Gibbs Measures with Multilinear Forms

In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized $\mathrm{U}$-statistic and with a general base measure. Expressing the asymptotic free energy as an optimization problem over a space of functions, we obtain necessary and sufficient conditions for replica-symmetry. Utilizing this, we obtain weak limits for a large class of statistics of interest, which includes the ''local fields/magnetization'', the Hamiltonian, the global magnetization, etc. An interesting consequence is a universal weak law for contrasts under replica symmetry, namely, $n^{-1}\sum_{i=1}^n c_i X_i\to 0$ weakly, if $\sum_{i=1}^n c_i=o(n)$. Our results yield a probabilistic interpretation for the optimizers arising out of the limiting free energy. We also prove the existence of a sharp phase transition point in terms of the temperature parameter, thereby generalizing existing results that were only known for quadratic Hamiltonians. As a by-product of our proof technique, we obtain exponential concentration bounds on local and global magnetizations, which are of independent interest.Comment: 44 page

PC Adjusted Testing for Low Dimensional Parameters

In this paper we consider the effect of high dimensional Principal Component (PC) adjustments while inferring the effects of variables on outcomes. This problem is particularly motivated by applications in genetic association studies where one performs PC adjustment to account for population stratification. We consider simple statistical models to obtain asymptotically precise understanding of when such PC adjustments are supposed to work in terms of providing valid tests with controlled Type I errors. We also verify these results through a class of numerical experiments

Inferences on Mixing Probabilities and Ranking in Mixed-Membership Models

Network data is prevalent in numerous big data applications including economics and health networks where it is of prime importance to understand the latent structure of network. In this paper, we model the network using the Degree-Corrected Mixed Membership (DCMM) model. In DCMM model, for each node $i$, there exists a membership vector $\boldsymbol{\pi}_ i = (\boldsymbol{\pi}_i(1), \boldsymbol{\pi}_i(2),\ldots, \boldsymbol{\pi}_i(K))$, where $\boldsymbol{\pi}_i(k)$ denotes the weight that node $i$ puts in community $k$. We derive novel finite-sample expansion for the $\boldsymbol{\pi}_i(k)$s which allows us to obtain asymptotic distributions and confidence interval of the membership mixing probabilities and other related population quantities. This fills an important gap on uncertainty quantification on the membership profile. We further develop a ranking scheme of the vertices based on the membership mixing probabilities on certain communities and perform relevant statistical inferences. A multiplier bootstrap method is proposed for ranking inference of individual member's profile with respect to a given community. The validity of our theoretical results is further demonstrated by via numerical experiments in both real and synthetic data examples

Machine learning-based Naive Bayes approach for divulgence of Spam Comment in Youtube station

In the 21st Century, web-based media assumes an indispensable part in the interaction and communication of civilization. As an illustration of web-based media viz. YouTube, Facebook, Twitter, etc., can increase the social regard of a person just as a gathering. Yet, every innovation has its pros as well as cons. In some YouTube channels, a machine-made spam remark is produced on that recordings, moreover, a few phony clients additionally remark a spam comment which creates an adverse effect on that YouTube channel.  The spam remarks can be distinguished by using AI (artificial intelligence) which is based on different Algorithms namely Naive Bayes, SVM, Random Forest, ANN, etc. The present investigation is focussed on a machine learning-based Naive Bayes classifier ordered methodology for the identification of spam remarks on YouTub

Machine learning-based Naive Bayes approach for divulgence of Spam Comment in Youtube station

In the 21st Century, web-based media assumes an indispensable part in the interaction and communication of civilization. As an illustration of web-based media viz. YouTube, Facebook, Twitter, etc., can increase the social regard of a person just as a gathering. Yet, every innovation has its pros as well as cons. In some YouTube channels, a machine-made spam remark is produced on that recordings, moreover, a few phony clients additionally remark a spam comment which creates an adverse effect on that YouTube channel.  The spam remarks can be distinguished by using AI (artificial intelligence) which is based on different Algorithms namely Naive Bayes, SVM, Random Forest, ANN, etc. The present investigation is focussed on a machine learning-based Naive Bayes classifier ordered methodology for the identification of spam remarks on YouTub