A Generalized Jarque-Bera Test of Conditional Normality

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test

Unifying and Merging Well-trained Deep Neural Networks for Inference Stage

We propose a novel method to merge convolutional neural-nets for the inference stage. Given two well-trained networks that may have different architectures that handle different tasks, our method aligns the layers of the original networks and merges them into a unified model by sharing the representative codes of weights. The shared weights are further re-trained to fine-tune the performance of the merged model. The proposed method effectively produces a compact model that may run original tasks simultaneously on resource-limited devices. As it preserves the general architectures and leverages the co-used weights of well-trained networks, a substantial training overhead can be reduced to shorten the system development time. Experimental results demonstrate a satisfactory performance and validate the effectiveness of the method.Comment: To appear in the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence, 2018. (IJCAI-ECAI 2018

Probing triple-Higgs productions via 4b2γ4b2\gamma decay channel at a 100 TeV hadron collider

The quartic self-coupling of the Standard Model Higgs boson can only be measured by observing the triple-Higgs production process, but it is challenging for the Large Hadron Collider (LHC) Run 2 or International Linear Collider (ILC) at a few TeV because of its extremely small production rate. In this paper, we present a detailed Monte Carlo simulation study of the triple-Higgs production through gluon fusion at a 100 TeV hadron collider and explore the feasibility of observing this production mode. We focus on the decay channel $HHH\rightarrow b\bar{b}b\bar{b}\gamma\gamma$, investigating detector effects and optimizing the kinematic cuts to discriminate the signal from the backgrounds. Our study shows that, in order to observe the Standard Model triple-Higgs signal, the integrated luminosity of a 100 TeV hadron collider should be greater than $1.8\times 10^4$ ab$^{-1}$. We also explore the dependence of the cross section upon the trilinear ($\lambda_3$) and quartic ($\lambda_4$) self-couplings of the Higgs. We find that, through a search in the triple-Higgs production, the parameters $\lambda_3$ and $\lambda_4$ can be restricted to the ranges $[-1, 5]$ and $[-20, 30]$, respectively. We also examine how new physics can change the production rate of triple-Higgs events. For example, in the singlet extension of the Standard Model, we find that the triple-Higgs production rate can be increased by a factor of $\mathcal{O}(10)$.Comment: 33 pages, 11 figures, added references, corrected typos, improved text, affiliation is changed. This is the publication versio

Learning performance assessment approach using learning portfolio for e-learning systems

Learning performance assessment aims to evaluate what learners learnt during the learning process. In recent years, how to perform the learning performance assessment is a critical issue in the web-based learning field. The traditional summative evaluation can be applied to evaluate the learning performance both for the conventional classroom learning and web-based learning. However, it only considers final learning outcomes without considering the learning progress of learners. This paper proposes a learning performance assessment approach which combines four computational intelligence theories including grey relational analysis, K-means clustering method, fuzzy association rule mining and fuzzy inference to perform this task based on the learning portfolio of individual learner. Experimental results indicate that the evaluation result of proposed method is positive relevance with those of summative assessment. Namely, this method can help teachers to precisely perform the formative assessment for individual learner utilizing only the learning portfolio in web-based learning environment. 1