Multi-label classification allows a datapoint to be labelled with more than one class at the same time. Ensemble methods generally perform much better than single classifiers. Except bagging style ensembles like ECC, RAkEL, in multi-label classification, other ensemble methods have not been explored much. KFHE (Kalman Filter-based Heuristic Ensemble), is a recent ensemble method which uses the Kalman filter to combine several models. KFHE views the final ensemble to be learned as a state to be estimated which it estimates using multiple noisy "measurements". These "measurements" are essentially component classifiers trained under different settings. This work extends KFHE to multi-label domain by proposing KFHE-HOMER which enhances the performance of HOMER using the KFHE framework. KFHE-HOMER sequentially trains multiple HOMER classifiers using weighted training datapoints and random hyperparameters. These models are considered as measurements and their related error as the uncertainty of the measurements. Then the Kalman filter framework is used to combine these measurements to get a more accurate estimate. The method was tested on 10 multi-label datasets and compared with other multi-label classification algorithms. Results show that KFHE-HOMER performs consistently better than similar multi-label ensemble methods.
Here, @math indicates the class assignment of the prediction and @math indicates the class assigned to the datapoint @math . There are two variants discussed in @cite_6 where @math can be either the exponential function or the linear function in Eq. ). The use of exponential function is similar to AdaBoost, but the final combination in @math is done using the filter in the measurement update step using equation similar to Eq. )
@cite_6
2950541101 2154353836 1989016323 1522285917
A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of @math adaptively chosen functions on an unknown distribution given @math random samples. We show that, surprisingly, there is a way to estimate an exponential in @math number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question. An analytic solution to the multi-target Bayes recursion known as the @math -Generalized Labeled Multi-Bernoulli ( @math -GLMB) filter has been recently proposed by Vo and Vo in [“Labeled Random Finite Sets and Multi-Object Conjugate Priors,” IEEE Trans. Signal Process., vol. 61, no. 13, pp. 3460–3475, 2014]. As a sequel to that paper, the present paper details efficient implementations of the @math -GLMB multi-target tracking filter. Each iteration of this filter involves an update operation and a prediction operation, both of which result in weighted sums of multi-target exponentials with intractably large number of terms. To truncate these sums, the ranked assignment and K-th shortest path algorithms are used in the update and prediction, respectively, to determine the most significant terms without exhaustively computing all of the terms. In addition, using tools derived from the same framework, such as probability hypothesis density filtering, we present inexpensive (relative to the @math -GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the @math -error in the multi-target density arising from the truncation is presented. type="main" xml:id="rssb12047-abs-0001"> We introduce a new estimator, the simultaneous multiscale change point estimator SMUCE, for the change point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level α. The probability of overestimating the true number of change points K is controlled by the asymptotic null distribution of the multiscale test statistic. Further, we derive exponential bounds for the probability of underestimating K. By balancing these quantities, α will be chosen such that the probability of correctly estimating K is maximized. All results are even non-asymptotic for the normal case. On the basis of these bounds, we construct (asymptotically) honest confidence sets for the unknown step function and its change points. At the same time, we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate O ( n − 1 ) up to a log-term. Finally, the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n→∞, even for an unbounded number of change points. We illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions. The performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy. We present an algorithm for computing @math , the @math th moment of an @math -dimensional frequency vector of a data stream, for @math , to within @math factors, @math with high constant probability. Let @math be the number of stream records and @math be the largest magnitude of a stream update. The algorithm uses space in bits @math where, @math . Here @math is @math for @math and @math for @math . This improves upon the space required by current algorithms iw:stoc05,bgks:soda06,ako:arxiv10,bo:arxiv10 by a factor of at least @math . The update time is @math . We use a new technique for designing estimators for functions of the form @math , where, @math is a random variable and @math is a smooth function, based on a low-degree Taylor polynomial expansion of @math around an estimate of @math .