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Linear Regression: From Least Squares to Production-Ready Practice

Linear Regression: From Least Squares to Production-Ready Practice Tags : machinelearning , datascience , python , tutorial Linear regression is the first algorithm most people learn, and the one most people never study deeply. It is also the model you will still find in production after fancier algorithms fail, because it is fast, stable, and explainable. This article is not a "call .fit() and read the score" tutorial. We will cover the math, the statistical assumptions, the diagnostics, regularization, evaluation, production concerns, and the interview questions that separate beginners from engineers. Why Linear Regression Deserves a Second Look Linear regression is the foundation for understanding almost every other supervised model: Logistic regression is linear regression with a sigmoid on top. Ridge and Lasso are linear regression with constrained weights. Neural networks are stacked linear transformations with nonlinear activations. Tree models are judged against the same baseline: "can I beat a linear model?" More importantly, linear regression is still the right answer in many business problems. When you need to explain a prediction to a regulator, a client, or a finance team, a clean linear model with interpretable coefficients beats a black box. The Math: Least Squares and the Normal Equation Given features X and target y , a linear model assumes: y = X * beta + epsilon The goal is to minimize the residual sum of squares: L(beta) = ||y - X*beta||^2 Taking the derivative with respect to beta and setting it to zero gives the normal equation : beta = (X^T * X)^(-1) * X^T * y In practice, use the pseudoinverse ( pinv ) instead of the inverse, because X^T X may be singular or numerically unstable when features are collinear. import numpy as np def normal_equation ( X , y ): Xb = np . c_ [ np . ones ( X . shape [ 0 ]), X ] # add intercept beta = np . linalg . pinv ( Xb . T @ Xb ) @ Xb . T @ y return beta Three Equivalent Views of Least Squares 1. Geometric view

2026-08-01 原文 →
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Whizz: Your Esoteric Language that's Short as BF, but Easier to Write

I just made Whizz, an esoteric programming language that is full of capability and possible experimentation. Before I interest you in that, I'll explain to you something. What is an esoteric programming language? An esoteric language (or an esolang, colloquially), is a programming language designed to not fit the coding 'norms' or conventions. Take an example: BF ('BF' is an abbreviation and euphemism of brainf***). A standard language would notate a 'Hello, World!' program as something like: print ( " Hello, World! " ) BF, on the other hand, requires something like this: ++++++++ [ > ++++ [ > ++ > +++ > +++ > + <<<< - ] > + > + > - >> + [ < ] < - ] >> . > ---.+++++++..+++. >> . < -. < .+++.------.--------. >> +. > ++. As you can see, BF, like most esolangs, is different: it's hard to write and a puzzle. Whizz is inspired by BF, as its incrementing, decrementing and looping are inspired by it. I made Whizz because I thought languages like BF were way too monotonous to write. Esolangs should be hard and puzzling to write, but not laborious. BF requires you type '+' as many times you want to increment (without loops): so you have to find shortcuts and unscalable solutions, just to achieve your goal. In Whizz, just type that incrementation repetition count before the '+' sign, and there you have it! These wonderful features that Whizz boasts keep the challenge in esolang-ing, but contradictorily makes it more 'scalable'. Another notable feature is functions: the epitome of order. An example of a Whizz program would be: zeroToNine { [ create variables ] counter 10+ [ track state ] char 48+ [ print this one ] space 32+ [ space char ] ( char!+ [ print and increment char ] counter-; [ decrement counter and end if zero ] space! [ print space ] ) } zeroToNine* This, self explanatorily, outputs '0 1 2 3 4 5 6 7 8 9'. Again, in minimized form: c10+n48+s32+(n!+c-;s!) I genuinely hope you experiment with Whizz, and solve puzzles & challenges with it, as if it were BF! Install it

2026-07-31 原文 →
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NASA’s Curiosity rover found a ‘sea of polygons’ on Mars

The latest discovery from NASA's Curiosity Mars rover is a field of honeycomb-shaped polygons covering a Martian valley called Valle Grande. As Gizmodo reports, Curiosity has snapped pictures of the unusual terrain texture before, called polygonal fractures, each about 1.5 to 3 inches wide, but NASA says it's previously only found them in small patches, […]

2026-07-31 原文 →
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From Learning Machine Learning to Competing on Kaggle: My First End-to-End Playground Competition Journey

How I applied Exploratory Data Analysis, Feature Engineering, Pipelines, and Ensemble Models to solve a real-world machine learning problem—and the lessons I learned along the way. Introduction There comes a point in every machine learning learner's journey when watching tutorials and completing small practice exercises are no longer enough. After spending weeks understanding statistics, exploratory data analysis (EDA), feature engineering, preprocessing techniques, and classical machine learning algorithms, I wanted to answer one question: Can I apply everything I've learned to a real machine learning competition? That's when I decided to participate in a Kaggle Playground competition. Unlike classroom datasets, Kaggle competitions force you to think like a machine learning engineer. You're responsible for understanding messy data, building preprocessing pipelines, selecting models, evaluating performance, debugging errors, and finally creating a submission that competes with thousands of participants. This article documents my complete journey—from loading the dataset to building production-style preprocessing pipelines and training multiple ensemble models. Along the way, I'll also share the challenges I faced, what worked well, and the lessons I'll carry into future competitions. Why Kaggle? Learning machine learning isn't just about knowing algorithms. Real-world ML requires answering questions like: Which features are useful? How should missing values be handled? Should categorical variables be one-hot encoded or ordinal encoded? Which preprocessing steps belong inside a pipeline? How do different ensemble models compare? Kaggle provides an environment where all of these questions matter. Instead of building a model that works only inside a notebook, you're solving a problem under realistic constraints and evaluating your solution on unseen data. Competition Goal The objective of this Playground competition was to predict the target class based on a combinatio

2026-07-30 原文 →
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DoorDash is going airborne with new drone delivery division

DoorDash is launching a new drone delivery program called DoorDash Air. The largest food delivery app in the US said that it has approval from the Federal Aviation Administration that clears the way for drone delivery in the near future. DoorDash said it has received a Part 135 air carrier certification from the FAA that […]

2026-07-29 原文 →