Profile of Kenneth L. Lange

Recent advances in computing have accelerated researchers’ ability to amass and analyze data. University of California, Los Angeles mathematical scientist Kenneth Lange uses his expertise in mathematics, computer programming, and biology to develop advanced methods of data analysis that have wide-ranging applications. Lange, the Rosenfeld Professor of Computational Genetics at UCLA, was elected to the National Academy of Sciences in 2021. During his academic career, Lange has mentored numerous doctoral students and postdoctoral associates and authored six advanced textbooks on applied mathematics and statistics. For his contributions, Lange won the 1993 Snedecor Award from the Joint Statistical Societies and the 2020 Arno Motulsky-Barton Childs Award from the American Society of Human Genetics.

Image credit: University of California, Los Angeles.

Midwestern Background

Lange was born in Angola, Indiana, the third of five sons, and raised in the neighboring town of Auburn, Indiana. When he was growing up in the 1960s, the United States was playing catch up with the Soviet Union after the launch of the first artificial satellite, Sputnik 1. Lange benefited from the increase in national funding for science education at the time. His advanced high school courses in biology and chemistry inspired his later interests in biological modeling. Lange also took to mathematics at a young age, an affinity partially shared with his father, a civil engineer, and more strongly shared with his now-deceased oldest brother, Charles Lange, who served as a professor of applied mathematics at UCLA for 25 years.

Lange remained in the Midwest for college, first attending Case Institute of Technology and then graduating from Michigan State University. He pursued a PhD in mathematics at the Massachusetts Institute of Technology (MIT), writing his thesis with the Italian-American mathematician Gian-Carlo Rota. Lange’s dissertation on ergodic theory (1) proved valuable later as the Markov chain Monte Carlo (MCMC) revolution swept through statistics; MCMC enables high-dimensional numerical integration.

Transition to Medicine

After completing his PhD in 1971, Lange joined the University of New Hampshire as an assistant professor of mathematics. He left that tenure-track position after a year to pursue a postdoctoral fellowship in the biomathematics department (now computational medicine) at UCLA’s School of Medicine. The transition allowed him to reignite his latent interest in biology and rejoin his brother, who had arrived at UCLA a few years earlier.

“After high school, I hadn’t really engaged with biology until I got to UCLA,” Lange says. “The first thing I did was to audit courses mandated for freshman medical students. These gave me the vocabulary, biological basics, and perspective to identify and pose mathematical problems relevant to human biology.” Except for a stint at the University of Michigan from 1994 to 1998, Lange has been affiliated with UCLA since his arrival in 1972. At that time, his postdoctoral advisor, Carol Newton, was launching the department’s doctoral program in biological modeling. When he was offered the opportunity to stay on as a faculty member and doctoral mentor, Lange accepted.

Gene Mapping

One of the areas where Lange capitalized on his mathematical aptitude was the then-nascent field of gene mapping. He teamed up with geneticists Anne Spence at UCLA and Robert Elston at the University of North Carolina, Chapel Hill, to analyze large human pedigrees (2). In the mid-1970s when Lange, Elston, and Spence performed their linkage studies, only a few dozen genetic markers, primarily for protein antigens, existed. Computational power was also limited.

“It was a handful of markers back then,” Lange says, “but gradually more came along until the field exploded with [single-nucleotide polymorphisms] and genome sequencing.”

With UCLA pathologist Richard Gatti, Lange mapped the gene for the disease ataxia-telangiectasia (AT), which affects patients’ balance, movement, and DNA repair mechanisms (3). Lange says, “We hit two roadblocks. Some of the large pedigrees encountered overwhelmed existing computers, and the region harboring the AT gene was unmapped.”

UCLA graduate student Eric Sobel and Lange were able to harness MCMC methods to meet the challenges (4). Although their MCMC method was approximate, it helped build the necessary gene map and visualize extended haplotypes bearing the AT gene as they descended through affected individuals in the various pedigrees.

Software Synergy

Lange’s facility for translating complex biomathematical problems into computer code remains one of his lasting scientific contributions. Indeed, his interest in computers was one of the factors that attracted him to UCLA. The medical school housed an NIH-supported health sciences computing facility, complete with an IBM mainframe computer, which, although state-of-the-art at the time, required punch cards.

“The summer after I got my PhD, I remedied my computing ignorance by taking a PL/I [Programming Language/I] computer language course,” he says. “By the time I arrived at UCLA, I was definitely hooked. The health sciences computing facility created the first software package for statistical analysis. That emphasis spurred a lot of my subsequent interest in algorithms.”

The fields of genetics and statistics, Lange points out, have a long history of synergy. As a mathematical geneticist, he has witnessed how the fields have coevolved, with genetics benefiting from advances in computational statistics and in turn stimulating the development of new statistical methods.

Lange’s achievements in statistical genetics include the development of one of the earliest algorithms for calculating Mendelian likelihoods over inbred pedigrees; the early application of linear mixed models to human pedigree data; the early application of MCMC sampling in human genetics; the construction of accurate statistical models for gene mapping by radiation hybrids; and the introduction of lasso penalized statistical regression methods to genome-wide association studies (GWAS). Lange and his UCLA colleagues wrote the software programs SimWalk, Mendel, and Admixture, widely used and freely distributed to the scientific community. In 2019, they launched the OpenMendel project for cooperative software development in genomics. The Admixture program has helped companies such as 23andme and Ancestry deliver ethnic admixture coefficients (5).

Imaging Algorithms

Lange’s encounter with Harvard University statistician Nan Laird also influenced Lange’s quest to solve compelling biomedical problems. In the 1970s, Laird gave a lecture at UCLA on the expectation-maximization (EM) principle that she and colleagues developed. This iterative technique promotes the estimation of latent parameters in models with thousands to millions of parameters. The EM principle replaces the original objective function by a surrogate function that is easier to optimize while driving the objective function in the right direction.

Lange found an immediate use for EM algorithms in medical imaging, another major theme of his career (6). In PET and CT scans, for example, each pixel of an image has an attached parameter. “Newton’s method and Fisher scoring, the two mainstays of numerical optimization, become impractical in this context,” Lange says. Before the advent of EM reconstruction algorithms, most of the noise in imaging data was simply ignored, reducing image quality and resolution. “Explicit noise models and good algorithms produce quicker scans with less patient exposure to harmful radiation,” he explains.

MM Algorithms

In the 1990s, the MM principle, an optimization approach that is a generalization of the EM principle, gradually emerged from its obscure origin in Dutch statistician Jan de Leeuw’s research on multidimensional scaling. The MM principle dispenses with the notion of missing data. In 1987, de Leeuw left Holland and moved to UCLA. Once Lange and de Leeuw connected, Lange realized that his previous image reconstruction algorithms were actually MM algorithms.

de Leeuw and Lange have tirelessly promoted the MM principle and its potential in high-dimensional optimization (7); one of Lange’s books is devoted to the subject (8). Lange’s inaugural article further generalizes the MM principle and draws connections to other algorithm classes in numerical optimization. The MM is now a critical tool in fields as varied as imaging, DNA sequence analysis, microeconomics, speech synthesis, and mass spectrometry—to name a few.

The modeling philosophy of modern mathematical scientists has been largely shaped by advances in computing. The dominant scientific instrument in labs worldwide is the computer. However, advances in data acquisition can overwhelm statistical analysis. Lange’s career has been built around matching analysis algorithms to models. In honor of Lange’s contributions, UCLA recently launched a symposium on genomics and computational statistics.

“I’ve been fascinated by large-scale optimization problems and their application areas throughout the biological sciences,” he says. “I’ll probably keep that balance throughout the rest of my career.”