Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. The F-1 score is a popular binary classification metric representing a balance between precision and recall. It is the Harmonic mean of precision and recall.

While dealing with Linear Regression we can have multiple lines for different values of slopes and intercepts. But the main question that arises is which of those lines actually represents the right relationship between the X and Y and in order to find that we can use the Mean Squared Error or MSE as the parameter. For linear regression, this MSE is nothing but the Cost Function. Mean Squared Error is the sum of the squared differences between the prediction and true value. And the output is a single number representing the cost. So the line with the minimum cost function or MSE represents the relationship between X and Y in the best possible manner.

Brain shift makes the pre-operative MRI navigation highly inaccurate hence the intraoperative modalities are adopted in surgical theatre. Due to the excellent economic and portability merits, the Ultrasound imaging is used at our collaborating hospital, Charing Cross Hospital, Imperial College London, UK. However, it is found that intraoperative diagnosis on Ultrasound images is not straightforward and consistent, even for very experienced clinical experts. Hence, there is a demand to design a Computer-aided-diagnosis system to provide a robust second opinion to help the surgeons. The proposed CAD system based on "Mixed-Attention Res-U-net with asymmetric loss function" achieves the state-of-the-art results comparing to the ground truth by classification at pixel-level directly, it also outperforms all the current main stream pixel-level classification methods (e.g. U-net, FCN) in all the evaluation metrices.

This paper studies the $k$-means algorithm for clustering as well as the class of $D \ell$ sampling algorithms to which $k$-means belongs. It is shown that for any constant factor $\beta 1$, selecting $\beta k$ cluster centers by $D \ell$ sampling yields a constant-factor approximation to the optimal clustering with $k$ centers, in expectation and without conditions on the dataset. This result extends the previously known $O(\log k)$ guarantee for the case $\beta 1$ to the constant-factor bi-criteria regime. It also improves upon an existing constant-factor bi-criteria result that holds only with constant probability. Papers published at the Neural Information Processing Systems Conference.

I strongly advise you to read the article linked above. It will set the foundations on the topic, plus some math is already discussed there. To start out, I'll define my dataset -- only three points that are in a linear relationship. I've chosen so few points only because the math will be shorter -- needless to say, the math won't be more complex for longer dataset, it would just be longer, and I don't want to make some stupid arithmetic mistake. Then I'll set coefficients beta 0 and beta 1 to some constant and define the cost function as Sum of Squared Residuals (SSR/SSE).

The algorithm starts off with setting initial values for coefficients -- you are free to set the values to whatever you like (just not a string or boolean), but the common practice is to set them to 0. If I have two coefficients, let's say beta 0 and beta 1, I would set them to zero initially: Now just to keep things simple let's say I'm dealing with a linear regression task, and those betas are my coefficients (beta 0 being the bias intercept). It's quite simple to read. You make a prediction, then subtract that prediction from the actual value, and you take the square of that. Now comes the part where you should know a bit of Calculus to fully understand what's going on. You need to calculate partial derivatives for each of the coefficients, so the coefficients can be updated later. Some time ago I've written an article on taking derivatives in Python, and it covers to a degree those topics: As my model has only two coefficients, I need to calculate two partial derivatives, one with respect to beta 0, and the other with respect to beta 1. Here's how: Now comes the part in which you take those two functions and do something known as epoch -- just a fancy word for a single iteration through the dataset.

Apple released Tuesday the iOS 10.3 Beta 1 for iPhone, iPad and iPod Touch. The Beta 1 is a Developer Beta and not a Public Beta, which means that its availability would be restricted to iOS developers for now. Still, the iOS 10.3 Beta 1 holds clues to features that will be included in the final version of iOS 10.3 when it releases as official software update to all eligible iPhone, iPad and iPod models. Here are five features you can expect in iOS 10.3: While Apple introduced the AirPods back in September, the wireless earphones were just recently made available to customers.

In supervised learning, we are given a data set and already know what our correct output should look like, having the idea that there is a relationship between the input and the output. Linear regression with one variable is also known as "univariate linear regression." Univariate linear regression is used when you want to predict a single output value from a single input value . We're doing supervised learning here, so that means we already have an idea about what the input/output cause and effect should be. The "error", at each point, between the line fit and the data is the difference between the right- and left-hand sides of the equations above.