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This paper addresses a multi-label predictive fault classification problem for multidimensional time-series data. While fault (event) detection problems have been thoroughly studied in literature, most of the state-of-the-art techniques can't reliably predict faults (events) over a desired future horizon. In the most general setting of these types of problems, one or more samples of data across multiple time series can be assigned several concurrent fault labels from a finite, known set and the task is to predict the possibility of fault occurrence over a desired time horizon. This type of problem is usually accompanied by strong class imbalances where some classes are represented by only a few samples. Importantly, in many applications of the problem such as fault prediction and predictive maintenance, it is exactly these rare classes that are of most interest. To address the problem, this paper proposes a general approach that utilizes a multi-label recurrent neural network with a new cost function that accentuates learning in the imbalanced classes. The proposed algorithm is tested on two public benchmark datasets: an industrial plant dataset from the PHM Society Data Challenge, and a human activity recognition dataset. The results are compared with state-of-the-art techniques for time-series classification and evaluation is performed using the F1-score, precision and recall.