Dimensionality and domain knowledge Is it right to use the same distance measure for all features? E.g. height and sex? CPU and Disk space? Some features will have more of an effect than others due to their scales. ??? In this version of the algorithm all features are used in the distance calculation. This treats all features the same. So a measure of height has the same effect as the measure of sex.
Read moreMore than just similarities Classification: Predict the same class as the nearest observations Regression: Predict the same value as the nearest observations ??? Remember for classification tasks, we want to predict a class for a new observation. What we could do is predict a class that is the same as the nearest neighbour. Simple! For regression tasks, we need to predict a value. Again, we could use the value of the nearest neighbour!
Read moreThis section introduces the idea of “similarity”. Why?: Simplicity Many business tasks require a measure of “similarity” Works well Business reasoning Why would businesses want to use a measure of similarity? What business problems map well to similarity classifiers? Find similar companies on a CRM Find similar people in an online dating app Find similar configurations of machines in a data centre Find pictures of cats that look like this cat Recommend products to buy from similar customers Find similar wines Similarity What is similarity?
Read moreValidation curve One simple method of visualising overfitting is with a validation curve, (a.k.a fitting curve). This is a plot of a score (e.g. accuracy) verses some parameter in the model. Let’s compare the make_circles dataset again and vary the SVM->RBF->gamma value. ??? Performance of the SVM->RBF algorithm when altering the parameters of the RBF. We can see that we are underfitting at low values of \(\gamma\). So we can make the model more complex by allowing the SVM to fit smaller and smaller kernels.
Read moreHoldout We have been using: Training data Not representative of production. We want to pretend like we are seeing new data: Hold back some data ??? When we train the model, we do so on some data. This is called training data. Up to now, we have been using the same training data to measure our accuracy. If we create a lookup table, our accuracy will be 100%. But this doesn’t generalise to new examples.
Read moreGeneralisation and overfitting “enough rope to hang yourself with” We can create classifiers that have a decision boundary of any shape. Very easy to overfit the data. This section is all about what overfitting is and why it is bad. ??? Speaking generally, we can create classifiers that correspond to any shape. We have so much flexibility that we could end up overfitting the data. This is where chance data, data that is noise, is considered a valid part of the model.
Read moreNonlinear functions Sometimes data cannot be separated by a simple threshold or linear boundary. We can also use nonlinear functions as a decision boundary. ??? To represent more complex data, we can introduce nonlinearities. Before we do, bear in mind: More complex interactions between features yield solutions that overfit data; to compensate we will need more data. More complex solutions take a greater amount of computational power Anti-KISS The simplest way of adding a nonlinearities is to add various permutations of the original features.
Read moreClassification via a model Decision trees created a one-dimensional decision boundary We could easily imagine using a linear model to define a decision boundary ??? Previously we used fixed decision boundaries to segment the data based upon how informative the segmentation would be. The decision boundary represents a one-dimensional rule that separates the data. We could easily increase the number or complexity of the parameters used to define the boundary.
Read moreOptimisation When discussing regression we found that these have closed solutions. I.e. solutions that can be solved directly. For many other algorithms there is no closed solution available. In these cases we need to use an optimisation algorithm. The goals of these algorithms is to iteratively step towards the correct result. Gradient descent Given a cost function, the gradient decent algorithm calculates the gradient of the last step and move in the direction of that gradient.
Read moreRegression and Linear Classifiers Traditional linear regression (a.k.a. Ordinary Least Squares) is the simplest and classic form of regression. Given a linear model in the form of: \begin{align} f(\mathbf{x}) & = w_0 + w_1x_1 + w_2x_2 + \dots \\ & = \mathbf{w} ^T \cdot \mathbf{x} \end{align} Linear regression finds the parameters \(\mathbf{w}\) that minimises the mean squared error (MSE)… The MSE is the sum of the squared values between the predicted value and the actual value.
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