Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs

We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample small number of KPGM graphs and \emph{quilt} them together. Under a restricted set of technical conditions our algorithm runs in $O((\log_2(n))^3 |E|)$ time, where $n$ is the number of nodes and $|E|$ is the number of edges in the sampled graph. We demonstrate the scalability of our algorithm via extensive empirical evaluation; we can sample a MAGM graph with 8 million nodes and 20 billion edges in under 6 hours

Model-Independent Measurement of the Primordial Power Spectrum

In inflationary models with minimal amount of gravity waves, the primordial power spectrum of density fluctuations, $A_S^2(k)$, together with the basic cosmological parameters, completely specify the predictions for the cosmic microwave background (CMB) anisotropy and large scale structure. Here we show how we can strongly constrain both $A_S^2(k)$ and the cosmological parameters by combining the data from the Microwave Anisotropy Probe (MAP) and the galaxy redshift survey from the Sloan Digital Sky Survey (SDSS). We allow $A_S^2(k)$ to be a free function, and thus probe features in the primordial power spectrum on all scales. MAP and SDSS have scale-dependent measurement errors that decrease in opposite directions on astrophysically interesting scales; they complement each other and allow the measurement of the primordial power spectrum independent of inflationary models, giving us valuable information on physics in the early Universe, and providing clues to the correct inflationary model.Comment: 4 pages including 4 figures. To appear in "Particle Physics and the Early Universe (COSMO-98)", editor David O. Caldwell (American Institute of Physics

A Note on Poverty in Kosovo

Kosovo is a war-torn corner of the former Yugoslavia, where a civil war between ethnic Albanians and ethnic Serbs raged during most of the 1990s. We examine the incidence and depth of poverty and some of its correlates in post-conflict Kosovo using the Living Standards Measurement Survey.http://deepblue.lib.umich.edu/bitstream/2027.42/40193/3/wp807.pd

Distributed Stochastic Optimization of the Regularized Risk

Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many existing stochastic optimization algorithms cannot be parallelized efficiently. In this paper we show that one can rewrite the regularized risk minimization problem as an equivalent saddle-point problem, and propose an efficient distributed stochastic optimization (DSO) algorithm. We prove the algorithm's rate of convergence; remarkably, our analysis shows that the algorithm scales almost linearly with the number of processors. We also verify with empirical evaluations that the proposed algorithm is competitive with other parallel, general purpose stochastic and batch optimization algorithms for regularized risk minimization

Was the Mandal Commission Right? Living Standard Differences between Backward Classes and Other Social Groups in India

Affirmative action has been at the heart of public policies towards the socially disadvantaged in India. Compensatory discrimination policies which have been adopted for the Scheduled Castes (SC) and Scheduled Tribes (ST) since independence were recommended for Other Backward Classes (OBC) by the Mandal Commission established by the Indian government in 1979. We examine why OBC have lower living standards, as measured by per capita household consumption expenditures, relative to the mainstream population, and whether these reasons are similar to those observed for SC and ST. We find that while the causes of the living standard gap for the OBC are broadly similar to those for the SC and ST, the role of educational attainment in explaining the gap is higher in importance for the OBC.living standards, caste, reservation policy, decomposition

Was the Mandal Commission Right? Living Standard Differences between Backward Classes and Other Social Groups in India

Affirmative action has been at the heart of public policies towards the socially disadvantaged in India. Compensatory discrimination policies which have been adopted for the Scheduled Castes (SC) and Scheduled Tribes (ST) since independence were recommended for Other Backward Classes (OBC) by the Mandal Commission established by the Indian government in 1979. We examine why OBC have lower living standards, as measured by per capita household consumption expenditures, relative to the mainstream population, and whether these reasons are similar to those observed for SC and ST. We find that while the causes of the living standard gap for the OBC are broadly similar to those for the SC and ST, the role of educational attainment in explaining the gap is higher in imporatnce for the OBC.