Raja P. Velu

Enriching textbooks through data mining

Textbooks play an important role in any educational system. Unfortunately, many textbooks produced in developing countries are not written well and they often lack adequate coverage of important concepts. We propose a technological solution to address this problem based on enriching textbooks with authoritative web content. We augment textbooks at the section level for key concepts discussed in the section. We use ideas from data mining for identifying the concepts that need augmentation as well as to determine the links to the authoritative content that should be used for augmentation. Our evaluation, employing textbooks from India, shows that we are able to enrich textbooks on different subjects and across different grades with high quality augmentations using automated techniques.

Volume and volatility in a common-factor mixture of distributions model

This paper develops a multi-asset mixture distribution hypothesis model to investigate commonality in stock returns and trading volume. The model makes two main predictions: First, the factor structures of returns and trading volume are independent although they stem from the same valuation fundamentals and jointly depend on a latent information flow; second, cross-sectional positive volatility-volume relations arise solely from the dynamic features of the information flow. Empirical analyses at the market level support these predictions. Furthermore, the results indicate that removing the information flow significantly reduces the return volatility persistence and the extent of the reduction exhibits a size pattern.

Ameliorating buyer's remorse

Keeping in pace with the increasing importance of commerce conducted over the Web, several e-commerce websites now provide admirable facilities for helping consumers decide what product to buy and where to buy it. However, since the prices of durable and high-tech products generally fall over time, a buyer of such products is often faced with a dilemma: Should she buy the product now or wait for cheaper prices?n We present the design and implementation of Prodcast, an experimental system whose goal is to help consumers decide when to buy a product. The system makes use of forecasts of future prices based on price histories of the products, incorporating features such as sales volume, seasonality, and competition in making its recommendation. We describe techniques that are well-suited for this task and present a comprehensive evaluation of their relative merits using retail sales data for electronic products. Our back-testing of the system indicates that the system is capable of helping consumers time their purchase, resulting in significant savings to them.

Timing when to buy

Most e-commerce sites to-date have focused on helping consumers decide what to buy and where to buy. We study the complementary question of helping consumers decide when to buy, focusing on consumer durables. We introduce a utility-based model for evaluating different approaches to this question. We focus on how best to make use of forecasts in making recommendations, and propose three natural strategies. We establish a relationship between these strategies, and show that one of them is optimal. We conduct a large-scale experimental study to test the performance and robustness of these strategies. Across a wide range of conditions, the best strategy obtains 90% of the maximum possible gains.

Separable Covariance Matrices and Kronecker Approximation

Abstract When a model structure allows for the error covariance matrix to be written in the form of the Kronecker product of two positive definite covariance matrices, the estimation of the relevant parameters is intuitive and easy to carry out. In many time series models, the covariance matrix does not have a separable structure. Van Loan and Pitsanis (1993) provide an approximation with Kronecker products. In this paper, we apply their method to estimate the parameters of a multivariate regression model with autoregressive errors. An illustrative example is also provided.

Optimizing merchant revenue with rebates

We study an online advertising model in which the merchant reimburses a portion of the transacted amount to the customer in a form of rebate. The customer referral and the rebate transfer might be mediated by a search engine. We investigate how the merchants can set rebate rates across different products to maximize their revenue. We consider two widely used demand models in economics---linear and log-linear---and explain how the effects of rebates can be incorporated in these models. Treating the parameters estimated as inputs to a revenue maximization problem, we develop convex optimization formulations of the problem and combinatorial algorithms for solving them. We validate our modeling assumptions using real transaction data. We conduct an extensive simulation study to evaluate the performance of our approach on maximizing revenue, and found that it generates significantly higher revenues for merchants compared to other rebate strategies. The rebate rates selected are extremely close to the optimal rates selected in hindsight.

Multiple Time Series Modeling With Reduced Ranks

There has been growing interest in multiple time series modeling, particularly through use of vector autoregressive moving average models. The subject has found appeal and has applications in various disciplines, including engineering, physical sciences, business and economics, and the social sciences. In general, multiple time series analysis is concerned with modeling and estimation of dynamic relationships among m related time series y 1t, ... ,y mt, based on observations on these series over T equally spaced time points t = 1,... ,T, and also between these series and potential input or exogenous time series variables x 1t,..., x nt, observed over the same time period. In this chapter, we shall explore the use of certain reduced-rank modeling techniques for analysis of multiple time series in practice. We first introduce a general model for multiple time series modeling, but will specialize to multivariate autoregressive (AR) models for more detailed investigation.

Reduced-Rank Regression Model With Autoregressive Errors

The classical multivariate regression methods are based on the assumptions that (i) the regression coefficient matrix is of full rank and (ii) the error terms in the model are independent. In Chapters 2 and 3, we have presented regression models that describe the linear relationships between two or more large sets of variables with a fewer number of parameters than that posited by the classical model. The assumption (i) of full rank of the coefficient matrix was relaxed and the possibility of reduced rank for the coefficient matrix has produced a rich class of models. In this chapter we also weaken the assumption (ii) that the errors are independent, to allow for possible correlation in the errors which may be likely with time series data. For the ozone/temperature time series data considered in Chapter 3, the assumption of independence of errors appears to hold.

Seemingly Unrelated Regressions Models With Reduced Ranks

The classical multivariate linear regression model discussed in Chapter 1 can be generalized by allowing the different response variables y ik to have different input or predictor variables X ik = (x i1k ,... , x ink ,)’ for different i, so that y ik - X’ ik C (i) + ∈ ik , i = 1,... ,m, and the errors ∈ ik are contemporaneously correlated across the different response variables. Multivariate linear regression models of this form were considered by Zellner (1962), who referred to them as seemingly unrelated regression (SUR) equations models. In experimental design situations, the model is also referred to as the multiple design multivariate linear model (e.g., Srivastava, 1967; Roy, Gnanadesikan, and Srivastava, 1971). In the notation of Section 1.2, the linear regression model for the T × 1 vector of values for the ith response variable is n n