Large Scale Constrained Linear Regression Revisited: Faster Algorithms via Preconditioning

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new method called two-step preconditioning to achieve an approximate solution with a time complexity lower than that of the state-of-the-art techniques for the low precision case. Our idea can also be extended to the high precision case, which gives an alternative implementation to the Iterative Hessian Sketch (IHS) method with significantly improved time complexity. Experiments on benchmark and synthetic datasets suggest that our methods indeed outperform existing ones considerably in both the low and high precision cases.Comment: Appear in AAAI-1

A Case Study of an Urban Elementary School Chinese Language and Culture Program at the Boston Renaissance Charter Public Schools (BRCPS)

Very few urban elementary African American and Hispanic students have access to foreign language programs. Thus, students of color have historically been under-represented in foreign language study. At the same time, urban elementary foreign language programs for economically disadvantaged African American and Hispanic students might level the playing field for these students and help prepare them to participate more fully in a global economy and community in the future. The present case study is based on a mixed methods approach using logic model and overlapping spheres of influence theory to examine the impact of the Boston Renaissance Charter Public School (BRCPS) Chinese language and culture program on its stakeholders (students, parents, school teachers, administrators, and board members). A sequential explanatory strategy is used to investigate stakeholders\u27 perceptions and attitudes toward the BRCPS Chinese language and culture program. It further reveals discrepancies between the stakeholders\u27 perceptions/attitudes and their racial backgrounds, working length of time and involvement with BRCPS, SES (Socioeconomic Status), grade connection, and gender. It also identifies the factors that influence BRCPS students\u27 motivation and interest in learning Chinese. This study, therefore, finds out that the majority of the BRCPS stakeholders are satisfied with BRCPS Chinese language and culture program. The biggest challenge identified is Chinese teachers\u27 lack of classroom control and the difficulty in maintaining positive student discipline in Chinese class. Stakeholders suggest Chinese language should be taught as a core curriculum rather than as a specialist subject. They also suggest that all the stakeholders should work together to value Chinese learning

An Efficient Sum Query Algorithm for Distance-based Locally Dominating Functions

In this paper, we consider the following sum query problem: Given a point set P in R^d, and a distance-based function f(p,q) (i.e. a function of the distance between p and q) satisfying some general properties, the goal is to develop a data structure and a query algorithm for efficiently computing a (1+epsilon)-approximate solution to the sum sum_{p in P} f(p,q) for any query point q in R^d and any small constant epsilon>0. Existing techniques for this problem are mainly based on some core-set techniques which often have difficulties to deal with functions with local domination property. Based on several new insights to this problem, we develop in this paper a novel technique to overcome these encountered difficulties. Our algorithm is capable of answering queries with high success probability in time no more than ~O_{epsilon,d}(n^{0.5 + c}), and the underlying data structure can be constructed in ~O_{epsilon,d}(n^{1+c}) time for any c>0, where the hidden constant has only polynomial dependence on 1/epsilon and d. Our technique is simple and can be easily implemented for practical purpose