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Early classification of time series assigns each time series to one of a set of pre-defined classes using as few measurements as possible while preserving a high accuracy. This implies solving online the trade-off between the earliness and the prediction accuracy. This has been formalized in previous work where a cost-based framework taking into account both the cost of misclassification and the cost of delaying the decision has been proposed. The best resulting method, called Economy- $\gamma$ , is unfortunately so far limited to binary classification problems. This paper presents a set of six new methods that extend the Economy- $\gamma$ method in order to solve multiclass classification problems. Extensive experiments on 33 datasets allowed us to compare the performance of the six proposed approaches to the state-of-the-art one. The results show that: (i) all proposed methods perform significantly better than the state of the art one; (ii) the best way to extend Economy- $\gamma$ to multiclass problems is to use a confidence score, either the Gini index or the maximum probability.

The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies". In WSL use cases, a variety of situations exists where the collected "information" is imperfect. The paradigm of WSL attempts to list and cover these problems with associated solutions. In this paper, we review the research progress on WSL with the aim to make it as a brief introduction to this field. We present the three axis of WSL cube and an overview of most of all the elements of their facets. We propose three measurable quantities that acts as coordinates in the previously defined cube namely: Quality, Adaptability and Quantity of information. Thus we suggest that Biquality Learning framework can be defined as a plan of the WSL cube and propose to re-discover previously unrelated patches in WSL literature as a unified Biquality Learning literature.

The field of Weakly Supervised Learning (WSL) has recently seen a surge of popularity, with numerous papers addressing different types of "supervision deficiencies", namely: poor quality, non adaptability, and insufficient quantity of labels. Regarding quality, label noise can be of different types, including completely-at-random, at-random or even not-at-random. All these kinds of label noise are addressed separately in the literature, leading to highly specialized approaches. This paper proposes an original, encompassing, view of Weakly Supervised Learning, which results in the design of generic approaches capable of dealing with any kind of label noise. For this purpose, an alternative setting called "Biquality data" is used. It assumes that a small trusted dataset of correctly labeled examples is available, in addition to an untrusted dataset of noisy examples. In this paper, we propose a new reweigthing scheme capable of identifying noncorrupted examples in the untrusted dataset. This allows one to learn classifiers using both datasets. Extensive experiments that simulate several types of label noise and that vary the quality and quantity of untrusted examples, demonstrate that the proposed approach outperforms baselines and state-of-the-art approaches., 8 pages, 7 figures