Lasso

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HackerNoon Reporter: Please tell us briefly about your  background. I am a Finnish American software engineer. What's your startup called? And in a sentence or two, what does it do? is a Google and Facebook authenticated bidding-fee-auction app for Amazon items. Exhibia.com What is the origin story? The original Yale University 1971 dollar auction game was digitized in the early 2000, however it was digitized incorrectly and commonsense auction initiation criteria was ignore. What do you love about your team, and why are you the ones to solve this problem? We launched one of the first penny auction sites in the USA and learned really early on the game what was fundamentally wrong and how to fix it. The “precommitment mechanism” in penny auction method is not formal and it doesn’t check that every live auction has the “minimum required number of bidders”. If you weren’t building your startup, what would you be doing? building software At the moment, how do you measure success? What are your core metrics? Signups What’s most exciting about your traction to date? Granted patents and we are generating users daily. 90% of software startups fail because no one wants to use them. What technologies are you currently most excited about, and most worried about? And why? Cryptocurrencies. The original inventor from Yale University Dr.Martin Shubik compares the dollar auction game to a coin-toss, or token-toss game. The auction method can be used with any crypto currency and we plan to launch our own Bidcoin. What drew you to get published on HackerNoon? What do you like most about our platform? Being a software-engineer myself, HackerNoon is an important source of information. What advice would you give to the 21-year-old version of yourself? Save money. What is something surprising you've learned this year that your contemporaries would benefit from knowing? That the auction operator needs to make sure before auction is started, that “minimum required number of bidders is present“. Exhibia was nominated as in Startups of the Year hosted by HackerNoon. one of the best startups in Miami

"90% of software startups fail because no one wants to use them" according to Exhibia CEO Miko Lasso

Ted Lasso’s leadership style of servant leadership is rare to see on the screen. I fully expected Ted Lasso just be a bunch of skits with Jason Sudeikis be a bumbling fool. The hook of an American Football coach leading an English football team was a great fake out. The actual show turned out to contain numerous… Heartwarming moments. Despite having zero knowledge of English Football, Ted Lasso makes A.F.C. Richmond a better team. I love that Ted doesn’t have a magical skill or tool that helped him achieve this. Instead, Ted Lasso’s leadership style starts with a core philosophy: Ted will do everything he can to . help others achieve their goals Ted’s leadership style struck a chord with me because I approach leading teams in the same way. Ted’s philosophy is why I’m here with you to explore the five leadership lessons from Ted Lasso that made me a successful leader. Read on to the end to hear about one more mind-blowing detail I noticed when re-watching Ted Lasso for this essay. Spoilers ahead if you have not watched Season 1. Disclosure: This article includes affiliate links to any books I reference. I will receive a commission for any purchases. Ted Lasso’s Leadership Lesson 1: Ignore the Haters with Clear Goals In first half of the season, Ted Lasso goes through a gauntlet of negative criticism. doubts him. Rebbeca consistently sets him up to fail. The players think he is a joke. His first game has him walk out to a . How does this environment affect Ted? Everyone stadium of people calling him a wanker It doesn’t phase him at all. His enthusiasm doesn’t waver. He ignores being called a wanker. He doesn’t even care if A.F.C. Richmond loses! Why does Ted not care what others think? Ted Lasso ignores the haters because he has a clear goal. Ted explains his goal when talking with Trent Crimm, played by James Lance, in Episode 3: For me, success is not about the wins and losses. It’s about helping those young fellas be the best versions of themselves on and off the field. And it ain’t always easy, Trent, but neither is growing up without someone believing in you. “Trent Crimm: The Independent.” Ted Lasso, episode 3, 2020. Apple TV+, This goal gives Ted clarity. He knows that helping others become the best version of themselves takes a long time. It requires focus, understanding, and incremental steps. The outside world doesn’t see the emotional work Ted puts in for the team, so he disregard them. Just as important though, are the people Ted Lasso does not ignore. These are the people that understand his goal. He listens to their feedback and puts it into action. Ted’s relationship with the community is a great example of . You’ll achieve more by understanding your goals, finding allies that support you, and focusing on the domain you have complete influence over. changing what you can control Ted Lasso’s Leadership Lesson 2: Each Person Matters Great leaders believe that everyone on the team matters. From the owners to the equipment manager, the team succeeds with everyone’s contribution. Since the start, Ted values everyone’s contribution to the team: Ted builds trust with Nathan by giving Nathan space to voice his opinion. Ted sees Higgins as a partner and regularly gets . lunch with him to build a bond Ted understands how important A.F.C. Richmond is to the community. He reciprocates this care by learning all he can about the town. Ted manages up to Rebecca, played by Hannah Waddingham, by bonding with her via “Biscuits with the Boss.” As the season goes on, Ted leverages these relationships to achieve his goals: Nathan contributes innovative new plays, which helps the team win games. Higgins supports Ted by advocating for Ted to Rebecca and tracking Dani Rojas’ health. Mae, the pub owner, provides Ted space to meet with the team to resolve “The Curse”. Rebecca mentors Ted in the season finale by showing that his lack of experience is a strength. Each of these moments depended on the relationships that Ted developed. He showed up. He paid attention. He supported each person. These relationships paid off such that when Ted needed help, each of these people aided him in turn. Remember that each person on your team and broader life matters. When you support them in their lives, they will help you in your times of need. Lesson 3: Teach Others to Believe in Themselves My favorite storyline in Season 1 is the growth of Nathan Shelley, played by Nick Mohammed. Nathan’s doubt in himself with how he’s astounded that Ted remembers his name in episode one. Nathan is the representation of someone who doesn’t believe in himself. He gets bullied, is intimidated by everyone, and feels that his ideas aren’t valuable. Ted changes Nathan Shelley with mentorship and advocacy. Ted builds Nathan’s confidence by . It starts with remembering Nate’s name, but Ted does so much more: consistently supporting Nathan with positive feedback Ted shows excitement about each donation box Nathan brings to the team. Ted welcomes Nathan’s ideas for new plays, which shows that great ideas come from anyone. Ted gets the team to stop bullying Nathan while also teaching leadership lessons to Roy Kent. Ted gives Nathan feedback that his suit doesn’t fit and then buys a new one for him. Ted cares deeply about helping everyone around him achieve their full potential. He doesn’t care about titles, skills, or background – everyone has room to grow. So, what does Nathan do with newfound belief in himself? Nathan Shelley roasts all of A.F.C. Richmond. Nathan’s words, something he didn’t believe was valuable, were the reason A.F.C. Richmond one a critical match. Everything snowballed for Nathan from here, resulting in my favorite moment of the show. Nathan being promoted to Assistance Coach. Sometimes, the main thing holding people back is believing in themselves. Great leaders, like Ted, build that belief by supporting their team everyday. Lesson 4: Surround Yourself with Experts We all know the hook of Ted Lasso – an American Football coach is asked to coach an English football team. Ted does not have the skills to succeed, and he’s aware of it! This knowledge is one of the reasons why he invests so much in the people around him. Ted surrounds himself with experts in English football to make up for his weaknesses. How does this play out? , we see Coach Beard, played by Brendan Hunt, reading and . Beard builds on this knowledge to own the tactical plays for the team. In the first episode Coaching Soccer for Dummies Inverting the Pyramid Ted pushes Nathan for feedback, which is often spot on. As the kit manager, Nate observes how the team behaves and has a deep knowledge of their weaknesses. Ted builds a relationship with Higgins, the Director of Communications, played by Jeremy Swift. Higgins understands how to navigate the team’s back office. Higgins’ experience is important when Ted manages up to Rebbeca. As the season progresses, we see Ted develop the specific skills to effectively coach A.F.C. Richmond. He even utilizes his weakness as a strength to create Trick Plays in the season finale. Turns out this approach is not too far from how I go about . What we learned from Ted is: managing existing engineering teams Surround yourself with experts in the domain you wish to lead. Stay curious and learn as much as you can by asking lots of questions. Become comfortable with your ignorance of the team’s environment. Your new perspective can be a strength. Lesson 5: Success Requires Teamwork The philosophical conflict of Season 1 is between Ted Lasso and A.F.C. Richmond’s ace player, Jamie Tartt. Ted prioritizes the personal development of the entire team. Jamie, played by Phil Dunster, only cares about being number one. Jamie is right to feel he’s the top player on A.F.C. Richmond. He’s loaned from a higher-performing team. Jamie is the only one scoring goals. Both Jamie and the community feels he’s carrying the team. Without him, the team will lose. Yet, even with him there, the team still loses. Football is a team sport. Ted knows this and understands that A.F.C. Richmond won’t win if he only focuses on Jamie. Ted works on the personal development in two ways: Working with individual players to elevate their specific skills. Creating an environment where the team trusts and supports one another. Some ways Ted develops the skills of individuals are: Building up the morale of Sam Obisanya, played by Toheeb Jimoh, by teaching him to “think like a Goldfish”. Teaching Roy Kent, played by Brett Goldstein, to be a compassionate leader. Ted pushes Roy to defend Nathan and mak him read a Wrinkle in Time. Ted Lasso’s Line: Prioritizing Only Yourself All of this effort is the reason why Ted gets angry at someone in the show. . Unsurprisingly, it’s Jamie Tartt Fortunately, Ted’s hard work pays off as trust is built within the team: Ted gets everyone to chip in for a birthday present for Sam to build his morale. Ted organizes a “Reverse the Curse” ceremony. In it, each player must sacrifice an emotionally significant item to the team. Ted has the entire team watch The Iron Giant to create an emotional experience for the team. It’s not until the team finally trusts one another that they start winning. The trust enables A.F.C. Richmond to beat Liverpool for the first time in 60 years. The players rely upon, support, and elevate one another throughout the journey. You can still Succeed when Losing Seeing everyone elevate one another is why I love the final moments of the season. In the game’s final moments, when success is in their hands, the team loses to Jamie and Manchester City. It’s not because the team failed, but that Ted’s definition of success won. To win the game, Jamie couldn’t go for the final goal himself. There was too much defense in front of him. So instead, he passed the ball and trusted his teammate to score the final goal. In the end, while A.F.C. Richmond lost, Ted still won. In the end, true success is the result of helping everyone around you achieve their goals. ⭐BONUS⭐: The Secret Principles of Ted Lasso’s Leadership Style When watching the first episode, there’s a scene where Ted and Coach Beard are setting up their office. It’s a simple montage, but Beard hangs up one picture that caught my eye: The Pyramid of Success. I had never heard of the Pyramid of Success before, but I had to learn more given the context. created the pyramid over his career. It contains 25 behaviors that build-up to create a successful life. Coach John Wooden Seeing this was mind-blowing to me. Not only does it define the foundation of Ted Lasso’s character, but there is also so much to learn from it. I look forward to reading more about in the future. Coach Wooden’s Pyramid of Success Conclusion I love the show Ted Lasso and can’t wait for Season 2. While I learned a number of lessons from Ted Lasso, there are many more in Season 1. What’s one lesson you learned from Ted Lasso about how to be a successful leader? Let me know on or . Twitter LinkedIn Before you go The purpose of Build the Stage is to . teach YOU how to be a successful leader If you learned something new from this essay, : I’d appreciate it if you’d complete one of the following actions : By sharing this essay, you help others grow their skills and spark discussion. Share this essay : What’s one thing you learned from this essay? Let me know on . Join the Discussion Twitter ! If you’re not a part of the Build the Stage community, it’s never too late. to never miss new ways to become more successful. Subscribe Sign up to the newsletter Further Reading Change What You Control How to Manage Existing Engineering Teams Creativity, Inc.: Overcoming the Unseen Forces That Stand in the Way of True Inspiration Amazon Bookshop Coach Wooden’s Pyramid of Success Amazon Bookshop

Ted Lasso’s Leadership Lessons Made Me a Successful Leader

Regression analysis is a statistical technique that models and approximates the relationship between a dependent and one or more independent variables. This article will quickly introduce three commonly used regression models using R and the Boston housing data-set: Ridge, Lasso, and Elastic Net. First we need to understand the basics of regression and what parameters of the equation are changed when using a specific model. Simple linear regression, also known as ordinary least squares (OLS) attempts to minimize the sum of error squared. The error in this case is the difference between the actual data point and its predicted value. Visualization of the squared error (from Setosa.io) The equation for this model is referred to as the cost function and is a way to find the optimal error by minimizing and measuring it. The gradient descent algorithm is used to find the optimal cost function by going over a number of iterations. But the data we need to define and analyze is not always so easy to characterize with the base OLS model. Equation for least ordinary squares One situation is the data showing multi-collinearity, this is when predictor variables are correlated to each other and to the response variable. To picture this let’s say we’re doing a study that looks at a response variable — patient weight, and our predictor variables would be height, sex, and diet. The problem here is that height and sex are also correlated and can inflate the standard error of their coefficients which may make them seem statistically insignificant. To produce a more accurate model of complex data we can add a penalty term to the OLS equation. A penalty adds a towards certain values. These are known as L1 regularization(Lasso regression) and L2 regularization(ridge regression). bias The best model we can hope to come up with minimizes both the and the : bias variance Variance/bias trade off (KDnuggets.com) Ridge Regression Ridge regression uses L2 regularization which adds the following penalty term to the OLS equation. L2 regularization penalty term The L2 term is equal to the square of the magnitude of the coefficients. In this case if lambda( is zero then the equation is the basic OLS but if it is greater than zero then we add a constraint to the coefficients. This constraint results in minimized coefficients (aka shrinkage) that trend towards zero the larger the value of lambda. Shrinking the coefficients leads to a lower variance and in turn a lower error value. Therefore Ridge regression decreases the complexity of a model but does not reduce the number of variables, it rather just shrinks their effect. λ) Lasso regression Lasso regression uses the L1 penalty term and stands for . The penalty applied for L2 is equal to the absolute value of the magnitude of the coefficients: Least Absolute Shrinkage and Selection Operator L1 regularization penalty term Similar to ridge regression, a lambda value of zero spits out the basic OLS equation, however given a suitable lambda value lasso regression can drive some coefficients to zero. The larger the value of lambda the more features are shrunk to zero. This can eliminate some features entirely and give us a subset of predictors that helps mitigate multi-collinearity and model complexity. Predictors not shrunk towards zero signify that they are important and thus L1 regularization allows for feature selection (sparse selection). Elastic Net A third commonly used model of regression is the Elastic Net which incorporates penalties from both L1 and L2 regularization: Elastic net regularization In addition to setting and choosing a lambda value elastic net also allows us to tune the alpha parameter where 𝞪 = 0 corresponds to ridge and 𝞪 = 1 to lasso. Simply put, if you plug in 0 for alpha, the penalty function reduces to the L1 (ridge) term and if we set alpha to 1 we get the L2 (lasso) term. Therefore we can choose an alpha value between 0 and 1 to optimize the elastic net. Effectively this will shrink some coefficients and set some to 0 for sparse selection. Preparing the data We will be using the following packages: library(tidyverse)library(caret)library(glmnet) We’ll also be using R’s built in Boston housing market data set as it has many predictor variables data(“Boston”, package = “MASS”) #set a seed so you can reproduce the resultsset.seed(1212) #split the data into training and test datasample_size <- floor(0.75 * nrow(Boston)) training_index <- sample(seq_len(nrow(Boston)), size = sample_size) train <- Boston[training_index, ] test <- Boston[-training_index, ] We also should create two objects to store predictor (x) and response variables (y, median value) # Predictorx <- model.matrix(medv~., train)[,-1] # Responsey <- train$medv Performing Ridge regression As we mentioned in the previous sections, lambda values have a large effect on coefficients so now we will compute and chose a suitable one. Here we perform a cross validation and take a peek at the lambda value corresponding to the lowest prediction error before fitting the data to the model and viewing the coefficients. cv.r <- cv.glmnet(x, y, alpha = 0) cv.r$lambda.min model.ridge <- glmnet(x, y, alpha = 0, lambda = cv.r$lambda.min) coef(model.ridge) We can see here that certain coefficients have been pushed towards zero and minimized while RM (number of rooms) has a significantly higher weight than the rest Ridge regression coefficients We now look at how our model performs by using our test data on it. x.test.ridge <- model.matrix(medv ~., test)[,-1] predictions.ridge <- model.ridge%>% predict(x.test.ridge)%>% as.vector() data.frame(RMSE.r = RMSE(predictions.ridge, test$medv),Rsquare.r = R2(predictions.ridge, test$medv)) RMSE = 4.8721 and R² = 0.7205 Performing Lasso regression The steps will be identical to what we have done for ridge regression. The value of alpha is the only change here (remember 𝞪 = 1 denotes lasso) cv.l <- cv.glmnet(x, y, alpha = 1) cv.l$lambda.min model.lasso <- glmnet(x, y, alpha = 1, lambda = cv.l$lambda.min) coef(model.lasso) x.test.lasso <- model.matrix(medv ~., test)[,-1]predictions.lasso <- model.lasso %>%predict(x.test.lasso) %>%as.vector() data.frame(RMSE.l = RMSE(predictions.lasso, test$medv),Rsquare.l = R2(predictions.lasso, test$medv)) RMSE = 4.8494 and R² = 0.7223 Performing Elastic Net regression Performing Elastic Net requires us to tune parameters to identify the best alpha and lambda values and for this we need to use the package. We will tune the model by iterating over a number of alpha and lambda pairs and we can see which pair has the lowest associated error. caret model.net <- train(medv ~., data = train, method = "glmnet",trControl = trainControl("cv", number = 10),tuneLength = 10) model.net$bestTune coef(model.net$finalModel, model.net$bestTune$lambda) x.test.net <- model.matrix(medv ~., test)[,-1] predictions.net <- model.net %>% predict(x.test.net) data.frame(RMSE.net = RMSE(predictions.net, test$medv),Rsquare.net = R2(predictions.net, test$medv)) RMSE = 4.8523 and R² = 0.7219 Conclusion We can see that the R mean-squared values using all three models were very close to each other, but both did marginally perform better than ridge regression (Lasso having done best). Lasso regression also showed the highest R² value.

An Introduction to Ridge, Lasso, and Elastic Net Regression

For many years, programmers have tried to solve extremely complex computer science problems using traditional algorithms which are based on the most basic condition statement: if this then that. For example, if the email contains the word “free!” it should be classified as spam. In recent years, with the rise of exceptional , the machine learning approach for solving complex problems has been magnificently accelerated. Machine learning is the science of providing computers the ability to learn and solve problems without being explicitly programmed. Sounds like a black magic? Maybe. In this post, I will introduce you to problems which can be solved using machine learning, as well as practical machine learning solutions for solving them. cloud computing technologies Exactly like humans learn on a daily basis, in order to let a machine to learn, you need to provide it with enough data. Once it processed the data, it can make predictions about the future. Assuming you want to classify emails by whether they are spam emails or not. In order to solve this problem using machine learning, you need to provide the machine with many emails — which are already classified in the correct classes of spam vs. not spam. The will iterate over the samples and learn what are the that define a spam email. Assuming you trained the machine learning model right, it will be able to whether a future email should be classified as spam or not, with high accuracy. In many cases, you’ll not be able to completely understand how the model predicts the class. labeled classifier features predict Machine learning hierarchy The world of machine learning can be divided into two types of problems: and . In this post, we will focus only on supervised learning, which is a subset of problems which contain data (That is, every email is labeled as spam or not spam). For cases where you have unlabeled data, unsupervised learning might be a proper solution. supervised learning unsupervised learning labeled Underneath the supervised learning problems, there is another division of problems vs. problems. In regression problems, the value you wish to predict is . For example, house price. In classification problems, on the other hand, the value you are about to predict is discrete, like spam vs. not spam. regression classification continuous The data you need to provide in order to train your model depends on the problem and the value you wish to predict. Let’s assume you want to predict a house price based on different properties. So in this case, each row in your dataset should (for example) consist of: house size, the number of rooms, floor, whether elevator exists, etc. features: house price. label: Choosing and collecting the features that best describe a house for predicting its price can be challenging. It requires market knowledge as well as access to big data sources. The features are the keys in which the prediction of the house price will be based upon. Machine learning as an optimization problem Every machine learning problem is basically an . That is, you wish to find either a maximum or a minimum of a specific function. The function that you want to optimize is usually called the (or ). The loss function is defined for each machine learning algorithm you use, and this is the main metric for evaluating the accuracy of your trained model. optimization problem loss function cost function For the house price prediction example, after the model is trained, we are able to predict new house prices based on their features. For each house price we predict, denoted as Ŷi, and the actual house price Yi we can calculate the loss by: l = ( Ŷi- Yi)2 This is the most basic form of a loss for a specific data-point, That is used mostly for algorithms. The loss function as a whole can be denoted as: linear regression L = ∑( Ŷi- Yi)2 Which simply defines that our model’s loss is the sum of distances between the house price we’ve predicted and the . This loss function, in particular, is called or . We wish to the loss function (L) as much as possible so the prediction will be as close as possible to the ground truth. ground truth quadratic loss least squares minimize If you followed me up until now, you are familiar with the basic concept of every practical machine learning problem. every machine learning algorithm defines its own loss function according to its goal in life. Remember, Linear regression Linear regression is a basic yet super powerful machine learning algorithm. As you gain more and more experience with machine learning, you’ll notice how most of the time. Linear regression is widely used in different supervised machine learning problems, and as you may guessed already, it focuses on regression problem (the value we wish the predict is continuous). It is extremely important to have a good understanding of linear regression simple is better than complex before studying more complex learning methods. Many extensions have been developed for linear regression which I will introduce later in this post. The most basic form of linear regression deals with dataset of a single feature per data point (think of it as the house size). Because we are dealing with supervised learning, each row (house) in the dataset should include the price of the house (which is the value we wish the predict). An example of our dataset: In a visual representation: In linear regression we wish to fit a function (model) in this form: Ŷ = β0+β1X Where X is the vector of features (the first column in the table below), and β0, β1 are the coefficients we wish to . learn By learning the parameters I mean executing an iterative process that updates β at every step by reducing the loss function as much as possible. Once we reach the minimum point of the loss function we can say that we completed the iterative process and learned the parameters. Just to make it even more clear, the combination of the β coefficients are our trained model — which means that we have a solution to the problem! After executing the iterative process, we can visualize the solution on the same graph: Where the trained model is: Ŷ = -0.5243+1.987X Now let’s assume we want to predict based on our trained model, what will be the price of a house of size 85. In order to predict the price, we will substitute the β values we found into the model function, including the house size, and get the predicted house price: Ŷ = 168.37 To recap what we’ve covered so far: Every machine learning problem is basically an optimization problem. That is, we want to minimize (or maximize) some function. Our dataset is consist of features (X) and a label (Y). In our case — house size is the single feature, house price is the label. In linear regression problems, we want to minimize the quadratic loss which is the sum of distances between the predictions and the actual value (ground truth). In order to minimize the loss function and find the optimal β coefficients, we will execute an iterative process. To predict the label (house price) of a new house based on its size, we will use the trained model. The iterative process for minimizing the loss function (a.k.a learning the coefficients β), will be discussed in another post. Although it can be done with one line of code, I highly recommend reading more about iterative algorithms for minimizing loss functions like . Gradient Descent Linear regression with multiple features In real world problems, you usually have more than one feature per row (house). Let’s see how linear regression can help us with multi-feature problems. Considering this dataset: So currently we have 3 features: house size number of rooms floor Therefore, we need to adapt our basic linear model to an extended one that can take into account the additional features for each house: Ŷ = β0+β1X1+β2X2+β3X3 In order to solve the multi-feature linear regression problem, we will the same iterative algorithm and minimize the loss function. The main difference will be that we will end up with four β coefficients instead of only two. Overfit in machine learning algorithms Having more features may seem like a perfect way for improving the accuracy of our trained model (reducing the loss) — because the model that will be trained will be more flexible and will take into account more parameters. On the other hand, we need to be extremely careful about the data. As we know, every dataset has noisy samples. For example, the house size wasn’t measured accurately or the price is not up to date. The inaccuracies can lead to a low-quality model if not trained carefully. The model might end up memorizing the noise instead of learning the trend of the data. overfitting A visual example of a nonlinear overfitted model: Overfit can happen in linear models as well when dealing with multiple features. If not filtered and explored up front, some features can be more destructive than helpful, repeat information that already expressed by other features and add high noise to the dataset. Overcoming overfit using regularization Because overfit is an extremely common issue in many machine learning problems, there are different approaches to solving it. The main concept behind avoiding overfit is simplifying the models as much as possible. Simple models do not (usually) overfit. On the other hand, we need to pay attention the to gentle trade-off between overfitting and underfitting a model. One of the most common mechanisms for avoiding overfit is called regularization. Regularized machine learning model, is a model that its loss function contains another element that should be minimized as well. Let’s see an example: L = ∑( Ŷi- Yi)2 + λ∑ β2 This loss function includes two elements. The first one is the one you’ve seen before — the sum of distances between each prediction and its ground truth. The second element though, a.k.a the regularization term, might seem a bit bizarre. It sums over squared β values and multiplies it by another parameter λ. The reason for doing that is to “punish” the loss function for high values of the coefficients β. As aforesaid, simple models are better than complex models and usually do not overfit. Therefore, we need to try and simplify the model as much as possible. Remember that our goal of the iterative process is to minimize the loss function. By punishing the β values we add a constraint to minimize them as much as possible. There is a gentle trade-off between fitting the model, but not overfitting it. This approach is called . Ridge regression Ridge regression Ridge regression is an extension for linear regression. It’s basically a regularized linear regression model. The λ parameter is a scalar that should be learned as well, using a method called that will be discussed in another post. cross validation A super important fact we need to notice about ridge regression is that it enforces the β coefficients to be lower, but it enforce them to be zero. That is, it will not get rid of irrelevant features but rather . does not minimize their impact on the trained model Lasso method Lasso is another extension built on regularized linear regression, but with a small twist. The loss function of Lasso is in the form: L = ∑( Ŷi- Yi)2 + λ∑ |β| The only difference from Ridge regression is that the regularization term is in absolute value. But this difference has a huge impact on the trade-off we’ve discussed before. Lasso method overcomes the disadvantage of Ridge regression by not only punishing high values of the coefficients β but actually setting them to zero if they are not relevant. Therefore, you might end up with fewer features included in the model than you started with, which is a huge advantage. Conclusions Machine learning is getting more and more practical and powerful. With zero knowledge in programming, you can train a model to predict house prices in no time. We’ve covered the basics of machine learning, loss function, linear regression, ridge and lasso extensions. There is more Math involved from what I’ve covered in this post, I tried to keep it as practical and, on the other hand, high-level as possible (Someone said trade-off?). I encourage you to take a deep dive into this amazing world. Check out my blog for more posts to come — — coders with entrepreneurial mindset. https://codingStartups.com

Practical machine learning: Ridge Regression vs. Lasso

Smarter Systems, Less Hassle: Inside DBMS Auto-Tuning

Authors:
(1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia;
(2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.3 Reinforcement Learning 7.4 Search-based Solutions 8 Experimental Setting 9 Related Work 10 Discussion and Conclusion, and References 5.3 Summary Given the complex configuration space and the diversity of workloads, employing pruning techniques to reduce workload running time and configuration search space emerges as a natural approach in addressing these complexities. In this section, we aim to provide direction for future practitioners and researchers on improving data collection efficiency and training efficiency through various pruning strategies. Specifically, we classify the pruning techniques into two levels: workload-level and configuration space. Regarding the workload level, we categorize it into two directions: eliminating redundant queries and workload feature reduction techniques. For the configuration level, we present the existing feature reduction methods applied in the state-of-the-art tuning methods, mainly focusing on feature projection, importance ranking, or feature clustering. Moreover, future researchers and practitioners can also try to explore different dimensionality reduction techniques tailored to specific data characteristics, as outlined in the survey by Hou et al. [31]. Furthermore, advancements in high-dimensional data technology offer opportunities to enhance the performance of feature pruning methods. For instance, Yang et al. [32] proposed an innovative variant of LASSO, named Efficient Tuning of Lasso (ET-Lasso), which focuses on ensuring feature selection consistency. This method has demonstrated effectiveness in efficiently selecting active features contributing to the response, achieved by integrating permuted features as pseudo-features within linear models. This paper is available on arxiv under CC BY 4.0 DEED. Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Authors: Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 2 Tuning Objectives 3 Overview of Tuning Framework 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 5.3 Summary 6 Knowledge from Experience 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.2 Neural Network 7.3 Reinforcement Learning 7.3 Reinforcement Learning 7.4 Search-based Solutions 7.4 Search-based Solutions 8 Experimental Setting 8 Experimental Setting 9 Related Work 9 Related Work 10 Discussion and Conclusion, and References 10 Discussion and Conclusion, and References 5.3 Summary Given the complex configuration space and the diversity of workloads, employing pruning techniques to reduce workload running time and configuration search space emerges as a natural approach in addressing these complexities. In this section, we aim to provide direction for future practitioners and researchers on improving data collection efficiency and training efficiency through various pruning strategies. Specifically, we classify the pruning techniques into two levels: workload-level and configuration space. Regarding the workload level, we categorize it into two directions: eliminating redundant queries and workload feature reduction techniques. For the configuration level, we present the existing feature reduction methods applied in the state-of-the-art tuning methods, mainly focusing on feature projection, importance ranking, or feature clustering. Moreover, future researchers and practitioners can also try to explore different dimensionality reduction techniques tailored to specific data characteristics, as outlined in the survey by Hou et al. [31]. Furthermore, advancements in high-dimensional data technology offer opportunities to enhance the performance of feature pruning methods. For instance, Yang et al. [32] proposed an innovative variant of LASSO, named Efficient Tuning of Lasso (ET-Lasso), which focuses on ensuring feature selection consistency. This method has demonstrated effectiveness in efficiently selecting active features contributing to the response, achieved by integrating permuted features as pseudo-features within linear models. This paper is available on arxiv under CC BY 4.0 DEED. This paper is available on arxiv under CC BY 4.0 DEED. available on arxiv

Pruning Techniques for Reducing Workload and Configuration Space Complexity

Authors:
(1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia;
(2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.3 Reinforcement Learning 7.4 Search-based Solutions 8 Experimental Setting 9 Related Work 10 Discussion and Conclusion, and References 5.2 Configuration-level Pruning Another approach to mitigating the optimization time required by machine learning-based methodologies is to reduce configuration space necessitating tuning. Configuration-level pruning endeavors to discern and prioritize the tuning of parameters that exert substantial influence on the DBMSs based on historical observations. • Spearman Rank Correlation Coefficient (SRCC) [26]: is a nonparametric measure of rank correlation on the strength of a monotonic relationship between paired data. It is defined as the Pearson correlation coefficient between the rank variables. By leveraging its capacity to gauge monotonic relationships, SRCC facilitates the identification and removal of redundant parameters, contributing to a more efficient and simplified configuration. LOCAT [7] calculates SRCC between each configuration parameter and the workload execution time to filter out some redundant configuration parameters and narrow down the parameter search space.” • Principal Component Analysis (PCA): is a dimensionality reduction method that transforms correlated variables into uncorrelated ones, known as principal components. It does so by calculating the covariance matrix, performing eigendecomposition, and selecting a subset of principal components based on their variance. After SRCC, LOCAT [7] applies Gaussian kernel Principal Component Analysis (KPCA) to further extract and form new lower-dimensional parameters derived after removal of redundant configuration parameters for subsequent optimal parameter searching. • Least Absolute Shrinkage and Selection Operator (LASSO) and Lasso Path Algorithm. In the context of linear regression, LASSO modifies this objective function by adding a L1 penalty term equals to λ times the sum of absolute values of the regression coefficients, where λ controls the strength of the penalty, and it helps to reduce the effect of irrelevant variables by penalizing models with large weights. A higher λ value results in more coefficients being pushed toward zero, thereby achieving interpretable, stable, and computationally efficient feature selection. OtterTune [8] uses the LASSO path algorithm to assess the importance of configuration parameters by gradually reducing the penalty term. The order in 6 which parameters are included during this process is then considered as the importance order, and OtterTune uses this information to prune less important parameters. • Random Forest (RF): is a supervised machine learning method to deal with classification and regression problems. It can be deemed a voting algorithm consisting of multiple decision trees, used to calculate the importance of features. In the study [27], the authors utilize Latin Hypercube Sampling (LHS) to select a subset of configurations. Subsequently, they employ Random Forests with 300 Classification and Regression Trees (CART) to ascertain the importance of each parameter. Their findings reveal that when employing the YCSB workload-A on Cassandra, optimizing just five parameters can yield performance levels comparable to 99% of the best configurations attained through extensive parameter tuning. HUNTER [13] adopt the RF classifier with CARTs and adopts the majority voting principle to determine the importance of the knobs. It then selects the top-20 knobs to reduce the configuration search space in its tuning framework. • Hashing-enhanced Subspace BO (HeSBO) [28]: is a randomized low-dimensional projection approach that operates by deducing the search space for Bayesian Optimization-based solutions (discussed in Section 7.1). By utilizing two uniform hash functions to construct the rows and signs of the random projection matrix, it performs a count-sketch projection to transform the original high-dimensional configuration space into lower-dimensional subspace. This process is intuitively designed to effectively preserve the characteristics, such as pairwise point distances, of the original high-dimensional space for the reduced (important) dimensions. LlamaTune [16] adopts it to perform a projection of the configuration space from all documentations to a lowerdimensional subspace and then use the Bayesian Optimization-based optimizer to tune this smaller subspace. • Alternative approaches: Due to the challenges of tuning in high-dimensional configuration spaces, the identification of parameters that significantly affect DBMS performance has gained considerable attention. Among them, Researchers in [29] propose Caver to select a subset of storage parameters. Given a set of initial parameters and configurations, Carver first employs LHS to select a small number of configurations for evaluation. Subsequently, it greedily selects the most important parameters based on their parameter importance values. The first parameter is determined by the highest importance value, after which Carver fixes its value and computes the parameter importance values for the remaining parameters. During this process, importance is calculated as the difference between the variance of the original set of configurations and the sum of variances within the subset when parameters take different values. The algorithm selects parameters with the maximum difference. Recently, OpAdviser [30] proposed constructing an effective configuration region that contains promising configurations. It leverages performance similarity among historical workloads to guide the construction process. Specifically, it extracts a relatively compact region based on similar workloads and a larger region based on less similar ones. Furthermore, OpAdviser constructs the target search space by employing a majority weighted voting strategy to aggregate suggestions from candidate tasks. This paper is available on arxiv under CC BY 4.0 DEED. Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Authors: Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 2 Tuning Objectives 3 Overview of Tuning Framework 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 5.3 Summary 6 Knowledge from Experience 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.2 Neural Network 7.3 Reinforcement Learning 7.3 Reinforcement Learning 7.4 Search-based Solutions 7.4 Search-based Solutions 8 Experimental Setting 8 Experimental Setting 9 Related Work 9 Related Work 10 Discussion and Conclusion, and References 10 Discussion and Conclusion, and References 5.2 Configuration-level Pruning Another approach to mitigating the optimization time required by machine learning-based methodologies is to reduce configuration space necessitating tuning. Configuration-level pruning endeavors to discern and prioritize the tuning of parameters that exert substantial influence on the DBMSs based on historical observations. • Spearman Rank Correlation Coefficient (SRCC) [26]: is a nonparametric measure of rank correlation on the strength of a monotonic relationship between paired data. It is defined as the Pearson correlation coefficient between the rank variables. By leveraging its capacity to gauge monotonic relationships, SRCC facilitates the identification and removal of redundant parameters, contributing to a more efficient and simplified configuration. LOCAT [7] calculates SRCC between each configuration parameter and the workload execution time to filter out some redundant configuration parameters and narrow down the parameter search space.” • Principal Component Analysis (PCA): is a dimensionality reduction method that transforms correlated variables into uncorrelated ones, known as principal components. It does so by calculating the covariance matrix, performing eigendecomposition, and selecting a subset of principal components based on their variance. After SRCC, LOCAT [7] applies Gaussian kernel Principal Component Analysis (KPCA) to further extract and form new lower-dimensional parameters derived after removal of redundant configuration parameters for subsequent optimal parameter searching. • Least Absolute Shrinkage and Selection Operator (LASSO) and Lasso Path Algorithm. In the context of linear regression, LASSO modifies this objective function by adding a L1 penalty term equals to λ times the sum of absolute values of the regression coefficients, where λ controls the strength of the penalty, and it helps to reduce the effect of irrelevant variables by penalizing models with large weights. A higher λ value results in more coefficients being pushed toward zero, thereby achieving interpretable, stable, and computationally efficient feature selection. OtterTune [8] uses the LASSO path algorithm to assess the importance of configuration parameters by gradually reducing the penalty term. The order in 6 which parameters are included during this process is then considered as the importance order, and OtterTune uses this information to prune less important parameters. • Random Forest (RF): is a supervised machine learning method to deal with classification and regression problems. It can be deemed a voting algorithm consisting of multiple decision trees, used to calculate the importance of features. In the study [27], the authors utilize Latin Hypercube Sampling (LHS) to select a subset of configurations. Subsequently, they employ Random Forests with 300 Classification and Regression Trees (CART) to ascertain the importance of each parameter. Their findings reveal that when employing the YCSB workload-A on Cassandra, optimizing just five parameters can yield performance levels comparable to 99% of the best configurations attained through extensive parameter tuning. HUNTER [13] adopt the RF classifier with CARTs and adopts the majority voting principle to determine the importance of the knobs. It then selects the top-20 knobs to reduce the configuration search space in its tuning framework. • Hashing-enhanced Subspace BO (HeSBO) [28]: is a randomized low-dimensional projection approach that operates by deducing the search space for Bayesian Optimization-based solutions (discussed in Section 7.1). By utilizing two uniform hash functions to construct the rows and signs of the random projection matrix, it performs a count-sketch projection to transform the original high-dimensional configuration space into lower-dimensional subspace. This process is intuitively designed to effectively preserve the characteristics, such as pairwise point distances, of the original high-dimensional space for the reduced (important) dimensions. LlamaTune [16] adopts it to perform a projection of the configuration space from all documentations to a lowerdimensional subspace and then use the Bayesian Optimization-based optimizer to tune this smaller subspace. • Alternative approaches: Due to the challenges of tuning in high-dimensional configuration spaces, the identification of parameters that significantly affect DBMS performance has gained considerable attention. Among them, Researchers in [29] propose Caver to select a subset of storage parameters. Given a set of initial parameters and configurations, Carver first employs LHS to select a small number of configurations for evaluation. Subsequently, it greedily selects the most important parameters based on their parameter importance values. The first parameter is determined by the highest importance value, after which Carver fixes its value and computes the parameter importance values for the remaining parameters. During this process, importance is calculated as the difference between the variance of the original set of configurations and the sum of variances within the subset when parameters take different values. The algorithm selects parameters with the maximum difference. Recently, OpAdviser [30] proposed constructing an effective configuration region that contains promising configurations. It leverages performance similarity among historical workloads to guide the construction process. Specifically, it extracts a relatively compact region based on similar workloads and a larger region based on less similar ones. Furthermore, OpAdviser constructs the target search space by employing a majority weighted voting strategy to aggregate suggestions from candidate tasks. This paper is available on arxiv under CC BY 4.0 DEED. This paper is available on arxiv under CC BY 4.0 DEED. available on arxiv

How Configuration-level Pruning Reduces Optimization Time in DBMS Tuning

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MagicEraser.Pro offers a seamless solution for refining your photographs and removing unwanted elements. Explore the numerous ways you can utilize MagicEraser.Pro to elevate your images. Removing People from Photos Swiftly clear out unwanted figures, like random tourists or event spectators, to keep the spotlight on your intended subject. Eliminating Text and Logos Wipe away any distracting text, captions, or logos to craft images that are clean and visually striking. Enhancing Image Focus Trim away background distractions such as buildings, trees, or clutter to accentuate the main subject of your photograph. Getting Rid of Watermarks Effortlessly erase obtrusive watermarks, date stamps, or location markers that detract from the overall beauty of your images. Improving Image Quality Seamlessly eliminate eyesores like litter, power lines, or unwanted shadows, resulting in a polished and professional appearance. Correcting Imperfections Refine your photos by removing minor flaws like scratches, dust, or stains, ensuring every detail shines with clarity. MagicEraser.Pro is designed for photographers, graphic designers, and hobbyists seeking an efficient and user-friendly tool to optimize their images. What's The Standout Benefits of This Magic Eraser? The following features collectively make MagicEraser.Pro a versatile and powerful tool for anyone looking to enhance their photography with ease. Free to Use: Completely free with unlimited usage after a simple sign-up, making it accessible for everyone. Free to Use: Completely free with unlimited usage after a simple sign-up, making it accessible for everyone. High-Quality Results: Utilizes advanced image processing technology to deliver clear and precise edits, ensuring excellent image quality. High-Quality Results: Utilizes advanced image processing technology to deliver clear and precise edits, ensuring excellent image quality. 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