Significant Pattern Mining for Time Series

To determine whether a subsequence is present in a time series, we can now set a distance threshold $\Theta$ and say

Now that we have a notion of subsequence distance and occurrence, we can set up a contingency table, and perform hypothesis tests such as $\chi^2$ or Fisher’s exact test. Going back to the scenario with TS of length 100, subsequence length $w=10$, and assuming a data set with 300 patients, we extract $300 \times 91=27{,}300$ subsequences. This approach is based on the concept of the “minimal attainable $p$-value” $p_{min}$:

“If we know $r_S$ (e.g. how often $S$ occurs in the data set), $n_1$, and $n$, we can construct the contingency table that will lead to the smallest $p$-value this subsequence can ever reach $\rightarrow p_{min}$.”

Source: christian.bock.ml