So now that we have defined our hypothesis for logistic regression lets talk about what is called a decision boundary. We can translate the output of the hypothesis to say if h(x) >= 0.5 then y = 1 otherwise h(x) < 0.5 and y = 0. This is fair because it gives a half/half split. …
Continue reading "Decision Boundaries with Logistic Regression"
Let’s say we want to create a model to solve a binary classification problem; yes or no. For example based on the tumor size is a specific tumor malignant; yes or no? Let’s look more into this example with the hypothetical data below: If we apply linear regression to this data set we get: Now …
Continue reading "Intro to Logistic Regression"
(Refer to Figure 1 first) Not a lot has changed from the last time we talked about gradient descent (please look at that article before reading on). It is hard to explain how the summation and 1/m comes into play, but when you take the partial derivative with respect to the variable that you are …
Continue reading "Gradient Descent With Multiple Variables + Improvements"
Before we go more into looking at data sets and creating more hypotheses lets hold a quick review on matrices. Basic multiplication, addition, subtraction, and division between vectors and scalars should be pretty easy to grasp from multiple tutorials online. We will primarily go over the properties of matrices in this article. First, matrices are …
Continue reading "Linear Algebra Integration with Hypothesis Function"
Continuing from the last article to narrow down the theta1 and theta 0 we use a learning technique called gradient descent. So we have our cost function J(theta, theta1) and we want the result of the function to be the smallest possible. What gradient descent does is that it randomly starts with a theta and …
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Though the equation does look daunting don’t worry we’ll go over it. Okay so the inside term is y^I – yi. y^i is basically the work function h(x). We subtract the value of h(x) from y (our actual point) for all points (that’s why we use summation). We square the expression because we eliminate any …
Continue reading "A Mathematical View on the Cost Function: 2-D, 3-D, and Contour Graphs"
Sorry for not posting these last few months, I have just been trying to get adjusted to an exhausting sophomore life. I have quite a few drafts almost ready to publish, so more articles about machine learning and algorithmic designs will be coming out soon! For 2020 my goal is to upload an article once …
Continue reading "Plans for 2020 and Update on Uploading Status"
Welcome to the Machine Learning part of the blog! Let's start out with finding the differences between supervised and unsupervised learning. By definition, “the main difference between the two types is that supervised learning is done using a ground truth, or in other words, we have prior knowledge of what the output values for our …
This is one of the more complex problems so looking at my solution while reading the explanation would be ideal! The problem statement is here. This problem, the K-tree is perhaps one of my favorite problems for dynamic programming and soon I hope you see why as well. So we start out this problem by …
What if we want to track the kinematics and behavior of an object with strings and blocks flailing all over the place. Which point on the object should we measure to find the displacement, acceleration, force etc.? So lets just talk about one atom i in the object. The force acting on the atom is …
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