Typical machine learning regression applications aim to report the mean or the median of the predictive probability distribution, via training with a squared or an absolute error scoring function. The importance of issuing predictions of more functionals of the predictive probability distribution (quantiles and expectiles) has been recognized as a means to quantify the uncertainty of the prediction. In deep learning (DL) applications, that is possible through quantile and expectile regression neural networks (QRNN and ERNN respectively). Here we introduce deep Huber quantile regression networks (DHQRN) that nest QRNN and ERNN as edge cases. DHQRN can predict Huber quantiles, which are more general functionals in the sense that they nest quantiles and expectiles as limiting cases. The main idea is to train a DL algorithm with the Huber quantile scoring function, which is consistent for the Huber quantile functional. As a proof of concept, DHQRN are applied to predict house prices in Melbourne, Australia and Boston, United States (US). In this context, predictive performances of three DL architectures are discussed along with evidential interpretation of results from two economic case studies. Additional simulation experiments and applications to real-world case studies using open datasets demonstrate a satisfactory absolute performance of DHQRN.

Time-series shapelets are discriminative subsequences, recently found effective for time series classification (tsc). It is evident that the quality of shapelets is crucial to the accuracy oftsc. However, major research has focused on building accurate models from some shapelet candidates. To determine such candidates, existing studies are surprisingly simple, e.g., enumerating subsequences of some fixed lengths, or randomly selecting some subsequences as shapelet candidates. The major bulk of computation is then on building the model from the candidates. In this paper, we propose a novelefficient shapelet discoverymethod, calledbspcover, to discover a set of high-quality shapelet candidates for model building. Specifically,bspcovergenerates abundant candidates via Symbolic Aggregate approXimation with sliding window, then prunes identical and highly similar candidates viaBloom filters, andsimilarity matching, respectively. We next propose a$p$p-Cover algorithmto efficiently determine discriminative shapelet candidates that maximally represent each time-series class. Finally, any existing shapelet learning method can be adopted to build a classification model. We have conducted extensive experiments with well-known time-series datasets and representative state-of-the-art methods. Results show thatbspcoverspeeds up the state-of-the-art methods by more than 70 times, and the accuracy is often comparable to or higher than existing works.

Time series shapelets are short discriminative subsequences that recently have been found not only to be accurate but also interpretable for the classification problem of univariate time series (UTS). However, existing work on shapelets selection cannot be applied to multivariate time series classification (MTSC) since the candidate shapelets of MTSC may come from different variables of different lengths and thus cannot be directly compared. To address this challenge, in this paper, we propose a novel model called ShapeNet, which embeds shapelet candidates of different lengths into a unified space for shapelet selection. The network is trained using cluster-wise triplet loss, which considers the distance between anchor and multiple positive (negative) samples and the distance between positive (negative) samples, which are important for convergence. We compute representative and diversified final shapelets rather than directly using all the embeddings for model building to avoid a large fraction of non-discriminative shapelet candidates. We have conducted experiments on ShapeNet with competitive state-of-the-art and benchmark methods using UEA MTS datasets. The results show that the accuracy of ShapeNet is the best of all the methods compared. Furthermore, we illustrate the shapelets’ interpretability with two case studies.

Time-series shapelets are discriminative subsequences, recently found effective for time series classification (TSC). It is evident that the quality of shapelets is crucial to the accuracy of TSC. However, major research has focused on building accurate models from some shapelet candidates. To determine such candidates, existing studies are surprisingly simple, e.g., enumerating subsequences of some fixed lengths, or randomly selecting some subsequences as shapelet candidates. The major bulk of computation is then on building the model from the candidates. In this paper, we propose a novel efficient shapelet discovery method, called BSPCOVER, to discover a set of high-quality shapelet candidates for model building. We have conducted extensive experiments with well-known UCR time-series datasets and representative state-of-the-art methods. Results show that BSPCOVER speeds up the state-of-the-art methods by more than 70 times, and the accuracy is often comparable to or higher than existing works.

Time series classification (TSC) has attracted considerable attention from both academia and industry. TSC methods that are based on shapelets (intuitively, small highly-discriminative subsequences have been found effective and are particularly known for their interpretability, as shapelets themselves are subsequences. A recent work has significantly improved the efficiency of shapelet discovery. For instance, the shapelets of more than 65% of the datasets in the UCR Archive (containing data from different application domains) can be computed within an hour, whereas those of 12 datasets can be computed within a minute. Such efficiency has made it possible for demo attendees to interact with shapelet discovery and explore high-quality shapelets. In this demo, we present Visualet -- a tool for visualizing shapelets, and exploring effective and interpretable ones.