Passive Learning with Target Risk

In this paper we consider learning in passive setting but with a slight modification. We assume that the target expected loss, also referred to as target risk, is provided in advance for learner as prior knowledge. Unlike most studies in the learning theory that only incorporate the prior knowledge into the generalization bounds, we are able to explicitly utilize the target risk in the learning process. Our analysis reveals a surprising result on the sample complexity of learning: by exploiting the target risk in the learning algorithm, we show that when the loss function is both strongly convex and smooth, the sample complexity reduces to \O(\log (\frac{1}{\epsilon})), an exponential improvement compared to the sample complexity \O(\frac{1}{\epsilon}) for learning with strongly convex loss functions. Furthermore, our proof is constructive and is based on a computationally efficient stochastic optimization algorithm for such settings which demonstrate that the proposed algorithm is practically useful

Optimising continuous microstructures: a comparison of gradient-based and stochastic methods

This work compares the use of a deterministic gradient based search with a stochastic genetic algorithm to optimise the geometry of a space frame structure. The goal is not necessarily to find a global optimum, but instead to derive a confident approximation of fitness to be used in a second optimisation of topology. The results show that although the genetic algorithm searches the space more broadly, and this space has several global optima, gradient descent achieves similar fitnesses with equal confidence. The gradient descent algorithm is advantageous however, as it is deterministic and results in a lower computational cost

The LX-sigma Relation for Galaxies and Clusters of Galaxies

We demonstrate that individual elliptical galaxies and clusters of galaxies form a continuous X-ray luminosity---velocity dispersion (LX-sigma) relation. Our samples of 280 clusters and 57 galaxies have LX ~ sigma^4.4 and LX ~ sigma^10, respectively. This unified LX - sigma relation spans 8 orders of magnitude in LX and is fully consistent with the observed and theoretical luminosity---temperature scaling laws. Our results support the notion that galaxies and clusters of galaxies are the luminous tracers of similar dark matter halos.Comment: 11 pages, including 2 tables and 2 figures. Accepted for publication in The Astrophysical Journal Letters; the Letters version excludes Table 1, which is available in ASCII format at http://tdc-www.harvard.edu/lxsigm

The Tax Spending Nexus: Evidence from a Panel of US State-Local Governments

We re-examine the tax-spending nexus using, for the first time, a panel of fifty US state-local government units over the period 1963-97 and panel techniques that allow for cross-sectional dependence. We find that, unlike tax revenues, expenditures adjust to revert back to a long-term equilibrium relationship. The evidence on the short-term dynamics is also consistent with the tax-and-spend hypothesis at the one percent level of significance. One implication of this finding is that the size of the government at the state-local level is not determined by expenditure demand, but rather by resource supply. This is consistent with the fact that many US state and local governments operate under constitutional or legislative limitations that seek to constrain deficits.tax-spend, state and local government, public finance, and panel cointegration.