AI News, Machine Learning FAQ
- On Thursday, June 7, 2018
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Machine Learning FAQ
Index In order to explain the differences between alternative approaches to estimating the parameters of a model, let’s take a look at a concrete example: Ordinary Least Squares (OLS) Linear Regression. The
Or, in other words, we define the best-fitting line as the line that minimizes the sum of squared errors (SSE) or mean squared error (MSE) between our target variable (y) and our predicted output over all samples i in our dataset of size n.
Now, we can implement a linear regression model for performing ordinary least squares regression using one of the following approaches: The closed-form solution may (should) be preferred for “smaller” datasets – if computing (a “costly”) matrix inverse is not a concern.
For very large datasets, or datasets where the inverse of XTX may not exist (the matrix is non-invertible or singular, e.g., in case of perfect multicollinearity), the GD or SGD approaches are to be preferred. The
Essentially, we can picture GD optimization as a hiker (the weight coefficient) who wants to climb down a mountain (cost function) into a valley (cost minimum), and each step is determined by the steepness of the slope (gradient) and the leg length of the hiker (learning rate).
In case of very large datasets, using GD can be quite costly since we are only taking a single step for one pass over the training set – thus, the larger the training set, the slower our algorithm updates the weights and the longer it may take until it converges to the global cost minimum (note that the SSE cost function is convex).
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