Stochastic gradient descent
Stochastic gradient descent is like trying to find a buried treasure. Imagine you are in a big field with a lot of small hills. Each hill represents a possible solution to a problem that you are trying to solve. The treasure is hidden somewhere on one of these hills, but you don't know where it is.
To find the treasure, you need a map and a way to get to the hill where the treasure is hidden. The map tells you the height and contours of each hill, and the way to get to each hill is by walking in a specific direction, either uphill or downhill.
Stochastic gradient descent is like taking small steps uphill or downhill, following the gradient of each hill you encounter until you reach the top of the hill where the treasure is hidden.
But there is a problem: each hill is too big to climb in one step, and there are too many of them to climb them all. So instead of climbing each hill completely, you take a small step and look around to see if you are closer to the treasure or not. If you are, you take another step in the same direction, and if you are not, you take a step in the opposite direction.
This process of taking small steps and adjusting your direction based on the feedback you get is called stochastic gradient descent. The word "stochastic" means that the process is random or probabilistic because you don't know where the treasure is and you need to explore different directions to find it.
In machine learning, we use stochastic gradient descent to find the best values of the parameters of a function that describes a dataset. The dataset is like the map, and the function is like the hills. We want to find the set of parameters that makes the function fit the data best, just like we want to find the hill where the treasure is hidden.
Stochastic gradient descent is one way to solve this optimization problem efficiently, without having to evaluate the function for all possible parameters. By taking small steps and adjusting our direction, we can explore the space of parameters and find a good solution much faster than brute-force methods.
Overall, stochastic gradient descent is a simple but powerful algorithm that allows us to find the best solutions to complex optimization problems in machine learning and other fields.
To find the treasure, you need a map and a way to get to the hill where the treasure is hidden. The map tells you the height and contours of each hill, and the way to get to each hill is by walking in a specific direction, either uphill or downhill.
Stochastic gradient descent is like taking small steps uphill or downhill, following the gradient of each hill you encounter until you reach the top of the hill where the treasure is hidden.
But there is a problem: each hill is too big to climb in one step, and there are too many of them to climb them all. So instead of climbing each hill completely, you take a small step and look around to see if you are closer to the treasure or not. If you are, you take another step in the same direction, and if you are not, you take a step in the opposite direction.
This process of taking small steps and adjusting your direction based on the feedback you get is called stochastic gradient descent. The word "stochastic" means that the process is random or probabilistic because you don't know where the treasure is and you need to explore different directions to find it.
In machine learning, we use stochastic gradient descent to find the best values of the parameters of a function that describes a dataset. The dataset is like the map, and the function is like the hills. We want to find the set of parameters that makes the function fit the data best, just like we want to find the hill where the treasure is hidden.
Stochastic gradient descent is one way to solve this optimization problem efficiently, without having to evaluate the function for all possible parameters. By taking small steps and adjusting our direction, we can explore the space of parameters and find a good solution much faster than brute-force methods.
Overall, stochastic gradient descent is a simple but powerful algorithm that allows us to find the best solutions to complex optimization problems in machine learning and other fields.
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