No Free Lunch for Early Stopping

We show that, with a uniform prior on hypothesis functions having the same training error, early stopping at some fixed training error above the training error minimum results in an increase in the expected generalization error. We also show that regularization methods are equivalent to early stopping with certain non-uniform prior on the early stopping solutions

No Free Lunch for Noise Prediction

No-free-lunch theorems have shown that learning algorithms cannot be universally good. We show that no free funch exists for noise prediction as well. We show that when the noise is additive and the prior over target functions is uniform, a prior on the noise distribution cannot be updated, in the Bayesian sense, from any finite data set. We emphasize the importance of a prior over the target function in order to justify superior performance for learning systems

Predictors of Swimming Ability among Children and Adolescents in the United States

Swimming is an important source of physical activity and a life skill to prevent drowning. However, little research has been conducted to understand predictors of swimming ability. The purpose of this study was to understand factors that predict swimming ability among children and adolescents in the United States (US). This was a cross-sectional survey conducted between February and April of 2017 across five geographically diverse cities. Participants were accessed through the Young Christian Men’s Association (YMCA) and included parents of children aged 4–11 years old and adolescents aged 12–17 years old. Independent t-test, analysis of variance (ANOVA), and univariate and multivariate analyses were conducted. Several factors were significant (p ≤ 0.05) predictors of swimming ability and explained 53% of the variance in swimming ability. Variables that were positively associated with swimming ability included: ability of parent(s) to swim, child/adolescent age, a best friend who enjoys swimming, water-safety knowledge, pool open all year, and encouragement to swim from parent(s). Variables that were negatively associated with swimming ability included: fear of drowning, being African American, and being female. Interventions and programs to improve the swimming ability of children and adolescents could be developed with these predictors in mind

Application of Stochastic Optimal Control to Financial Market Debt Crises

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis.stochastic optimal control, dynamic optimization, mortgage crisis, Ito equation, risk aversion, debt management, warning signals

It's About Time: Learning Time and Educational Opportunity in California High Schools

A new study by the UCLA Institute for Democracy, Education and Access (IDEA) found that teachers in high-poverty schools are more likely than their peers in low-poverty schools to report more time lost for academic instruction due to poor access to libraries, technology and qualified substitute teachers. Moreover, economic and social stressors on students -- such as unstable housing, hunger and lack of access to medical or dental care -- also undermine learning time, according to the study