Convex optimization linear regression

  • How is linear regression optimized?

    Models like linear regression and logistic regression are trained by least squares optimization, and this is the most efficient approach to finding coefficients that minimize error for these models.
    Nevertheless, it is possible to use alternate optimization algorithms to fit a regression model to a training dataset..

  • Is linear regression a convex optimization?

    The Least Squares cost function for linear regression is always convex regardless of the input dataset, hence we can easily apply first or second order methods to minimize it..

  • Is linear regression convex optimization?

    Abstract—A convex optimization model predicts an output from an input by solving a convex optimization problem.
    The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression..

  • In linear regression, we typically optimize the parameters of the model to minimize the difference between the predicted.
    John Fowler.
    Works at California Institute of Technology (Caltech) Author has 251 answers and 492.
    1. K answer views 6y.
      2. In the most common forms of linear regression, “optimizing” is actually
Mar 11, 2018The short answer is: Logistic regression is considered a generalized linear model because the outcome always depends on the sum of the inputs and parameters. Or  Is convex optimization still relevant in the era of machine learning What makes minimizing an objective function difficult in general Why are most of the machine learning algorithms a convex - QuoraMore results from www.quora.com
Mar 11, 2018The short answer is: Logistic regression is considered a generalized linear model because the outcome always depends on the sum of the inputs and parameters. Or  What makes minimizing an objective function difficult in general Is convex optimization still relevant in the era of machine learning More results from www.quora.com

Does linear regression lead to a convex optimization problem?

I know that linear regression leads to a convex optimization problem

I'd like to visually show this with a simple example

Assume that there are two parameters (x and y) and a single data point <1, 1> with 2 as the y value (no intercept term

Then the cost function becomes

What is a convex optimization model?

(Authors listed in alphabetical order

) IEEE/CAA Journal of Automatica Sinica, 8 (8):1355–1364, 2021

A convex optimization model predicts an output from an input by solving a convex optimization problem

The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic regression

Training linear regression models is a classic example of a convex optimization problem in which the goal is to find the best-fit line that minimizes the sum of squared errors between the predicted and actual values.

Statistical classification in machine learning

In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class it belongs to.
A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics.
An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector.
Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.

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