Foundational principles for large scale inference: Illustrations through correlation mining

When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number $n$ of acquired samples (statistical replicates) is far fewer than the number $p$ of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size $n$ is fixed, and the dimension $p$ grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks

A SYSTEMIC FUNCTIONAL ANALYSIS ON JAVANESE POLITENESS: TAKING SPEECH LEVEL INTO MOOD STRUCTURE

Speech level is an important aspect in Javanese grammar. It is just like, among others, tenses in English. Thus, the involvement of speech level in any study of Javanese grammar is highly necessary. On the other hand, speech level must also be studied the grammatical point of view. So far, however, there are very limited numbers—if any does really exist—of grammatical study on Javanese speech level. Most major studies on Javanese speech level are of sociolinguistics, lexical taxonomy or grouping, and prescriptive analysis. It is probably due to the idea of speech level as merely a social phenomenon has been taken for granted. Therefore, taking the speech level system into a grammatical analysis seems hardly possible. It is assumed that the seemingly impossible attempt comes only to the formal approach of the grammar study tradition for it has neglected the social aspect. Hence, it is necessary to look for an alternative grammatical approach which is able to cope with the speech level both grammatically and socially. A particular approach of grammar which involves social context is systemic functional grammar (SFG). SFG proposes that language has three kinds of functional component. One of them is the interpersonal function. This function sees language as an interaction between addresser and addressee—language is used for enacting participants‘ roles and relation among them. The interpersonal function is expressed through a particular grammatical structure, namely mood structure. This article is going present a demonstration of systemic functional analysis on Javanese speech level by taking it into the mood structure analysis. In addition, this paper aims for two kinds of potential significance. First, it could be an adequate description of Javanese speech level grammaticalization. Second, it can be a typological supplement for SFG in dealing with languages which apply a speech level system

RANCANGAN APLIKASI INTEROPERABILITAS SISTEM INFORMASI INTER DEPARTEMEN

Rancangan aplikasi layanan untuk interoperabilitas sistem informasi instansi pemerintah ini direncanakan dapat menghubungkan beberapa sistem informasi pemerintahan yang berbeda platform (baik dari sisi Sistem Operasi, Bahasa Pemrograman maupun Databasenya), sehingga antar sistem informasi tersebut bisa saling tukar data satu dengan yang lainnya melalui layanan berbasis web/internet menggunakan konsep web service. Rancangan aplikasi interoperabilitas yang dibuat dipergunakan untuk menghubungkan beberapa instansi yaitu : Kependudukan (Depdagri), Kesehatan (Depkses), Bappenas dan BPS (Badan Pusat Statistik) agar bisa saling menukar data dan informasi. Masing-masing instansi dapat menggunakan aplikasi ini untuk mengirim data mereka sesuai dengan format standar yang telah ditentukan yaitu format xml dan dikirimkan ke sebuah server repositori nasional. Dari server inilah instansi yang lain dapat saling melihat data dari instansi lain dan menggunakannya sesuai kebutuhan. Dalam penelitian kali ini diajukan rancangan aplikasi interoperabilitas serta diujicobakan menggunakan data yang berasal dari empat instansi diatas. Aplikasi yang dihasilkan terdiri dari tiga macam aplikasi yaitu : aplikasi xmlCreator, aplikasi xmlReader dan Sistem Informasi yang berbentuk web. Dalam sistem informasi selain disajikan menu informasi data dari masing-masing instansi juga disajikan daftar file xml dan web service

Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

We consider the $k$-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the $k$-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and H\"older's inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ($k=1$) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result

On Measure Transformed Canonical Correlation Analysis

In this paper linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets