The present study introduces a method for improving the classification performance of imbalanced multiclass data streams from wireless body worn sensors. Data imbalance is an inherent problem in activity recognition caused by the irregular time distribution of activities, which are sequential and dependent on previous movements. We use conditional random fields (CRF), a graphical model for structured classification, to take advantage of dependencies between activities in a sequence. However, CRFs do not consider the negative effects of class imbalance during training. We propose a class-wise dynamically weighted CRF (dWCRF) where weights are automatically determined during training by maximizing the expected overall F-score. Our results based on three case studies from a healthcare application using a batteryless body worn sensor, demonstrate that our method, in general, improves overall and minority class F-score when compared to other CRF based classifiers and achieves similar or better overall and class-wise performance when compared to SVM based classifiers under conditions of limited training data. We also confirm the performance of our approach using an additional battery powered body worn sensor dataset, achieving similar results in cases of high class imbalance.
These previously mentioned methods @cite_25 @cite_30 @cite_24 require empirical calculation of parameters. This process can be cumbersome and computationally expensive. For example, in an extensive grid search for suitable weights, the number of validation operations is of the form @math , where @math is the cardinality of the parameters' value range and @math the number of parameters. In addition, objective function optimization based on classification error (1-accuracy) minimization is not suitable for imbalanced data. This is because the resulting measure, accuracy, is largely favoured by the dominant class and does not provide performance information regarding the predicted minority class @cite_14 .
@cite_30 @cite_14 @cite_25 @cite_24
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Virtually every commercial query optimizer chooses the best plan for a query using a cost model that relies heavily on accurate cardinality estimation. Cardinality estimation errors can occur due to the use of inaccurate statistics, invalid assumptions about attribute independence, parameter markers, and so on. Cardinality estimation errors may cause the optimizer to choose a sub-optimal plan. We present an approach to query processing that is extremely robust because it is able to detect and recover from cardinality estimation errors. We call this approach "progressive query optimization" (POP). POP validates cardinality estimates against actual values as measured during query execution. If there is significant disagreement between estimated and actual values, execution might be stopped and re-optimization might occur. Oscillation between optimization and execution steps can occur any number of times. A re-optimization step can exploit both the actual cardinality and partial results, computed during a previous execution step. Checkpoint operators (CHECK) validate the optimizer's cardinality estimates against actual cardinalities. Each CHECK has a condition that indicates the cardinality bounds within which a plan is valid. We compute this validity range through a novel sensitivity analysis of query plan operators. If the CHECK condition is violated, CHECK triggers re-optimization. POP has been prototyped in a leading commercial DBMS. An experimental evaluation of POP using TPC-H queries illustrates the robustness POP adds to query processing, while incurring only negligible overhead. A case-study applying POP to a real-world database and workload shows the potential of POP, accelerating complex OLAP queries by almost two orders of magnitude. In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10 –20 selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates. In this paper, we combine ideas from machine learning (ML) and operations research and management science (OR MS) in developing a framework, along with specific methods, for using data to prescribe decisions in OR MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications of OR MS, we consider data consisting, not only of observations of quantities with direct effect on costs revenues, such as demand or returns, but predominantly of observations of associated auxiliary quantities. The main problem of interest is a conditional stochastic optimization problem, given imperfect observations, where the joint probability distributions that specify the problem are unknown. We demonstrate that our proposed solution methods are generally applicable to a wide range of decision problems. We prove that they are computationally tractable and asymptotically optimal under mild conditions even when data is not independent and identically distributed (iid) and even for censored observations. As an analogue to the coefficient of determination @math , we develop a metric @math termed the coefficient of prescriptiveness to measure the prescriptive content of data and the efficacy of a policy from an operations perspective. To demonstrate the power of our approach in a real-world setting we study an inventory management problem faced by the distribution arm of an international media conglomerate, which ships an average of 1 billion units per year. We leverage both internal data and public online data harvested from IMDb, Rotten Tomatoes, and Google to prescribe operational decisions that outperform baseline measures. Specifically, the data we collect, leveraged by our methods, accounts for an 88 improvement as measured by our coefficient of prescriptiveness. Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on ℝN with smoothness of order s can in general be captured with accuracy at most O(n−s N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x)=g(a⋅x) when both a∈ℝN and g∈C[0,1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g∈Cs[0,1]. We also study the role of sparsity or compressibility of a in such query problems.