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

Open Charm Mesons at the LHC with ALICE

The ALICE experiment will be able to detect hadrons containing charm and beauty quarks in proton-proton and heavy ion collisions in the new energy regime of the CERN Large Hadron Collider (LHC). Open charmed mesons are a powerful tool to study the medium produced in heavy ion collisions, since charm quarks are produced on a very short time scale and they experience the whole history of the collision. In addition, the measurements of heavy flavour yield provide a natural normalization for those of charmonia and bottomonia production at LHC. In this talk, after a general overview of ALICE perspectives for heavy flavour physics, we will report some study of D-meson reconstruction through their hadronic decay channels with Monte Carlo simulated data.Comment: 7 pages, 4 figure

Open Charm Analysis at Central Rapidity in ALICE using the first year of pp data at \sqrt{s}=7 TeV

ALICE is the dedicated heavy-ion experiment at the LHC. Its main physics goal is to study the properties of the strongly-interacting matter in the conditions of high energy density (>10 GeV/fm3) and high temperature (> 0.3 GeV) expected to be reached in central Pb\^aPb collisions. Charm and beauty quarks are a powerful tool to investigate this high density and strongly interacting state of matter as they are produced in initial hard scatterings, and due to their long life time, they probe all the stages of the system evolution. The detector design was optimized for heavy ions but is also well suited for pp studies. ALICE recorded pp data at s= 7 TeV since march 2010 and the first run with heavy ion collisions took place in November 2010. The measurement of charm production cross section in pp collisions provides interesting insight into QCD processes and is important as a reference for heavy ion studies. The measurement of the D- meson yield in pp collisions can be used to extract the charm cross section. In this contribution, the ongoing study of reconstruction of D-mesons through hadronic decay channels and the first preliminary results obtained with \sqrt{s}= 7 TeV pp data will be presented.Comment: 4 pages, 2 figures, Conference proceeding to be published in Nucl. Phys.

The Hoffmann-Jorgensen inequality in metric semigroups

We prove a refinement of the inequality by Hoffmann-Jorgensen that is significant for three reasons. First, our result improves on the state-of-the-art even for real-valued random variables. Second, the result unifies several versions in the Banach space literature, including those by Johnson and Schechtman [Ann. Probab. 17 (1989)], Klass and Nowicki [Ann. Probab. 28 (2000)], and Hitczenko and Montgomery-Smith [Ann. Probab. 29 (2001)]. Finally, we show that the Hoffmann-Jorgensen inequality (including our generalized version) holds not only in Banach spaces but more generally, in a very primitive mathematical framework required to state the inequality: a metric semigroup $\mathscr{G}$. This includes normed linear spaces as well as all compact, discrete, or (connected) abelian Lie groups.Comment: 11 pages, published in the Annals of Probability. The Introduction section shares motivating examples with arXiv:1506.0260

Economic Policy and State Owned Enterprises: Evolution Towards Privatisation in India

The paper endeavours to look into the evolution of the role of the state and move towards privatisation in India. It starts with a discussion on the role of State intervention in the economic development within the contours of socio-economic and political circumstances. It recognises the fact that different scholars have advocated various ways through which state can intervene in an advanced capitalist economy and a developing economy or a colony. The nature of intervention is different in each case. The paper argues that State owned enterprises (SOEs) are one such manifestation of state Intervention. In many developing countries, state enterprises are assigned the responsibility of fulfilling specific social goals, which have their origin in colonial period. Whatever may be the idea behind the creation of such enterprises, they come into existence either by direct state investment or through nationalisation of private enterprises. The state intervenes through state owned enterprises in the countries where investment needs for different projects are large and the expected returns at least in the short run are too low to motivate private capital to invest. Since 1980, however, the intervention by the state through state owned enterprises has been undergoing a close scrutiny in many developing countries including India. The argument is that excessive political interference and lack of managerial interests (autonomy) hamper the performance of state enterprises. It has resulted in the reflection of various theories on assessing the performance of state enterprises which includes property rights theory, public choice theory, non-market failure and competition theory. Since economic policy making by the state requires balance of accumulation and legitimisation, then generally, the adopted economic policy serves the interests of a few major social groups. These dominant social groups react to the adopted policy and their reactions are normally taken into account while amending the existing policy or making the new economic policy. Hence, the proper understanding of the economic policy of an economy like India necessitates its historical evaluation. Therefore, in this chapter, the whole period of interaction of economic policy and state owned sector in the post-independence India has been divided into following four phases: (i) 1950-1965, (ii) 1966-1984, (iii) 1984-91 and (iv) post-1991 policy regime. During the first phase, i.e. 1950-65, the growth rates of the economy were generally high and state owned sector was occupying the position of 'commanding heights'. Despite the economy passing through crisis during this phase, the state owned sector enjoyed by and large a significant position. The policy adopted in 1982 was a step forward towards the process of liberalisation. In state owned enterprises, a visible change in the attitude took place. The economy was made predominantly dependent upon market forces rather than on the state. The industrial policy that was initiated in 1985 was the culmination of the process of drifting away, which started during the second phase of the economic policy in India. In the Post 1991, Policy Regime, the Eighth, Ninth and Tenth Plan documents suggested many policy initiatives towards restructuring, modernisation, rationalisation of capacity, product-mix changes, privatisation, autonomy, performance accountability and disinvestments policy. However many studies emerged in favour of and against the policy of privatisation and disinvestment of SOEs and also on the performance of those enterprises that were privatised. While referring to those studies, the chapter looks into the trends of the privatisation of State Owned Enterprises from 1991 to 2000 and points out that during this period, the government offloaded shares in as many as 39 state owned enterprises. However, since March 2000 emphasis has increasingly been on strategic sales of identified state owned enterprises (SOEs). The chapter ends with a critical analysis of the performance of disinvestment process in india and observes that the policy of disinvestment has been looked upon with scepticism. JEL Classifications: O11, P41, P47, P52economic policy, privatisation, state owned enterprises, evolution, disinvestment

Retaining positive definiteness in thresholded matrices

Positive definite (p.d.) matrices arise naturally in many areas within mathematics and also feature extensively in scientific applications. In modern high-dimensional applications, a common approach to finding sparse positive definite matrices is to threshold their small off-diagonal elements. This thresholding, sometimes referred to as hard-thresholding, sets small elements to zero. Thresholding has the attractive property that the resulting matrices are sparse, and are thus easier to interpret and work with. In many applications, it is often required, and thus implicitly assumed, that thresholded matrices retain positive definiteness. In this paper we formally investigate the algebraic properties of p.d. matrices which are thresholded. We demonstrate that for positive definiteness to be preserved, the pattern of elements to be set to zero has to necessarily correspond to a graph which is a union of disconnected complete components. This result rigorously demonstrates that, except in special cases, positive definiteness can be easily lost. We then proceed to demonstrate that the class of diagonally dominant matrices is not maximal in terms of retaining positive definiteness when thresholded. Consequently, we derive characterizations of matrices which retain positive definiteness when thresholded with respect to important classes of graphs. In particular, we demonstrate that retaining positive definiteness upon thresholding is governed by complex algebraic conditions