The problem of numerical analysis to which this study is directed is that of determining an optimum approximation (in the least squares sense) to a given function f by a function of the form p/q, where p and q are confined to certain prescribed linear spaces. The analogous approximation problem employing the uniform norm has received much recent attention. See, for example, [1, 2, 3, 4, 5, 9]. ...

We introduce a new framework for unifying and systematizing the performance analysis of first-order black-box optimization algorithms unconstrained convex minimization. The low-cost iteration complexity enjoyed by renders them particularly relevant applications in machine learning large-scale data analysis. Relying on sum-of-squares (SOS) optimization, we hierarchy semidefinite programs that gi...

Data envelopment analysis (DEA) is an axiomatic, mathematical programming approach to productive efficiency analysis and performance measurement. This paper shows that DEA can be interpreted as a nonparametric least squares regression subject to shape constraints on production frontier and sign constraints on residuals. Thus, DEA can be seen as a nonparametric counter-part of the corrected ordi...

An eight-equation model embodies the hypothesis that cultural differences among ethnic-religious groups give rise to differences in psychological dispositions, which, though not directly observable, influence occupational achievement, directly or via educational attainment, while being subject to feedback from one or the other of these endogenous variables. Dispositions are reflected in three f...

Waldén, Karlson, and Sun found an elegant explicit expression of backward error for the linear least squares problem. However, it is difficult to compute this quantity as it involves the minimal singular value of certain matrix. In this paper we present a simple estimation to this bound which can be easily computed especially for large problems. Numerical results demonstrate the validity of the...

Directly solving the ordinary least squares problem will (in general) require O(nd) operations. From Table 5.1, the Gaussian sketch does not actually improve upon this scaling for unconstrained problems: when m d (as is needed in the unconstrained case), then computing the sketch SA requires O(nd) operations as well. If we compute sketches using the JLT, then this cost is reduced to O(nd log(d)...

Previously identified predictors of public punitiveness include attitudinal, experiential, background, and demographic characteristics. Given the influence of parenthood on certain attitudes and beliefs, it may also affect how strongly individuals endorse harsh punishment for criminals. Few studies have explored how parenthood influences general policy preferences or support for criminal justic...