Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series classification. The largest dataset in the UCR archive holds 10 thousand time series only; which may explain why the primary research focus has been in creating algorithms that have high accuracy on relatively small datasets. This paper introduces Proximity Forest, an algorithm that learns accurate models from datasets with millions of time series, and classifies a time series in milliseconds. The models are ensembles of highly randomized Proximity Trees. Whereas conventional decision trees branch on attribute values (and usually perform poorly on time series), Proximity Trees branch on the proximity of time series to one exemplar time series or another; allowing us to leverage the decades of work into developing relevant measures for time series. Proximity Forest gains both efficiency and accuracy by stochastic selection of both exemplars and similarity measures. Our work is motivated by recent time series applications that provide orders of magnitude more time series than the UCR benchmarks. Our experiments demonstrate that Proximity Forest is highly competitive on the UCR archive: it ranks among the most accurate classifiers while being significantly faster. We demonstrate on a 1M time series Earth observation dataset that Proximity Forest retains this accuracy on datasets that are many orders of magnitude greater than those in the UCR repository, while learning its models at least 100,000 times faster than current state of the art models Elastic Ensemble and COTE.
Existing fuzzy neural networks (FNNs) are mostly developed under a shallow network configuration having lower generalization power than those of deep structures. This paper proposes a novel self-organizing deep fuzzy neural network, namely deep evolving fuzzy neural networks (DEVFNN). Fuzzy rules can be automatically extracted from data streams or removed if they play little role during their lifespan. The structure of the network can be deepened on demand by stacking additional layers using a drift detection method which not only detects the covariate drift, variations of input space, but also accurately identifies the real drift, dynamic changes of both feature space and target space. DEVFNN is developed under the stacked generalization principle via the feature augmentation concept where a recently developed algorithm, namely Generic Classifier (gClass), drives the hidden layer. It is equipped by an automatic feature selection method which controls activation and deactivation of input attributes to induce varying subsets of input features. A deep network simplification procedure is put forward using the concept of hidden layer merging to prevent uncontrollable growth of input space dimension due to the nature of feature augmentation approach in building a deep network structure. DEVFNN works in the sample-wise fashion and is compatible for data stream applications. The efficacy of DEVFNN has been thoroughly evaluated using six datasets with non-stationary properties under the prequential test-then-train protocol. It has been compared with four state-of the art data stream methods and its shallow counterpart where DEVFNN demonstrates improvement of classification accuracy.
This paper introduces a novel parameter estimation method for the probability tables of Bayesian network classifiers (BNCs), using hierarchical Dirichlet processes (HDPs). The main result of this paper is to show that improved parameter estimation allows BNCs to outperform leading learning methods such as Random Forest for both 0-1 loss and RMSE, albeit just on categorical datasets. As data assets become larger, entering the hyped world of "big", efficient accurate classification requires three main elements: (1) classifiers with low-bias that can capture the fine-detail of large datasets (2) out-of-core learners that can learn from data without having to hold it all in main memory and (3) models that can classify new data very efficiently. The latest Bayesian network classifiers (BNCs) satisfy these requirements. Their bias can be controlled easily by increasing the number of parents of the nodes in the graph. Their structure can be learned out of core with a limited number of passes over the data. However, as the bias is made lower to accurately model classification tasks, so is the accuracy of their parameters' estimates, as each parameter is estimated from ever decreasing quantities of data. In this paper, we introduce the use of Hierarchical Dirichlet Processes for accurate BNC parameter estimation. We conduct an extensive set of experiments on 68 standard datasets and demonstrate that our resulting classifiers perform very competitively with Random Forest in terms of prediction, while keeping the out-of-core capability and superior classification time.
This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern - a concept on which most interestingness measures directly rely - with (2) SkOPUS: a new branch-and-bound algorithm for the exact discovery of top-k sequential patterns under a given measure of interest. Our interestingness measure employs the partition approach. A pattern is interesting to the extent that it is more frequent than can be explained by assuming independence between any of the pairs of patterns from which it can be composed. The larger the support compared to the expectation under independence, the more interesting is the pattern. We build on these two elements to exactly extract the k sequential patterns with highest leverage, consistent with our definition of expected support. We conduct experiments on both synthetic data with known patterns and real-world datasets; both experiments confirm the consistency and relevance of our approach with regard to the state of the art. This article was published in Data Mining and Knowledge Discovery and is accessible at http://dx.doi.org/10.1007/s10618-016-0467-9.
We propose two general and falsifiable hypotheses about expectations on generalization error when learning in the context of concept drift. One posits that as drift rate increases, the forgetting rate that minimizes generalization error will also increase and vice versa. The other posits that as a learner's forgetting rate increases, the bias/variance profile that minimizes generalization error will have lower variance and vice versa. These hypotheses lead to the concept of the sweet path, a path through the 3-d space of alternative drift rates, forgetting rates and bias/variance profiles on which generalization error will be minimized, such that slow drift is coupled with low forgetting and low bias, while rapid drift is coupled with fast forgetting and low variance. We present experiments that support the existence of such a sweet path. We also demonstrate that simple learners that select appropriate forgetting rates and bias/variance profiles are highly competitive with the state-of-the-art in incremental learners for concept drift on real-world drift problems.
We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call \emph{specious rules}. Specious dependencies, also known as \emph{spurious}, \emph{apparent}, or \emph{illusory associations}, refer to a well-known phenomenon where marginal dependencies are merely products of interactions with other variables and disappear when conditioned on those variables. The most extreme example is Yule-Simpson's paradox where two variables present positive dependence in the marginal contingency table but negative in all partial tables defined by different levels of a confounding factor. It is accepted wisdom that in data of any nontrivial dimensionality it is infeasible to control for all of the exponentially many possible confounds of this nature. In this paper, we consider the problem of specious dependencies in the context of statistical association rule mining. We define specious rules and show they offer a unifying framework which covers many types of previously proposed redundant or misleading association rules. After theoretical analysis, we introduce practical algorithms for detecting and pruning out specious association rules efficiently under many key goodness measures, including mutual information and exact hypergeometric probabilities. We demonstrate that the procedure greatly reduces the number of associations discovered, providing an elegant and effective solution to the problem of association mining discovering large numbers of misleading and redundant rules.
Concept drift is a major issue that greatly affects the accuracy and reliability of many real-world applications of machine learning. We argue that to tackle concept drift it is important to develop the capacity to describe and analyze it. We propose tools for this purpose, arguing for the importance of quantitative descriptions of drift in marginal distributions. We present quantitative drift analysis techniques along with methods for communicating their results. We demonstrate their effectiveness by application to three real-world learning tasks.
Learning algorithms that learn linear models often have high representation bias on real-world problems. In this paper, we show that this representation bias can be greatly reduced by discretization. Discretization is a common procedure in machine learning that is used to convert a quantitative attribute into a qualitative one. It is often motivated by the limitation of some learners to qualitative data. Discretization loses information, as fewer distinctions between instances are possible using discretized data relative to undiscretized data. In consequence, where discretization is not essential, it might appear desirable to avoid it. However, it has been shown that discretization often substantially reduces the error of the linear generative Bayesian classifier naive Bayes. This motivates a systematic study of the effectiveness of discretizing quantitative attributes for other linear classifiers. In this work, we study the effect of discretization on the performance of linear classifiers optimizing three distinct discriminative objective functions --- logistic regression (optimizing negative log-likelihood), support vector classifiers (optimizing hinge loss) and a zero-hidden layer artificial neural network (optimizing mean-square-error). We show that discretization can greatly increase the accuracy of these linear discriminative learners by reducing their representation bias, especially on big datasets. We substantiate our claims with an empirical study on $42$ benchmark datasets.
Most machine learning models are static, but the world is dynamic, and increasing online deployment of learned models gives increasing urgency to the development of efficient and effective mechanisms to address learning in the context of non-stationary distributions, or as it is commonly called concept drift. However, the key issue of characterizing the different types of drift that can occur has not previously been subjected to rigorous definition and analysis. In particular, while some qualitative drift categorizations have been proposed, few have been formally defined, and the quantitative descriptions required for precise and objective understanding of learner performance have not existed. We present the first comprehensive framework for quantitative analysis of drift. This supports the development of the first comprehensive set of formal definitions of types of concept drift. The formal definitions clarify ambiguities and identify gaps in previous definitions, giving rise to a new comprehensive taxonomy of concept drift types and a solid foundation for research into mechanisms to detect and address concept drift.
Deep learning has demonstrated the power of detailed modeling of complex high-order (multivariate) interactions in data. For some learning tasks there is power in learning models that are not only Deep but also Broad. By Broad, we mean models that incorporate evidence from large numbers of features. This is of especial value in applications where many different features and combinations of features all carry small amounts of information about the class. The most accurate models will integrate all that information. In this paper, we propose an algorithm for Deep Broad Learning called DBL. The proposed algorithm has a tunable parameter $n$, that specifies the depth of the model. It provides straightforward paths towards out-of-core learning for large data. We demonstrate that DBL learns models from large quantities of data with accuracy that is highly competitive with the state-of-the-art.