# linear-regression Published articles for linear-regression. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Leveraging PyFixest for High-Cardinality Marketplace Modeling at Instacart DevFeed: [Leveraging PyFixest for High-Cardinality Marketplace Modeling at Instacart]() Original publisher: [Read original article]() Author: Benjamin Knight Published: 2026-06-29T16:06:24Z Content type: article Language: en Sources: [Instacart]() Topics: [benchmarking](), [math](), [Algorithms, Complexity](), [Software](), [Programming](), [Routing (disambiguation)]() Tags: [benchmarking](), [bias](), [cardinality](), [data-science](), [delivery](), [efficiency](), [estimator](), [fixed-effects-model](), [instacart](), [linear-regression](), [measurement](), [memory](), [precision](), [pyfixest](), [regression](), [routing](), [speed](), [statistics](), [techniques]() ### AI overview This Instacart article explains why ordinary least squares regression becomes computationally impractical for marketplace experiments with high-cardinality categories. It presents the mathematical basis for using Fixest and Pyfixest, discusses switchback experiment designs for addressing treatment spillover, and describes benchmarks comparing processing speed, memory efficiency, and estimator precision. ### Source excerpt Benjamin S. Knight Scaling Marketplace experiments requires specialized statistical techniques. We examine why standard ordinary least squares regression (OLS) becomes computationally intractable when controlling for high-cardinality categories. We then dive into the underlying math and demonstrate how modern packages -- specifically Fixest and Pyfixest -- bypass these limitations. We conclude by benchmarking these methods to show their real-world impact on processing speed, memory efficiency, and estimator precision. At Instacart we strive to give our customers access to all the fresh foods and ingredients that they would normally get from a trip to the grocery store, but without the hassle of driving, finding parking, waiting in line, etc. Instacart's Marketplace team is responsible for surfacing customers' orders to shoppers, aligning Instacart's delivery windows with shoppers' projected availabilities as efficiently as possible. This entails a careful balancing act. If we offer delivery windows that are sooner / more popular, then we risk overextending shoppers' ability to fulfill those orders on time. If we are too conservative in our delivery option offerings, then we risk losing potential orders. Accurately measuring the impact of changes in our batching and routing algorithms requires thoughtful experiment design and software. Better predictions of future demand / time-to-fulfill allow Instacart to offer more convenient delivery windows.Experimentation on Marketplace One of our primary concerns in Marketplace is treatment spillage. For example, if we adjust our batching algorithm and increase the rate at which multiple orders are combined into batches in Brooklyn and Queens, then we face a real risk of also influencing the rate of batch creation / completion in Staten Island, the Bronx, and Manhattan. In this case the treatment impacts the control group -- a classic source of measurement bias as a consequence of violating the Stable Unit Treatment Value Assumpt ## Regression and Linear Combinations DevFeed: [Regression and Linear Combinations]() Original publisher: [Read original article]() Published: 2021-03-29T09:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [linear-regression](), [math](), [Optimization](), [Algorithms, Complexity]() Tags: [data](), [gradient-descent](), [kernelization](), [linear-algebra](), [linear-combination](), [linear-regression](), [mathematics](), [optimization](), [programming](), [regression]() ### 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$. ## Linear Regression DevFeed: [Linear Regression]() Original publisher: [Read original article]() Published: 2013-08-18T17:43:20Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [linear-regression](), [Machine learning](), [data]() Tags: [conditional-probability](), [covariance](), [data](), [expectation](), [linear-regression](), [machine-learning](), [python](), [regression](), [statistics](), [variance]() ### AI overview This tutorial introduces linear regression as a basic form of statistical learning. It explains independent and dependent variables, uses a two-variable linear model to predict one variable from another, and describes estimating the model parameters from sample pairs. ### Source excerpt Machine learning is broadly split into two camps, statistical learning and non-statistical learning. The latter we've started to get a good picture of on this blog; we approached Perceptrons, decision trees, and neural networks from a non-statistical perspective. And generally "statistical" learning is just that, a perspective. Data is phrased in terms of independent and dependent variables, and statistical techniques are leveraged against the data. In this post we'll focus on the simplest example of this, linear regression, and in the sequel see it applied to various learning problems.