Study of Learning Entropy for Novelty Detection in lung tumor motion prediction for target tracking radiation therapy

Learning Entropy as a Learning-Based Information Concept

“…denotes a function that quantifies the unusuality of the learning effort via learning increments (assuming the learning system has been pretrained on the training data). So far in our research of LE [34,36,38,[41][42][43], a summation has been applied as the aggregation function A(.) as follows:…”

“…The concept of learning entropy is based on the evaluation of unusual weight updates as the unusual learning pattern can indicate novelty in training data; i.e., the new information that new samples of data carry in respect to what the NN contemporary has learned already [34]. This methodology to evaluate the learning entropy through the unusually large weight updates was recently introduced [34] and then reviewed with some simplifications recently in [35,36,38]. The first important parameters here are as follows:…”

“…It is not necessary to find the exact value of α max (see (16) and (17)), because α can in principle contain even larger values of α when calculated by (19). Thus, E A in (19) was introduced as approximate individual sample learning entropy (AISLE) when the sample-by-sample adaptation learning rule is used; e.g., the gradient descent learning in [34] and it was used also in works [35,36,38]. An example of AISLE of various orders is shown in Figure 1.…”

“…Novelty detection via LE is based on real-time learning of systems after they had been pretrained on an initial pretraining data set. Aside from the founding work [34], other examples of works that indicate the usefulness of LE in biomedical or technical data and for novelty detection in data with concept drift can be found in [36][37][38][39].…”

“…In fact, the learning entropy E in (18) is considered to be the first-order learning entropy because the detection function (13) is calculated with the first difference (≈ first-order derivative) of weights (as it results from (11)). It appeared useful to practically enhance LE computation with higher-order differences of weight updates that contribute to more reliable novelty detection as the higher order weight difference terms indicates useful noise filtering [34][35][36]38]. To compute the LE of various orders, the corresponding weight differences can be used in formulas (12)- (14) as in Table 1.…”