We can compare high-dimensional statistics to multivariate statistics. In multivariate statistics, we monitor and analyze possible outcomes of multiple variables. As dimensions get higher, multivariate statistics tend to break down and become less useful. Hence, high-dimensional statistics, statistics that depend on the theory of random vectors and use algorithms built to deal with hundreds or even thousands of dimensions of data, are used. Usually, high-dimensional statistics are especially useful when dealing with data sets that have more dimensions than the sample size.
For more information on high-dimensional statistics, the Simons Institute recorded several lectures on the topic, starting with this one.
Applications in Artificial Intelligence
Having a need to work with high-dimensional data is very common, and sometimes well-known statistical algorithms just don’t cut it. More complicated and robust algorithms are needed as computational complexity increases.