Isaac Newton had many amazing scientific and mathematical accomplishments. His law of universal gravitation and his creation of calculus are at the top of the list! But in the field of numerical analysis, "Newton's Method" was a groundbreaking advancement for solving for a root of a nonlinear smooth function. The
A common way to visualize the sample correlations between many numeric variables is to display a heat map that shows the Pearson correlation for each pair of variables, as shown in the image to the right. The correlation is a number in the range [-1, 1], where -1 indicated perfect
Since the pandemic began in 2020, the SAS IML developers have added about 50 new functions and enhancements to the SAS IML language in SAS Viya. Among these functions are new modern methods for optimization that have a simplified syntax as compared to the older 'NLP' functions that are available
Isotonic regression (also called monotonic regression) is a type of regression model that assumes that the response variable is a monotonic function of the explanatory variable(s). The model can be nondecreasing or nonincreasing. Certain physical and biological processes can be analyzed by using an isotonic regression model. For example, a
Given a set of N points in k-dimensional space, can you find the location that minimizes the sum of the distances to the points? The location that minimizes the distances is called the geometric median of the points. For univariate data, the "points" are merely a set of numbers \(\{p_1,
You can use a Markov transition matrix to model the transition of an entity between a set of discrete states. A transition matrix is also called a stochastic matrix. A previous article describes how to use transition matrices for stochastic modeling. You can estimate a Markov transition matrix by using
A genetic algorithm (GA) is a heuristic optimization technique. The method tries to mimic natural selection and evolution by starting with a population of random candidates. Candidates are evaluated for "fitness" by plugging them into the objective function. The characteristics of the better candidates are combined to create a new
This article uses an example to introduce to genetic algorithms (GAs) for optimization. It discusses two operators (mutation and crossover) that are important in implementing a genetic algorithm. It discusses choices that you must make when you implement these operations. Some programmers love using genetic algorithms. Genetic algorithms are heuristic
Sometimes we can learn as much from our mistakes as we do from our successes. Recently, I needed to solve an optimization problem for which the solution vector was a binary vector subject to a constraint. I was in a hurry. Without thinking much about what I was doing, I
Many optimization problems in statistics and machine learning involve continuous parameters. For example, maximum likelihood estimation involves optimizing a log-likelihood function over a continuous domain, possibly with constraints. Recently, however, I had to solve an optimization problem for which the solution vector was a 0/1 binary variable. To solve the
