One of the drawbacks of frequent episode mining is that overwhelmingly many of the discovered patterns are redundant. Free-rider episode, as a typical example, consists of a real pattern doped with some additional noise events. Because of the possible high support of the inside noise events, such free-rider episodes may have abnormally high support that they cannot be filtered by frequency based framework. An effective technique for filtering free-rider episodes is using a partition model to divide an episode into two consecutive subepisodes and comparing the observed support of such episode with its expected support under the assumption that these two subepisodes occur independently. In this paper, we take more complex subepisodes into consideration and develop a novel partition model named EDP for free-rider episode filtering from a given set of episodes. It combines (1) a dual partition strategy which divides an episode to an underlying real pattern and potential noises; (2) a novel definition of the expected support of a free-rider episode based on the proposed partition strategy. We can deem the episode interesting if the observed support is substantially higher than the expected support estimated by our model. The experiments on synthetic and real-world datasets demonstrate EDP can effectively filter free-rider episodes compared with existing state-of-the-arts.
Our EDP model belongs to such category. That is to define the expected support for an episode and compare with its observed support for filtering or ranking tasks. Some existing efforts compare the observed support against the independence model @cite_6 @cite_13 @cite_12 . In such models, they use a null hypothesis that the data are generated by a stationary and independent stochastic process. Recent work estimated the expected support by considering different partitions of episodes. Tatti @cite_9 divided an episode into two consecutive subepisodes and downplayed the importance of such episode if its observed support could be explained by the two subepisodes. Such model failed to take non-prefix subepisodes into account when perform partitioning. Therefore it may be difficult to detect free-rider episodes when noise events are interweaved with a real pattern. Some idea for filtering sequential patterns can be adapted to episodes as well. For example, proposed SkOPUS @cite_18 in which re-ordering candidates were made from two subpattern partitions, and the expected support was defined based on the mean of support of all possible candidates in the original sequences. However, such work may distort the expected support as some re-orderings may be surprisingly rare in the original sequence.
@cite_18 @cite_9 @cite_6 @cite_13 @cite_12
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One of the biggest setbacks in traditional frequent pattern mining is that overwhelmingly many of the discovered patterns are redundant. A prototypical example of such redundancy is a freerider pattern where the pattern contains a true pattern and some additional noise events. A technique for filtering freerider patterns that has proved to be efficient in ranking itemsets is to use a partition model where a pattern is divided into two subpatterns and the observed support is compared to the expected support under the assumption that these two subpatterns occur independently. In this paper we develop a partition model for episodes, patterns discovered from sequential data. An episode is essentially a set of events, with possible restrictions on the order of events. Unlike with itemset mining, computing the expected support of an episode requires surprisingly sophisticated methods. In order to construct the model, we partition the episode into two subepisodes. We then model how likely the events in each subepisode occur close to each other. If this probability is high--which is often the case if the subepisode has a high support--then we can expect that when one event from a subepisode occurs, then the remaining events occur also close by. This approach increases the expected support of the episode, and if this increase explains the observed support, then we can deem the episode uninteresting. We demonstrate in our experiments that using the partition model can effectively and efficiently reduce the redundancy in episodes. We present a novel approach to proving the absence of timing channels. The idea is to partition the programâ s execution traces in such a way that each partition component is checked for timing attack resilience by a time complexity analysis and that per-component resilience implies the resilience of the whole program. We construct a partition by splitting the program traces at secret-independent branches. This ensures that any pair of traces with the same public input has a component containing both traces. Crucially, the per-component checks can be normal safety properties expressed in terms of a single execution. Our approach is thus in contrast to prior approaches, such as self-composition, that aim to reason about multiple (kâ � 2) executions at once. We formalize the above as an approach called quotient partitioning, generalized to any k-safety property, and prove it to be sound. A key feature of our approach is a demand-driven partitioning strategy that uses a regex-like notion called trails to identify sets of execution traces, particularly those influenced by tainted (or secret) data. We have applied our technique in a prototype implementation tool called Blazer, based on WALA, PPL, and the brics automaton library. We have proved timing-channel freedom of (or synthesized an attack specification for) 24 programs written in Java bytecode, including 6 classic examples from the literature and 6 examples extracted from the DARPA STAC challenge problems. Discovering the most interesting patterns is the key problem in the field of pattern mining. While ranking or selecting patterns is well-studied for itemsets it is surprisingly under-researched for other, more complex, pattern types. In this paper we propose a new quality measure for episodes. An episode is essentially a set of events with possible restrictions on the order of events. We say that an episode is significant if its occurrence is abnormally compact, that is, only few gap events occur between the actual episode events, when compared to the expected length according to the independence model. We can apply this measure as a post-pruning step by first discovering frequent episodes and then rank them according to this measure. In order to compute the score we will need to compute the mean and the variance according to the independence model. As a main technical contribution we introduce a technique that allows us to compute these values. Such a task is surprisingly complex and in order to solve it we develop intricate finite state machines that allow us to compute the needed statistics. We also show that asymptotically our score can be interpreted as a @math P value. In our experiments we demonstrate that despite its intricacy our ranking is fast: we can rank tens of thousands episodes in seconds. Our experiments with text data demonstrate that our measure ranks interpretable episodes high. Automatic sleep staging has been often treated as a simple classification problem that aims at determining the label of individual target polysomnography epochs one at a time. In this paper, we tackle the task as a sequence-to-sequence classification problem that receives a sequence of multiple epochs as input and classifies all of their labels at once. For this purpose, we propose a hierarchical recurrent neural network named SeqSleepNet (source code is available at http: github.com pquochuy SeqSleepNet ). At the epoch processing level, the network consists of a filterbank layer tailored to learn frequency-domain filters for preprocessing and an attention-based recurrent layer designed for short-term sequential modeling. At the sequence processing level, a recurrent layer placed on top of the learned epoch-wise features for long-term modeling of sequential epochs. The classification is then carried out on the output vectors at every time step of the top recurrent layer to produce the sequence of output labels. Despite being hierarchical, we present a strategy to train the network in an end-to-end fashion. We show that the proposed network outperforms the state-of-the-art approaches, achieving an overall accuracy, macro F1-score, and Cohen’s kappa of 87.1 , 83.3 , and 0.815 on a publicly available dataset with 200 subjects.