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Learning to predict ahead of time events in open time series is challenging. While Early Classification of Time Series (ECTS) tackles the problem of balancing online the accuracy of the prediction with the cost of delaying the decision when the individuals are time series of finite length with a unique label for the whole time series. Surprisingly, this trade-off has never been investigated for open time series with undetermined length and with different classes for each subsequence of the same time series. In this paper, we propose a principled method to adapt any technique for ECTS to the Early Classification in Open Time Series (ECOTS). We show how the classifiers must be constructed and what the decision triggering system becomes in this new scenario. We address the challenge of decision making in the predictive maintenance field. We illustrate our methodology by transforming two state-of-the-art ECTS algorithms for the ECOTS scenario and report numerical experiments on a real dataset for predictive maintenance that demonstrate the practicality of the novel approach.

More and more applications require early decisions, i.e. taken as soon as possible from partially observed data. However, the later a decision is made, the more its accuracy tends to improve, since the description of the problem to hand is enriched over time. Such a compromise between the earliness and the accuracy of decisions has been particularly studied in the field of Early Time Series Classification. This paper introduces a more general problem, called Machine Learning based Early Decision Making (ML-EDM), which consists in optimizing the decision times of models in a wide range of settings where data is collected over time. After defining the ML-EDM problem, ten challenges are identified and proposed to the scientific community to further research in this area. These challenges open important application perspectives, discussed in this paper.

An increasing number of applications require to recognize the class of an incoming time series as quickly as possible without unduly compromising the accuracy of the prediction. In this paper, we put forward a new optimization criterion which takes into account both the cost of misclassification and the cost of delaying the decision. Based on this optimization criterion, we derived a family of non-myopic algorithms which try to anticipate the expected future gain in information in balance with the cost of waiting. In one class of algorithms, unsupervised-based, the expectations use the clustering of time series, while in a second class, supervised-based, time series are grouped according to the confidence level of the classifier used to label them. Extensive experiments carried out on real data sets using a large range of delay cost functions show that the presented algorithms are able to satisfactorily solving the earliness vs. accuracy trade-off, with the supervised-based approaches faring better than the unsupervised-based ones. In addition, all these methods perform better in a wide variety of conditions than a state of the art method based on a myopic strategy which is recognized as very competitive.

Early classification of time series is becoming increasingly a valuable task for assisting in decision making
process in many application domains. In this setting, information can be gained by waiting for more evidences to arrive, thus helping to make better decisions that incur lower misclassification costs, but, meanwhile, the cost associated with delaying the decision generally increases, rendering the decision less attractive. Making early predictions provided that are accurate requires then to solve an optimization problem combining two
types of competing costs.
This thesis introduces a new general framework for time series early classification problem. Unlike classical approaches that implicitly assume that misclassification errors are cost equally and the cost of delaying the decision is constant over time, we cast the the problem as a cost-sensitive online decision making problem when delaying the decision is costly. We then propose a new formal criterion that expresses the trade-off between the gain of information that is expected to incur lower misclassification costs when delaying the decision against the cost of such a delay.
On top of this generic formulation, we propose two different approaches that estimate the optimal decision time for a new incoming yet incomplete time series. In particular, the first approach (i) captures the evolutions of typical complete time series in the training set thanks to a clustering technique that forms meaningful groups, and (ii) leverages these complete information to estimate the costs for all future time steps where data points still missing. This allows one to forecast what should be the optimal horizon for the classification
of the incoming time series. The second approach performs also steps (i) and (ii), but instead of using a clustering technique, it uses a more informed segmentation method that exploits the class labels of the complete time series thanks to the confidence levels computed by a probabilistic classifier.
These approaches are interesting in two ways. First, they estimate, online, the earliest time in the future where a minimization of the criterion can be expected. They thus go beyond the classical approaches that myopically decide at each time step whether to make a decision or to postpone the call one more time step. Second, they are adaptive, in that the properties of the incoming time series are taken into account to decide when is the optimal time to output a prediction.
We conduct extensive experimental studies and make systematic comparisons between both approaches on synthetic and real data sets. The obtained results show that both approaches meet the behaviors expected from early classification systems (i.e. the easier the classification task, the earlier the decision), with a significant superiority of the second approach when the classification of the incomplete time series is difficult.

Classification of time series as early as possible is a valuable goal. Indeed, in many application domains, the earliest the decision, the more rewarding it can be. Yet, often, gathering more information allows one to get a better decision. The optimization of this time vs. accuracy tradeoff must generally be solved online and is a complex problem.
This paper presents a formal criterion that expresses this trade-off in all generality together with a generic sequential meta algorithm to solve it. This meta algorithm is interesting in two ways. First, it pinpoints where choices can (have to) be made to obtain a computable algorithm. As a result a wealth of algorithmic solutions can be found. Second, it seeks online the earliest time in the future where a minimization of the criterion can be expected. It thus goes beyond the classical approaches that myopically decide at each time step whether to make a decision or to postpone the call one more time step.
After this general setting has been expounded, we study one simple declination of the meta-algorithm, and we show the results obtained on synthetic and real time series data sets chosen for their ability to test the robustness and properties of the technique. The general approach is vindicated by the experimental results, which allows us to point to promising perspectives.

Aiding to make decisions as early as possible by learning from past experiences is becoming increasingly important in many application domains. In these settings , information can be gained by waiting for more evidences to arrive, thus helping to make better decisions that incur lower misclassification costs, but, meanwhile, the cost associated with delaying the decision generally increases, rendering the decision less attractive. Learning requires then to solve an optimization problem combining two types of competing costs. In the growing literature on online decision making , very few works have explicitly incorporated the cost of delay in the decision procedure. One recent work [DBC15] has introduced a general formalization of this optimization problem. However, the algorithm presented there to solve it is based on a clustering step, with all the attendant necessary choices of parameters that can heavily impact the results. In this paper, we adopt the same conceptual framework but we present a more direct technique involving only one parameter and lower computational demands. Extensive experimental comparisons between the two methods on synthetic and real data sets show the superiority of our method when the classification of the incomplete time series is difficult, which corresponds to a large fraction of the applications.