.<\/p>\n

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After fitting a linear model to the training set, you can check its characteristics.<\/p>\n
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The coefficients and the intercept are the last pieces you needed to define your model and make predictions. The coefficients in the output array follow the order of the features in the dataset, so your model can be written as:<\/p>\n
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It\u2019s also useful to compute a few metrics to evaluate the quality of the model.<\/p>\n
R-squared<\/a>, also called the coefficient of determination, gives a sense of how good the model is at describing the patterns in the training data, and has values ranging from 0 to 1. It shows how much of the variability in the target is explained by the features[1].<\/p>\n
For instance, if you\u2019re fitting a linear model to the data but there\u2019s no linear relationship between target and features, R-squared is going to be very close to zero.<\/p>\n
Bias and variance are metrics that help balance the two sources of error a model can have:<\/p>\n