JMPer familiar with JMP knows that JMP has been committed to the development and application of experimental design. Looking back on the history of experimental design, from the 1920s (1920), Fisher first proposed the statistical concept of experimental design, and today, experimental design has developed a number of statistical methods, such as response surface, Taguchi design, mixture design, most Optimal design, uniform design, supersaturated experimental design, etc. Bradley Jones, chief R&D specialist at JMP, has also won the Brembo Award for individuals from the American Society for Quality twice for his innovative deterministic screening design.
After more than 30 years of development, the JMP experimental design platform has included all the experimental design methods mentioned above. At the same time, it also provides experimental design auxiliary functions such as experimental design evaluation, design scheme comparison, and sample efficacy evaluation to help more use of experiments. Design researchers choose the most appropriate and effective scheme among a variety of experimental design methodologies.
Overview of JMP Experiment Design Platform
Compared with the big data that is in full swing today, the experimental design is suitable for small sample data. In the case of small samples, how to better select the optimal model, which is not just fitting, but can effectively predict?
In recent years, many methods have also been applied, such as the common AICc (Akaike Information Content Criterion), Bayesian Inference and so on. This time we want to introduce another brand new method, namely: the automatic verification Fractionally Weighted Bootstrap (FWB) technology introduced by JMP Pro 16.
JMP Pro introduces automatic validation and model building with small sample data as two new practical techniques, No need for new experiments DOE data for predictive modeling . This technique forms a validation set based on the original training data and the concept of random sampling from Bootstrapping.
Before introducing JMP's new technology of automatic verification FWB, let's briefly review the application of cross-validation in big data machine learning.
First divide the data into training set, validation set, and even test set. In the model complexity determination process, the model with the smallest SSE (i.e., the sum of squared differences between groups) in the validation set is selected as the best model, as shown in the figure.
Model Cross Validation
For experimental design data or small sample data, is it possible to construct two uncorrelated SSEs based on a limited sample size, and use one of them as a validation set? Under this assumption, the automatic verification FWB technology introduced by JMP Pro 16 is aimed at small sample data.
Use Bootstrap's technology to construct multiple (customizable) pairs of samples for each experimental design, with random coefficients with the same distribution and negative correlation:
Apply the generated sets of random coefficients to the following calculation formula:
After deduction calculation, we get:
The two tend to be irrelevant, that is, they can achieve a similar effect of cross-validation. Using such techniques, JMP can build sets of models of varying complexity based on sets of pairs of random coefficients, while recording the non-zero proportion of parameter estimates for the model variables.
However, new problems arose.
If multiple pairs of random coefficients are generated, for example, if 2500 pairs of random coefficients are generated, 2500 models will be established. How do you ultimately identify which model variables are significant? How to define non-zero scale limits to help determine the final model?
Here, JMP introduces a randomly distributed null variable that is independent and uncorrelated with the prediction object. When building the model, this null variable is introduced into the modeling at the same time. In the final multi-group model, if the estimated value of the independent variable parameter is higher than that of the null variable, it is considered that the independent variable needs to be included in the model. The above text description may not be fully expressed, we use a real case to briefly illustrate.
Case Studies
The goal of this case is Reduce aggregation problems during protein purification , Adjustable experimental and process parameters, including protein content, formaldehyde, etc. 6 main factor . In this practical case, a deterministic screening design under the JMP "Experimental Design" platform was applied, with 6 main factors, as well as interaction factors and higher-order terms, a total of 27 factors.
After collecting the experimental results, first use the automatic verification function to randomly generate the first set of paired coefficients and null variables for each sample. Then use JMP's "fit model" function to introduce null variables and model at the same time. On this basis, 250 pairs of random coefficients are generated again to build a model.
Finally, according to the generated non-zero proportions, only variables with non-zero proportions higher than the null variable (protein concentration, temperature, formaldehyde concentration, interaction term of formaldehyde concentration and protein concentration, p<0.05, as shown below) are regarded as significant models items, included in the final model range.
Next, let's take a detailed look at how model building is implemented in JMP, while using FWB to automatically verify the calculation to find significant model factors.
In this real case, we found that only 3 main factors affect and positively affect the final protein aggregation degree through the model results. Among the many interaction factors and higher-order terms, only one, that is, the interaction term between formaldehyde and protein concentration, has a significant impact on the final degree of protein aggregation. This result greatly reduces the range of parameters that need to be optimized in the process, and clarifies the important parameters in the process of process adjustment. After optimizing all parameters, the protein polymerization degree was optimized from an initial average of 14.8% to an optimum of 2.5%, which greatly improved the safety and reliability of the protein product.
In this case, we also found that although there were as many as 27 factors considered at the beginning of the experimental design, only 4 factors were finally screened by FWB technology that significantly affected the process product. This also verifies the effect sparsity principle that we often say in experimental design.
original: https://mp.weixin.qq.com/s/BqiTKQcb9wJmFJweUqRrOA
