# kernelization

Published articles for kernelization.

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## Regression and Linear Combinations

DevFeed: [Regression and Linear Combinations](<https://devfeed.tech/articles/regression-and-linear-combinations-40446.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2021/03/29/regression-and-linear-combinations/>)

Published: 2021-03-29T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [linear-regression](<https://devfeed.tech/topics/linear-regression.md>), [math](<https://devfeed.tech/topics/math.md>), [Optimization](<https://devfeed.tech/topics/optimization.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>)

Tags: [data](<https://devfeed.tech/tags/data.md>), [gradient-descent](<https://devfeed.tech/tags/gradient-descent.md>), [kernelization](<https://devfeed.tech/tags/kernelization.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [linear-combination](<https://devfeed.tech/tags/linear-combination.md>), [linear-regression](<https://devfeed.tech/tags/linear-regression.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [programming](<https://devfeed.tech/tags/programming.md>), [regression](<https://devfeed.tech/tags/regression.md>)

### AI overview

The article explains why linear combinations matter to programmers, using linear regression as a practical example. It describes representing inputs and weights as vectors, incorporating an intercept into the input vector, and formulating regression as a least-squares optimization problem. The supplied excerpt then begins introducing basis functions for modeling nonlinearity.

### Source excerpt

Recently I've been helping out with a linear algebra course organized by Tai-Danae Bradley and Jack Hidary, and one of the questions that came up a few times was, "why should programmers care about the concept of a linear combination?" For those who don't know, given vectors $ v_1, \dots, v_n$, a linear combination of the vectors is a choice of some coefficients $ a_i$ with which to weight the vectors in a sum $ v = \sum_{i=1}^n a_i v_i$.

## Parameterizing the Vertex Cover Problem

DevFeed: [Parameterizing the Vertex Cover Problem](<https://devfeed.tech/articles/parameterizing-the-vertex-cover-problem-40363.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2014/08/25/parameterizing-the-vertex-cover-problem/>)

Published: 2014-08-25T06:50:11Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [complexity](<https://devfeed.tech/tags/complexity.md>), [complexity-theory](<https://devfeed.tech/tags/complexity-theory.md>), [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [conferences](<https://devfeed.tech/tags/conferences.md>), [fixed-parameter-tractability](<https://devfeed.tech/tags/fixed-parameter-tractability.md>), [graph](<https://devfeed.tech/tags/graph.md>), [kernel](<https://devfeed.tech/tags/kernel.md>), [kernelization](<https://devfeed.tech/tags/kernelization.md>), [np-hard](<https://devfeed.tech/tags/np-hard.md>), [vertex-cover](<https://devfeed.tech/tags/vertex-cover.md>)

### AI overview

This article introduces fixed-parameter complexity and explains how fixing a small parameter can make some hard problems tractable. It focuses on kernelization and uses the vertex cover problem as a canonical example, though the supplied text ends before the kernelization method is presented.

### Source excerpt

I'm presenting a paper later this week at the Matheamtical Foundations of Computer Science 2014 in Budapest, Hungary. This conference is an interesting mix of logic and algorithms that aims to bring together researchers from these areas to discuss their work. And right away the first session on the first day focused on an area I know is important but have little experience with: fixed parameter complexity. From what I understand it's not that popular of a topic at major theory conferences in the US (there appears to be only one paper on it at this year's FOCS conference), but the basic ideas are worth knowing.