Which term best describes a statistical learning method that varies results significantly with different training datasets?

The term that most accurately describes a statistical learning method that varies results significantly with different training datasets is one that indicates high flexibility. A highly flexible method can fit a wide range of functions and is capable of capturing complex patterns in the data. However, this flexibility also means that the method can be sensitive to the specific samples in the training dataset.

When a model has high flexibility, it can overfit the training data, meaning it captures not just the underlying pattern but also the noise present in that data. Consequently, when a different training dataset is used, the model's performance can fluctuate markedly, leading to significant variation in results. This characteristic is particularly relevant in scenarios where the underlying data distribution may vary or when the training sample is small or unrepresentative.

On the other hand, methods characterized by low flexibility tend to generalize better across different datasets, as they do not adapt too closely to the nuances of any single training set. Bias in a method indicates a systematic error or deviation from the true values, and robustness usually refers to a method's resilience to variations in data or model assumptions. Thus, high flexibility is indeed the best fit for describing a method that produces significantly different results with varying training datasets.