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Supervised Machine Learning: ML systems learn how to combine inputs to produce useful predictions on never before seen data.
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Label: The thing we're predicting, y variable in simple linear regression. ( eg: future price gold, animal type in picture ).
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Feature: The input variable, x variable in linear regression. Simple ML system might use a single feature, while more sophisticated systems could use millions of features.
x1, x2, ...xN eg: Email spam detector ML system features: - Words in email text - Senders address -
Example: Example is particular instance of the data, x. x is vector.
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Labeled Examples: {features, label}: (x, y)
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Unlabeled Examples: {features, ?}: (x, ?)
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You train model using labeled examples, then you use the model to predict labels on unlabled examples.
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Models: Model defines relationship between features and label.
- Training means creating or learning the model. Show the model label examples so it gradually learns relationship between features and label.
- Inference means applying trained model to unlabled examples. That is, you use the trained model to make useful predictions (y').
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Regression vs Classification
- Regression models predict continuous values ( eg: average house price Dublin ).
- Classification models predict discrete values ( eg: Is email spam or not spam)
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Overview:
- Drawing a line of best fit between two variables gives a relationship. y axis the thing we want to predict, x axis our input feature value.
- Linear relationship, can be represented using equation of a line y = mx + b.
- ML Convention: y' = b + w1x1 where
- y' is the predicted label ( desired output).
- b is bias, y intercept sometimes w0
- w1 is weight feature 1. Same concept as m
- x1 is a feature (known input)
- to infer y' for value x1, substitute in value in model.
- more sophisticated model rely on more than one feature: y' = b + w1x1 + w2x2 + w3x3
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Training:
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Training a model simply means learning (determining) good values for all the weights and the bias from labeled examples.
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ML algorithm builds a model by examining many examples and attempting to find a model which minimises loss ( empirical risk minimisation )
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Loss is a number indicating how bad the models prediction was on a single example.
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The goal of training a model is to find a set of weights and biases that have low loss, on average, across all examples.
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A loss function is a mathematical model which aggregates individual losses in a meaningful fashion.
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LR models generally use squared loss (L2), the squared loss for a given example.
L2 = sqaure diff between label and prediction. = (observation - prediction(x))^2 = (y-y')^2 -
Mean Squared Error (MSE) is the average loss per example over the whole the data set. Calculated by summing losses for individual examples and divide by number of examples.
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- Iterative Approach
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Explanation
- Considering y' = b + w1x1 we pick random starting values for b and w1.
- The Compute loss part of the diagram is done using squared loss function, L2.
- In the Compute parameter updates section of the diagram examines the value of the loss function and generates new values for b and w1. These values are chosen in a process called gradient descent.
- The ML system re-evaluates those values against all features and labels, and a new loss function value is yielded.
- This learning continues to iterate until the systems finds model parameters with the lowest loss, in other words when the model has converged.
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Gradient Descent
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Instead of calculating the loss for every value of w1 (computationally expensive), gradient descent is a better mechanism.
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Steps:
- Pick random starting value for w1.
- Then calculate the gradient of the loss curve at w1, which is the derivative (slope) at w1.
- When there are multiple weights, the gradient is a vector of partial derivatives with respect to the weights.
- Gradient is a vector, has magnitude and direction.
- Gradient always points in the direction of steepest increase in the loss function.
- So, the gradient descent algorithm takes a step in the direction of the negative gradient in order to reduce loss.
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Adds some fraction of the gradient's magnitude to the starting point to determine the next point along the loss function curve.
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The gradient descent then repeats this process, edging ever closer to the minimum.
- Note: When performing gradient descent, we generalize the above process to tune all the model parameters simultaneously. For example, to find the optimal values of both w1 and the bias , we calculate the gradients with respect to both w1 and b. Next, we modify the values of w1 and b based on their respective gradients. Then we repeat these steps until we reach minimum loss.
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Learning Rate
- GD Algorithms multiply the gradient by a scalar known as the learning rate (step size) to determine next point.
- If the gradient magnitude is 2.5 and the learning rate is 0.01, then the gradient descent algorithm will pick the next point 0.025 away from the previous point.
- Hyperparamters are the values tweaked by ML programmers.
- There's a 'Goldilocks' learning rate for every regression problem. The value is related to how flat the loss function is.
- Learning rate too small means learning takes too long.
- Learning rate too big means overshoot loss function minimum.
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Stochastic Gradient Descent
- In gradient descent, a batch is the total number of examples you use to calculate the gradient in a single iteration. Does not work well with enormous data sets.
- By choosing examples at random from our data set, we can estimate a big average from a much smaller one.
- Stochastic gradient descent (SGD) uses only a single example (a batch size of 1) per iteration. Given enough iterations, SGD works but is very noisy. The term "stochastic" indicates that the one example comprising each batch is chosen at random.
- Mini-batch stochastic gradient descent (mini-batch SGD) is a compromise between full-batch iteration and SGD. A mini-batch is typically between 10 and 1,000 examples, chosen at random.
- Mini-batch SGD reduces the amount of noise in SGD but is still more efficient than full-batch.
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Model Tuning Rules of thumb that may help guide you:
- Training error should steadily decrease, steeply at first, and should eventually plateau as training converges.
- If the training has not converged, try running it for longer.
- If the training error decreases too slowly, increasing the learning rate may help it decrease faster.
- But sometimes the exact opposite may happen if the learning rate is too high.
- If the training error varies wildly, try decreasing the learning rate.
- Lower learning rate plus larger number of steps or larger batch size is often a good combination.
- Very small batch sizes can also cause instability. First try larger values like 100 or 1000, and decrease until you see degradation.
- Never go strictly by these rules of thumb, because the effects are data dependent. Always experiment and verify.
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Common Hyperparameters:
- steps, which is the total number of training iterations. One step calculates the loss from one batch and uses that value to modify the model's weights once.
- batch size, which is the number of examples (chosen at random) for a single step. For example, the batch size for SGD is 1.
- periods, which controls the granularity of reporting. For example, if periods is set to 7 and steps is set to 70, then the exercise will output the loss value every 10 steps (or 7 times). Unlike hyperparameters, we don't expect you to modify the value of periods.
- Training a complex model to fit training set exactly is counterintuitive as the model will ill perform when new data is added to the set. This is called overfitting.
- An overfitting model gets a low loss during training but does a poor job predicting new data.
- For this reason we split the data into training, test and validation sets.
- Train subset to train the model on.
- Evaluate model on Validation set, tweak model according to results on validation set.
- Confirm best model results on Test set.
