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The bi-directional long short-term memory neural network model is widely used in natural language processing, but hyperparameter tuning of the model is difficult in practice. In this paper, we take the semantic role recognition task as an example, consider four candidate features (word, part of speech, target word and position) and two hyperparameters (the number of layers of the network and whether CRF classifier is used) as factors in robust design, and select the optimal combination of features and hyperparameters by setting levels of each factor and performing experiments. In particular, we perform 32 cross validation on a small datasets to select the optimal configuration combination of the model based on the SNR of robust design. Then, we analyze the influence of each factor on the performance of the model by quantitatively analyze so that the model has a certain degree of interpretability. Moreover, in order to verify the superiority of our tuning method, we use the standard segmentation of natural language processing on a big dataset, adopt the traditional greedy strategy to select the optimal configuration combination, and compare with our method on the test set. The results show that our method is better than the traditional tuning method.
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This paper investigates a bidimensional risk model with interference, in which the vectors of claim process and premium process are both compound Poisson-Geometric processes. Through martingale method and stopping time technique, we get the upper bound of the ruin probability. When the marginal of claim vector and premium vector follow bivariate FGM (Farlic-Gumbel-Morgenstern) class, we have discussed some properties of the upper bound.
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Journal impact factor is an important criterion for judging the quality of journals. In this paper, a Bayesian model is established for journal quality parameters, combined with existing journal impact factor calculation formulas, by using the theory of the credibility theory, a correction method for journal impact factors is given. We also obtained the estimation of structure parameters. The statistical properties of the estimation are discussed. Through simulations, the consistency and convergence speed of the estimators are tested. Finally, the empirical analysis of the correction formulas of the impact factors of more than twenty mathematics journals in China.
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For the comprehensive ranking of urban economic level and environmental level in China, there have been some index system ranking methods, but most of them involve multivariate data. With the rapid change of data acquisition technology, data become more and more complex. The observational data produced in some fields is no longer a single type of data, but a combination of various types of data. This paper studies how to rank them when the index system involves functional data. In this paper, four ranking methods are proposed and compared. The results are as follows: when the functional data is contaminated, the
entropy weight method results are relatively stable; when the scalar data is contaminated, the multivariate modified banding depth is more stable. The research shows that the selection of ranking methods for multi-type data depends on the characteristics of the data. This research enriches the comprehensive ranking of multi-type data and has good practical significance.
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When the response variables are missing randomly, in the process of statistical inference of the parameters of interest, two common working models are the regression function model and the selection probability model. In order to avoid the inference bias caused by the model setting error, the regression function model and selection probability models are necessary and meaningful for model testing. For this reason, for the first time in this paper, the feature functions are applied to the model testing problem of random missing response variables and discrete variable response variables, and a Euclidean distance between sample points is constructed based on test statistic. The proposed test avoids the selection of smoothing parameters such as bandwidth, and at the same time can detect the local alternative hypothesis at the fastest parameter speed. Further, this paper aims at the composite null hypothesis: at least one of the two working models is designed. It is correct, and a test method of the merged model is proposed. An important application scenario of this test is to determine whether the bistable estimation of the parameter is a coincident estimate. This article deeply studies the test of the merged model in the original hypothesis, the global alternative hypothesis, and the local alternative hypothesis. The asymptotic property of the following, and using the boostrap method to determine the rejection domain of the test, study the performance of the merge model test under a limited sample. Finally, this article applies the proposed merge model test method to
analyze the clinical research of AIDS research Test Data. It is worth mentioning that the combined model test mentioned in this article not only has good performance, but also the method is simple and easy to implement, and the corresponding p-value is easy to calculate.
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The paper investigates the optimal consumption and portfolio with consistence performance under Knightian uncertainty. The agent has Knightian uncertainty for the expected return of risky asset, which is characterized by \kappa-ignorance model. Consistent performance model asks for a dynamic wealth constraint, which requires the wealth always stays at or above the weighted average of the entire historical wealth levels. In the infinite time horizon, we obtain the
optimal consumption and portfolio explicit solution for the model by the HJB equation and verification theorem.
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In this summary report, we introduce some basic theory of single birth processes as the supplement of \ncite{1}, including the probabilistic meaning of some numerical characteristics, the distributions and moments of the integral-type functional of single birth processes, as well as the distributions of the staying
times, the first hitting time and the last exit times etc.
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This paper studies the statistical inference and algorithm design problems in the mixture model with change point. For multi-classified mixture data with change point, this paper designs an improved EM algorithm based on the maximum likelihood estimation of parameters, and proves the large sample nature of the change point estimator and the mixture parameter estimator. In order to verify the effectiveness of the method, we conducted some simulation experiments.
The results show that the EM algorithm that does not consider the change point has a poor estimate on the classification result, and even loses some categories; Our improved EM algorithm can accurately locate the location of the change point, and at the same time obtain accurate estimates for the corresponding parameters of each category.
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We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive L\'{e}vy process. As applications of this result, we obtain some asymptotic estimates for the conditional least squares estimators of
the means of the offspring and immigration distributions.
