On the occasion of Chris Gotwalt’s 25th anniversary at JMP, I want to make everyone aware of how important his work has been to us.
Chris has led our Statistical Development group for many years, and recently expanded it with two new development managers, Clay Barker and Laura Lancaster. Chris has also been at the forefront of JMP’s leadership in statistical software, implementing a huge number of important methods in JMP, as detailed below.
On May 16, 2001, Chris started at JMP as a graduate student with a statistical computing fellowship through the Department of Statistics at NC State University, where he completed his Ph.D. Under Dennis Boos, his education was very strong in computing, numerical methods, and mathematical statistics. Since his arrival at JMP, he has been at the center of much of what we have developed statistically.
Chris’s most recent project was the new Bayesian Optimization platform. Chris authored all the numerics, and Kasia Dobrzycka developed the UI. He had to solve many hard problems to make the Gaussian Process model more general, including:
- Handling categorical factors or responses.
- Batch augmentation, so that more than one run at a time can be materialized.
- Handling many factors, even more than 20.
- Handling multiple responses with competing goals with complicated sparsity
- Handling goals that matched the target rather than minimizing or maximizing.
- Handling randomization restrictions, including blocking and split-plotting.
- Handling cardinality constraints, using custom candidate sets.
The result is the Bayesian Optimization platform, a showcase feature of JMP Pro 19. Chris worked closely with Eastman Chemical and Procter & Gamble to help solve some of their thorniest optimization problems.
But one of the most valuable contributions Chris has made was assembling the talented team of statistical developers, testers, and documenters that are at the heart of our product.
Thank you, Chris, for helping make JMP a great product that our users treasure. Because of your leadership, JMP has become (and has remained) a leader in statistical computing.
-John Sall
A while ago, I compiled the following list of Chris’s accomplishments to nominate him for an award. It is a good representation of the impact he has had at JMP.
Mixed models
Chris at Discovery Summit 2018 in CarySAS has a long tradition of mixed models computational research, starting with Jim Goodnight (a co-inventor of Mivque in his dissertation), and continuing with Russ Wolfinger (author of SAS Proc Mixed, and pioneer author in generalized linear mixed models), Oliver Schabenberger (author of SAS Proc Glimmix), and Bradley Jones (developer for optimal design for mixed models). All four of these pioneers were honored as ASA Fellows, mostly for their work in computing for mixed models. Chris Gotwalt has extended that strong tradition in important ways.
When Brad developed software for optimal design of split-plot experiments, we realized that there were two big missing links to make it practical. First, we needed to make the right-sized tests for fixed effects. Earlier, in 1995, Kenward and Roger extended the work of Harville and Kackar to produce a right-sized denominator degrees of freedom for fixed-effects tests, but the calculation was complex. Chris’s ingenuity was much needed to make these calculations more tractable and efficient. The second problem was dealing with negative variance components. To get the right-sized tests, you also have to structure the problem to let the variance component used in the REML and K&R calculations stay negative. Letting them go negative sounds strange, but the components are really covariances in a compound symmetry model, and to make unbiased estimates, simulation studies have proven that keeping them negative is the right approach to get the tests sized right. With the DOEs coming out of optimal experimental design with small sample sizes, the probability of them going negative is increased. Chris reordered all the calculations with some innovative computational tricks for REML to support this without needing the n-by-n matrices that PROC MIXED needed to do the same trick. With these innovations, analyzing optimal split-plot experiments suddenly became very practical.
While researching mixed models and the properties of the Kenward-Roger adjustments for REML tests, Chris noticed some similarities in the calculations to those that Firth researched in bias reduction. This led to Chris proving that the REML method was equivalent to a Firth estimate, and thus endowed with all its properties. Although REML was long respected as producing the best mixed model estimates, it was derived as a practical method in order to reproduce method-of-moments calculations for balanced cases, rather than as a formal bias-reduction optimization method. Chris’s work legitimizes REML as a method of principle, as well as practice.
Later, Chris was challenged with fitting most of the repeated-measures covariance structures that PROC MIXED supported, but taking advantage of both sparsity and the latest numerical techniques. The result is an engine that produces estimates many times faster than the modern engines in SAS HPMixed. It enabled estimation of large variance components models in complex industrial production situations.
The mixed model algorithms Chris developed are at the foundation of multiple important platforms in JMP Pro; they are the basis of the spline models in the Functional Data Explorer, the core of the Generalized Linear Mixed Models platform, and the new Mixed Model Variable Selection platform. Laura Castro-Schilo and I identified a mathematical connection between SEM models and linear mixed models. The initial two releases of SEM were based on a transformation of the SEM model fitting problem into a special (but very complicated) case of a linear mixed model.
Chris with Florian Vogt at Discovery Summit Europe in 2023.Neural boosting
When we needed to produce better quality neural networks a few years ago, Chris noticed that the previous developers’ routines had spent too much time calculating derivatives and doing Newton-Raphson for large numbers of hidden layer nodes. Chris greatly sped up the calculations by using SR1. However, he also noticed that a boosting strategy allowed one to solve the problem in a stage-wise fashion, where a few hidden nodes were added at each stage, estimating only a few parameters at a time, with early stopping by cross-validation to produce one of the best neural nets. It was state-of-the-art until the more recent deep-learning convolution nets were developed.
Simulation sampling
Our group needed a way to calculate defect probabilities in the extreme tails of multivariate normals. We supported robust process engineering simulation models that optimized for low defect rates with respect to specification limits in multivariate simulations, and produced surrogate experiments to do the minimization. The key to making this work was to produce decent probabilities for points up to 12 standard deviations away. Chris used various theoretical results to develop a weighted sampler to calculate these probabilities, using a radial stratification method.
MSA profiling
In measurement systems analysis, Chris worked with Laura Lancaster and had several valuable breakthroughs. One was the development of a Bayesian approach to producing positive variance components for MSA. Another was the ability to hook a smart simulation engine to a profiler to get instant answers for shift detection in control charts, given the MSA calculations. Now there is an easy way to translate the MSA analysis to answer real questions about the ability to detect shifts in processes.
Chris chats at Discovery Summit 2016Text mining
The dimension reduction needed for latent semantic analysis in text mining requires a very fast sparse SVD. Chris developed that by using updated Lanczos methods, but then noticed that it would be possible to do a centered version of it to make it equivalent to principal components without sacrificing the speed of the sparse calculations. The new centered singular vectors should represent the text space better than the current state of the art. It also allowed us to use the sparse calculations in our principal components and association analysis platforms. Then Chris realized that the same sparsity patterns that he noticed when implementing latent class analysis (resolving multinomial mixture distributions) could be applied to become a fast clustering and topic-generation feature in text mining, a fast LCA alternative to latent Dirichlet allocation.
Functional Data Explorer
Chris led the development of the Functional Data Explorer. While taking on a minor role in assisting with its initial development, he worked directly with customers to design an easy-to-use tool that tremendously simplified the solution of complex product and process design problems across many industries.
Statistical software
The key to much of the success of JMP software has been a fast, accurate numerical computational foundation, and Chris designed and implemented most of it, as well as organizing better user interface development.
Leadership
As the director of Statistical Development for JMP, Chris has built and led a strong team of developers. JMP software has become important for engineers and scientists in industry, especially in the sectors of semiconductors, electronics, consumer products, chemicals, and pharmaceuticals. Chris has especially led in the areas of mixed models, reliability, and process quality. He has also become an effective communicator in the industry.
And more
Here are a few more innovations from Chris’s CV:
- Developed the sparse matrix library to speed linear model calculations.
- Developed SR1 and GMRES solver for penalized regression, with Clay Barker in GenReg.
- Developed Numerics for the Control Chart Power calculations.
- Extended the Portnoy-Sahai technique for estimating variance components from random effect models. These estimates are in the JMP Variability platform and give strictly positive estimates, which, although biased, have lower MSE than REML estimates.
- Developed a two-stage stratified sampling algorithm for model-based rare event simulation. The first stage uses equal sampling in the strata to determine the variance-minimizing sample sizes to use in the second stage. This is the core numerical algorithm for Profiler Simulator in JMP. (It also became important later for multivariate capability calculations.)
- Designed algorithms for the analysis of computer experiments, including minimum potential (of electrostatic particles) designs and D-optimal designs for Gaussian process models.
- Developed a combined quadrature and optimization algorithm for computing Bayesian D-optimal design of experiments for nonlinear and generalized linear models.
- Developed methods for computing the moment matrix that is exact for mixture problems and a simulation approach for more general linearly constrained problems. It has led to designs that give more accurate predictions on average and, thus, require fewer runs than earlier approaches.
- Invented a reparameterized approach to finding D-optimal and I-optimal designs that exposed the inherent sparsity of the problem. It led to update times that are O(1) for main effects models and O(p) for interaction models. Previous algorithms using low-rank updates alone were always O(p2). These algorithmic improvements greatly extend the size of the designs that are possible to compute.
- Generalized Huber regression to define a likelihood function of a multivariate distribution whose MLE estimates outlier-robust covariance matrices.
- Developed a comprehensive framework for fitting structural equation models (SEMs), which are the primary models used in psychology and behavioral sciences, that handles large datasets with grouping structure and arbitrary constraints. The framework exploits inherent sparsity and is faster than any other competing product we are aware of. This was probably the best-engineered project I ever worked on.
- Developed the JMP’s methods for the analysis of conjoint studies, which are used extensively in consumer research, and collaborated with Bradley Jones on the design computations for conjoint studies.
- Developed JMP’s algorithms for modern time series forecasting based on exponential smoothing models.
More recently
Another notable work from Chris was his implementation of REML mixed model estimation for wide problems, when a random effect is involved in a genomics model, but there are tens to hundreds of thousands of gene expressions as responses. Chris adapted REML algorithms for a small n but large p to make it practical.
