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# What is a Decision Tree?

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A decision tree is a useful machine learning algorithm used for both regression and classification tasks. The name “decision tree” comes from the fact that the algorithm keeps dividing the dataset down into smaller and smaller portions until the data has been divided into single instances, which are then classified. If you were to visualize the results of the algorithm, the way the categories are divided would resemble a tree and many leaves.

That’s a quick definition of a decision tree, but let’s take a deep dive into how decision trees work. Having a better understanding of how decision trees operate, as well as their use cases, will assist you in knowing when to utilize them during your machine learning projects.

General Format of a Decision Tree

A decision tree is a lot like a flowchart. To utilize a flowchart you start at the starting point, or root, of the chart and then based on how you answer the filtering criteria of that starting node you move to one of the next possible nodes. This process is repeated until an ending is reached.

Decision trees operate in essentially the same manner, with every internal node in the tree being some sort of test/filtering criteria. The nodes on the outside, the endpoints of the tree, are the labels for the datapoint in question and they are dubbed “leaves”. The branches that lead from the internal nodes to the next node are features or conjunctions of features. The rules used to classify the datapoints are the paths that run from the root to the leaves.

Steps and Algorithms

Decision trees operate on an algorithmic approach which splits the dataset up into individual data points based on different criteria. These splits are done with different variables, or the different features of the dataset. For example, if the goal is to determine whether or not a dog or cat is being described by the input features, variables the data is split on might be things like “claws” and “barks”.

So what algorithms are used to actually split the data into branches and leaves? There are various methods that can be used to split a tree up, but the most common method of splitting is probably a technique referred to as “recursive binary split”. When carrying out this method of splitting, the process starts at the root and the number of features in the dataset represents the possible number of possible splits. A function is used to determine how much accuracy every possible split will cost, and the split is made using the criteria that sacrifices the least accuracy. This process is carried out recursively and sub-groups are formed using the same general strategy.

In order to determine the cost of the split, a cost function is used. A different cost function is used for regression tasks and classification tasks. The goal of both cost functions is to determine which branches have the most similar response values, or the most homogenous branches. Consider that you want test data of a certain class to follow certain paths and this makes intuitive sense.

In terms of the regression cost function for recursive binary split, the algorithm used to calculate the cost is as follows:

sum(y – prediction)^2

The prediction for a particular group of data points is the mean of the responses of the training data for that group. All the data points are run through the cost function to determine the cost for all the possible splits and the split with the lowest cost is selected.

Regarding the cost function for classification, the function is as follows:

G = sum(pk * (1 – pk))

This is the Gini score, and it is a measurement of the effectiveness of a split, based on how many instances of different classes are in the groups resulting from the split. In other words, it quantifies how mixed the groups are after the split. An optimal split is when all the groups resulting from the split consist only of inputs from one class. If an optimal split has been created the “pk” value will be either 0 or 1 and G will be equal to zero. You might be able to guess that the worst-case split is one where there is a 50-50 representation of the classes in the split, in the case of binary classification. In this case, the “pk” value would be 0.5 and G would also be 0.5.

The splitting process is terminated when all the data points have been turned into leaves and classified. However, you may want to stop the growth of the tree early. Large complex trees are prone to overfitting, but several different methods can be used to combat this. One method of reducing overfitting is to specify a minimum number of data points that will be used to create a leaf. Another method of controlling for overfitting is restricting the tree to a certain maximum depth, which controls how long a path can stretch from the root to a leaf.

Another process involved in the creation of decision trees is pruning. Pruning can help increase the performance of a decision tree by stripping out branches containing features that have little predictive power/little importance for the model. In this way, the complexity of the tree is reduced, it becomes less likely to overfit, and the predictive utility of the model is increased.

When conducting pruning, the process can start at either the top of the tree or the bottom of the tree. However, the easiest method of pruning is to start with the leaves and attempt to drop the node that contains the most common class within that leaf. If the accuracy of the model doesn’t deteriorate when this is done, then the change is preserved. There are other techniques used to carry out pruning, but the method described above – reduced error pruning – is probably the most common method of decision tree pruning.

Considerations For Using Decision Trees

Decision trees are often useful when classification needs to be carried out but computation time is a major constraint. Decision trees can make it clear which features in the chosen datasets wield the most predictive power. Furthermore, unlike many machine learning algorithms where the rules used to classify the data may be hard to interpret, decision trees can render interpretable rules. Decision trees are also able to make use of both categorical and continuous variables which means that less preprocessing is needed, compared to algorithms that can only handle one of these variable types.

Decision trees tend not to perform very well when used to determine the values of continuous attributes. Another limitation of decision trees is that, when doing classification, if there are few training examples but many classes the decision tree tends to be inaccurate.

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Blogger and programmer with specialties in Machine Learning and Deep Learning topics. Daniel hopes to help others use the power of AI for social good.

### AI 101

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If you’ve read about how neural networks are trained, you’ve almost certainly come across the term “gradient descent” before. Gradient descent is the primary method of optimizing a neural network’s performance, reducing the network’s loss/error rate. However, gradient descent can be a little hard to understand for those new to machine learning, and this article will endeavor to give you a decent intuition for how gradient descent operates.

Gradient descent is an optimization algorithm. It’s used to improve the performance of a neural network by making tweaks to the parameters of the network such that the difference between the network’s predictions and the actual/expected values of the network (referred to as the loss) is a small as possible. Gradient descent takes the initial values of the parameters and uses operations based in calculus to adjust their values towards the values that will make the network as accurate as it can be. You don’t need to know a lot of calculus to understand how gradient descent works, but you do need to have an understanding of gradients.

Assume that there is a graph that represents the amount of error a neural network makes. The bottom of the graph represents the points of lowest error while the top of the graph is where the error is the highest. We want to move from the top of the graph down to the bottom. A gradient is just a way of quantifying the relationship between error and the weights of the neural network. The relationship between these two things can be graphed as a slope, with incorrect weights producing more error. The steepness of the slope/gradient represents how fast the model is learning.

A steeper slope means large reductions in error are being made and the model is learning fast, whereas if the slope is zero the model is on a plateau and isn’t learning. We can move down the slope towards less error by calculating a gradient, a direction of movement (change in the parameters of the network) for our model.

Let’s shift the metaphor just slightly and imagine a series of hills and valleys. We want to get to the bottom of the hill and find the part of the valley that represents the lowest loss. When we start at the top of the hill we can take large steps down the hill and be confident that we are heading towards the lowest point in the valley.

However, as we get closer to the lowest point in the valley, our steps will need to become smaller, or else we could overshoot the true lowest point. Similarly, it’s possible that when adjusting the weights of the network, the adjustments can actually take it further away from the point of lowest loss, and therefore the adjustments must get smaller over time. In the context of descending a hill towards a point of lowest loss, the gradient is a vector/instructions detailing the path we should take and how large our steps should be.

Now we know that gradients are instructions that tell us which direction to move in (which coefficients should be updated) and how large the steps we should take are (how much the coefficients should be updated), we can explore how the gradient is calculated.

Gradient descent starts at a place of high loss and by through multiple iterations, takes steps in the direction of lowest loss, aiming to find the optimal weight configuration. Photo: Роман Сузи via Wikimedia Commons, CCY BY SA 3.0 (https://commons.wikimedia.org/wiki/File:Gradient_descent_method.png)

In order to carry out gradient descent, the gradients must first be calculated. In order to calculate the gradient, we need to know the loss/cost function. We’ll use the cost function to determine the derivative. In calculus, the derivative just refers to the slope of a function at a given point, so we’re basically just calculating the slope of the hill based on the loss function. We determine the loss by running the coefficients through the loss function. If we represent the loss function as “f”, then we can state that the equation for calculating the loss is as follows (we’re just running the coefficients through our chosen cost function):

Loss = f(coefficient)

We then calculate the derivative, or determine the slope. Getting the derivative of the loss will tell us which direction is up or down the slope, by giving us the appropriate sign to adjust our coefficients by. We’ll represent the appropriate direction as “delta”.

delta = derivative_function(loss)

We’ve now determined which direction is downhill towards the point of lowest loss. This means we can update the coefficients in the neural network parameters and hopefully reduce the loss. We’ll update the coefficients based on the previous coefficients minus the appropriate change in value as determined by the direction (delta) and an argument that controls the magnitude of change (the size of our step). The argument that controls the size of the update is called the “learning rate” and we’ll represent it as “alpha”.

coefficient = coefficient – (alpha * delta)

We then just repeat this process until the network has converged around the point of lowest loss, which should be near zero.

It’s very important to choose the right value for the learning rate (alpha). The chosen learning rate must be neither too small or too large. Remember that as we approach the point of lowest loss our steps must become smaller or else we will overshoot the true point of lowest loss and end up on the other side. The point of smallest loss is small and if our rate of change is too large the error can end up increasing again. If the step sizes are too large the network’s performance will continue to bounce around the point of lowest loss, overshooting it on one side and then the other. If this happens the network will never converge on the true optimal weight configuration.

In contrast, if the learning rate is too small the network can potentially take an extraordinarily long time to converge on the optimal weights.

Now that we understand how gradient descent works in general, let’s take a look at some of the different types of gradient descent.

Batch Gradient Descent: This form of gradient descent runs through all the training samples before updating the coefficients. This type of gradient descent is likely to be the most computationally efficient form of gradient descent, as the weights are only updated once the entire batch has been processed, meaning there are fewer updates total. However, if the dataset contains a large number of training examples, then batch gradient descent can make training take a long time.

Stochastic Gradient Descent: In Stochastic Gradient Descent only a single training example is processed for every iteration of gradient descent and parameter updating. This occurs for every training example. Because only one training example is processed before the parameters are updated, it tends to converge faster than Batch Gradient Descent, as updates are made sooner. However, because the process must be carried out on every item in the training set, it can take quite a long time to complete if the dataset is large, and so use of one of the other gradient descent types if preferred.

Mini-Batch Gradient Descent: Mini-Batch Gradient Descent operates by splitting the entire training dataset up into subsections. It creates smaller mini-batches that are run through the network, and when the mini-batch has been used to calculate the error the coefficients are updated. Mini-batch Gradient Descent strikes a middle ground between Stochastic Gradient Descent and Batch Gradient Descent. The model is updated more frequently than in the case of Batch Gradient Descent, which means a slightly faster and more robust convergence on the model’s optimal parameters. It’s also more computationally efficient than Stochastic Gradient Descent

# What is Backpropagation?

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Deep learning systems are able to learn extremely complex patterns, and they accomplish this by adjusting their weights. How are the weights of a deep neural network adjusted exactly? They are adjusted through a process called backpropagation. Without backpropagation, deep neural networks wouldn’t be able to carry out tasks like recognizing images and interpreting natural language. Understanding how backpropagation works is critical to understanding deep neural networks in general, so let’s delve into backpropagation and see how the process is used to adjust a network’s weights.

Backpropagation can be difficult to understand, and the calculations used to carry out backpropagation can be quite complex. This article will endeavor to give you an intuitive understanding of backpropagation, using little in the way of complex math. However, some discussion of the math behind backpropagation is necessary.

## The Goal of Backprop

Let’s start by defining the goal of backpropagation. The weights of a deep neural network are the strength of connections between units of a neural network. When the neural network is established assumptions are made about how the units in one layer are connected to the layers joined with it. As the data moves through the neural network, the weights are calculated and assumptions are made. When the data reaches the final layer of the network, a prediction is made about how the features are related to the classes in the dataset. The difference between the predicted values and the actual values is the loss/error, and the goal of backpropagation is to reduce the loss. This is accomplished by adjusting the weights of the network, making the assumptions more like the true relationships between the input features.

## Training A Deep Neural Network

Before backpropagation can be done on a neural network, the regular/forward training pass of a neural network must be carried out. When a neural network is created, a set of weights is initialized. The value of the weights will be altered as the network is trained. The forward training pass of a neural network can be conceived of as three discrete steps: neuron activation, neuron transfer, and forward propagation.

When training a deep neural network, we need to make use of multiple mathematical functions. Neurons in a deep neural network are comprised of the incoming data and an activation function, which determines the value necessary to activate the node. The activation value of a neuron is calculated with several components, being a weighted sum of the inputs. The weights and input values depend on the index of the nodes being used to calculate the activation. Another number must be taken into account when calculating the activation value, a bias value. Bias values don’t fluctuate, so they aren’t multiplied together with the weight and inputs, they are just added. All of this means that the following equation could be used to calculate the activation value:

Activation = sum(weight * input) + bias

After the neuron is activated, an activation function is used to determine what the output of the actual output of the neuron will be. Different activation functions are optimal for different learning tasks, but commonly used activation functions include the sigmoid function, the Tanh function, and the ReLU function.

Once the outputs of the neuron are calculated by running the activation value through the desired activation function, forward propagation is done. Forward propagation is just taking the outputs of one layer and making them the inputs of the next layer. The new inputs are then used to calculate the new activation functions, and the output of this operation passed on to the following layer. This process continues all the way through to the end of the neural network.

## Backpropagation

The process of backpropagation takes in the final decisions of a model’s training pass, and then it determines the errors in these decisions. The errors are calculated by contrasting the outputs/decisions of the network and the expected/desired outputs of the network.

Once the errors in the network’s decisions have been calculated, this information is backpropagated through the network and the parameters of the network are altered along the way. The method that is used to update the weights of the network is based in calculus, specifically, it’s based in the chain-rule. However, an understanding of calculus isn’t necessary to understand the idea of behind backpropagation. Just know that when an output value is provided from a neuron, the slope of the output value is calculated with a transfer function, producing a derived output. When doing backpropagation, the error for a specific neuron is calculated according to the following formula:

error = (expected_output – actual_output) * slope of neuron’s output value

When operating on the neurons in the output layer, the class value is used as the expected value. After the error has been calculated, the error is used as the input for the neurons in the hidden layer, meaning that the error for this hidden layer is the weighted errors of the neurons found within the output layer. The error calculations travel backward through the network along the weights network.

After the errors for the network have been calculated, the weights in the network must be updated. As mentioned, calculating the error involves determining the slope of the output value. After the slope has been calculated, a process known as gradient descent can be used to adjust the weights in the network. A gradient is a slope, whose angle/steepness can be measured. Slope is calculated by plotting “y over” or the “rise” over the “run”. In the case of the neural network and the error rate, the “y” is the calculated error, while the “x” is the network’s parameters. The network’s parameters have a relationship to the calculated error values, and as the network’s weights are adjusted the error increases or decreases.

“Gradient descent” is the process of updating the weights so that the error rate decreases. Backpropagation is used to predict the relationship between the neural network’s parameters and the error rate, which sets up the network for gradient descent. Training a network with gradient descent involved calculating the weights through forward propagation, backpropagating the error, and then updating the weights of the network.

# What is Meta-Learning?

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One of the fastest-growing areas of research in machine learning is the area of meta-learning. Meta-learning, in the machine learning context, is the use of machine learning algorithms to assist in the training and optimization of other machine learning models. As meta-learning is becoming more and more popular and more meta-learning techniques are being developed, it’s beneficial to have an understanding of what meta-learning is and to have a sense of the various ways it can be applied. Let’s examine the ideas behind meta-learning, types of meta-learning, as well as some of the ways meta-learning can be used.

## Defining Meta-Learning

The term meta-learning was coined by Donald Maudsley to describe a process by which people begin to shape what they learn, becoming “increasingly in control of habits of perception, inquiry, learning, and growth that they have internalized”. Later, cognitive scientists and psychologists would describe meta-learning as “learning how to learn”.

For the machine learning version of meta-learning, the general idea of “learning how to learn” is applied to AI systems. In the AI sense, meta-learning is the ability of an artificially intelligent machine to learn how to carry out various complex tasks, taking the principles it used to learn one task and applying it to other tasks. AI systems typically have to be trained to accomplish a task through the mastering of many small subtasks. This training can take a long time and AI agents don’t easily transfer the knowledge learned during one task to another task. Creating meta-learning models and techniques can help AI learn to generalize learning methods and acquire new skills quicker.

## Types of Meta-Learning

Optimizer Meta-Learning

Meta-learning is often employed to optimize the performance of an already existing neural network. Optimizer meta-learning methods typically function by tweaking the hyperparameters of a different neural network in order to improve the performance of the base neural network. The result is that the target network should become better at performing the task it is being trained on. One example of a meta-learning optimizer is the use of a network to improve gradient descent results.

Few-Shots Meta-Learning

A few-shots meta-learning approach is one where a deep neural network is engineered which is capable of generalizing from the training datasets to unseen datasets. An instance of few-shot classification is similar to a normal classification task, but instead, the data samples are entire datasets. The model is trained on many different learning tasks/datasets and then it’s optimized for peak performance on the multitude of training tasks and unseen data. In this approach, a single training sample is split up into multiple classes. This means that each training sample/dataset could potentially be made up of two classes, for a total of 4-shots. In this case, the total training task could be described as a 4-shot 2-class classification task.

In few-shot learning, the idea is that the individual training samples are minimalistic and that the network can learn to identify objects after having seen just a few pictures. This is much like how a child learns to distinguish objects after seeing just a couple of pictures. This approach has been used to create techniques like one-shot generative models and memory augmented neural networks.

Metric Meta-Learning

Metric based meta-learning is the utilization of neural networks to determine if a metric is being used effectively and if the network or networks are hitting the target metric. Metric meta-learning is similar to few-shot learning in that just a few examples are used to train the network and have it learn the metric space. The same metric is used across the diverse domain and if the networks diverge from the metric they are considered to be failing.

Recurrent Model Meta-Learning

Recurrent model meta-learning is the application of meta-learning techniques to Recurrent Neural Networks and the similar Long Short-Term Memory networks. This technique operates by training the RNN/LSTM model to sequentially learn a dataset and then using this trained model as a basis for another learner. The meta-learner takes on board the specific optimization algorithm that was used to train the initial model. The inherited parameterization of the meta-learner enables it to quickly initialize and converge, but still be able to update for new scenarios.

## How Does Meta-Learning Work?

The exact way that meta-learning is conducted varies depending on the model and the nature of the task at hand. However, in general, a meta-learning task involves copying over the parameters of the first network into the parameters of the second network/the optimizer.

There are two training processes in meta-learning. The meta-learning model is typically trained after several steps of training on the base model have been carried out. After the forward, backward, and optimization steps that train the base model, the forward training pass is carried out for the optimization model. For example, after three or four steps of training on the base model, a meta-loss is computed. After the meta-loss is computed, the gradients are computed for each meta-parameter. After this occurs, the meta-parameters in the optimizer are updated.

One possibility for calculating the meta-loss is to finish the forward training pass of the initial model and then combine the losses that have already been computed. The meta-optimizer could even be another meta-learner, though at a certain point a discrete optimizer like ADAM or SGD must be used.

Many deep learning models can have hundreds of thousands or even millions of parameters. Creating a meta-learner that has an entirely new set of parameters would be computationally expensive, and for this reason, a tactic called coordinate-sharing is typically used. Coordinate-sharing involves engineering the meta-learner/optimizer so that it learns a single parameter from the base model and then just clones that parameter in place of all of the other parameters. The result is that the parameters the optimizer possesses don’t depend on the parameters of the model.