Locally Adaptive Optimization: Adaptive Seeding for Monotone Submodular Functions

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the choices in the first stage affect the realizations in the second stage, over which we aim to optimize. Our main result is a $(1-1/e)^2$-approximation for the adaptive seeding problem for any monotone submodular function. While adaptive policies are often approximated via non-adaptive policies, our algorithm is based on a novel method we call \emph{locally-adaptive} policies. These policies combine a non-adaptive global structure, with local adaptive optimizations. This method enables the $(1-1/e)^2$-approximation for general monotone submodular functions and circumvents some of the impossibilities associated with non-adaptive policies. We also introduce a fundamental problem in submodular optimization that may be of independent interest: given a ground set of elements where every element appears with some small probability, find a set of expected size at most $k$ that has the highest expected value over the realization of the elements. We show a surprising result: there are classes of monotone submodular functions (including coverage) that can be approximated almost optimally as the probability vanishes. For general monotone submodular functions we show via a reduction from \textsc{Planted-Clique} that approximations for this problem are not likely to be obtainable. This optimization problem is an important tool for adaptive seeding via non-adaptive policies, and its hardness motivates the introduction of \emph{locally-adaptive} policies we use in the main result

Influence Maximization in Social Networks: A Survey

Online social networks have become an important platform for people to communicate, share knowledge and disseminate information. Given the widespread usage of social media, individuals' ideas, preferences and behavior are often influenced by their peers or friends in the social networks that they participate in. Since the last decade, influence maximization (IM) problem has been extensively adopted to model the diffusion of innovations and ideas. The purpose of IM is to select a set of k seed nodes who can influence the most individuals in the network. In this survey, we present a systematical study over the researches and future directions with respect to IM problem. We review the information diffusion models and analyze a variety of algorithms for the classic IM algorithms. We propose a taxonomy for potential readers to understand the key techniques and challenges. We also organize the milestone works in time order such that the readers of this survey can experience the research roadmap in this field. Moreover, we also categorize other application-oriented IM studies and correspondingly study each of them. What's more, we list a series of open questions as the future directions for IM-related researches, where a potential reader of this survey can easily observe what should be done next in this field

Test Score Algorithms for Budgeted Stochastic Utility Maximization

Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance data, for solving the budgeted stochastic utility maximization problem. We extend an existing scoring mechanism, namely the replication test scores, to incorporate heterogeneous item costs as well as item values. We show that a natural greedy algorithm that selects items solely based on their replication test scores outputs solutions within a constant factor of the optimum for a broad class of utility functions. Our algorithms and approximation guarantees assume that test scores are noisy estimates of certain expected values with respect to marginal distributions of individual item values, thus making our algorithms practical and extending previous work that assumes noiseless estimates. Moreover, we show how our algorithm can be adapted to the setting where items arrive in a streaming fashion while maintaining the same approximation guarantee. We present numerical results, using synthetic data and data sets from the Academia.StackExchange Q&A forum, which show that our test score algorithm can achieve competitiveness, and in some cases better performance than a benchmark algorithm that requires access to a value oracle to evaluate function values

Foreign Capital, Inflation, Sterilization, Crowding-Out and

This paper discusses some puzzles in the contemporary macroeconomic scene in India, from the perspective of public finance and economic development. These include a fiscal deficit higher than it was during the 1991 crisis, but without a large current account deficit or rise in inflation or interest rates, a rising inflow of external capital, accompanied by the RBI’s sterilizing these inflows and accumulating large reserves, even in the face of low inflation. We offer a critique of some previous analyses, and some models that are suggestive of how real and monetary factors might be integrated in providing a firmer grounding for the policy debates current in India.foreign capital, sterilization, absorption, crowding out, inflation, growth

Hospital Cost and Efficiency Under Per Service and Per Case Payment in Maryland: A Tale of the Carrot and the Stick

The simultaneous operation of per case and per servicepayment systems in Maryland, and the varying levels of stringency used in setting per case rates allows comparison of effects of differing incentive structures on hospital costs. This paper presents such a comparison with 1977-1981 data. Cost per case and total cost regressions show evidence of lower costs only when per case payment limits are very stringent. Positive net revenue incentives appear insufficient to induce reductions in length of stay and in ancillary services use. Our results suggest these changes in medical practice patterns are more likely under the threat of financial losses.