Efficient Benchmarking of Algorithm Configuration Procedures via Model-Based Surrogates

The optimization of algorithm (hyper-)parameters is crucial for achieving peak performance across a wide range of domains, ranging from deep neural networks to solvers for hard combinatorial problems. The resulting algorithm configuration (AC) problem has attracted much attention from the machine learning community. However, the proper evaluation of new AC procedures is hindered by two key hurdles. First, AC benchmarks are hard to set up. Second and even more significantly, they are computationally expensive: a single run of an AC procedure involves many costly runs of the target algorithm whose performance is to be optimized in a given AC benchmark scenario. One common workaround is to optimize cheap-to-evaluate artificial benchmark functions (e.g., Branin) instead of actual algorithms; however, these have different properties than realistic AC problems. Here, we propose an alternative benchmarking approach that is similarly cheap to evaluate but much closer to the original AC problem: replacing expensive benchmarks by surrogate benchmarks constructed from AC benchmarks. These surrogate benchmarks approximate the response surface corresponding to true target algorithm performance using a regression model, and the original and surrogate benchmark share the same (hyper-)parameter space. In our experiments, we construct and evaluate surrogate benchmarks for hyperparameter optimization as well as for AC problems that involve performance optimization of solvers for hard combinatorial problems, drawing training data from the runs of existing AC procedures. We show that our surrogate benchmarks capture overall important characteristics of the AC scenarios, such as high- and low-performing regions, from which they were derived, while being much easier to use and orders of magnitude cheaper to evaluate

Censored Quantile Regression Redux

Quantile regression for censored survival (duration) data offers a more flexible alternative to the Cox proportional hazard model for some applications. We describe three estimation methods for such applications that have been recently incorporated into the R package quantreg: the Powell (1986) estimator for fixed censoring, and two methods for random censoring, one introduced by Portnoy (2003), and the other by Peng and Huang (2008). The Portnoy and Peng-Huang estimators can be viewed, respectively, as generalizations to regression of the Kaplan-Meier and Nelson-Aalen estimators of univariate quantiles for censored observations. Some asymptotic and simulation comparisons are made to highlight advantages and disadvantages of the three methods.

An Empirical Test of Reder Competition and Specific Human Capital Against Standard Wage Competition

A firm that faces insufficient supply of labor can either increase the wage offer to attract more applicants, or reduce the hiring standard to enlarge the pool of potential employees, or do both. This simultaneous adjustment of wages and hiring standards has been emphasized in a classical contribution by Reder (1955) and implies that wage reactions to employment changes can be expected to be more pronounced for low wage workers than for high wage workers. We test this hypothesis (together with a related hypothesis on firm-specific human capital) by applying a bootstrap-based quantile regression approach to censored panel data from the German employment register. Our findings suggest that market clearing is achieved by a combination of wage and hiring standards adjustment

An Empirical Test of the Reder Hypothesis

A firm that faces insufficient supply of labor can either increase the wage offer to attract more applicants, or reduce the hiring standard to enlarge the pool of potential employees, or do both. This simultaneous adjustment of wages and hiring standards in response to changes in market conditions has been emphasized in a classical contribution by Reder and leads to the effect that wage reactions to employment changes can be expected to be more pronounced for low wage workers than for high wage workers. This is the `Reder Hypothesis'. The present contribution sets out to test this hypothesis using German employment register data and a censored panel quantile regression approach. Our findings support the Reder Hypothesis, suggesting that market clearing in labor markets is achieved by a combination of wage adjustments and changes in hiring standards

On multivariate quantiles under partial orders

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study several statistical aspects of partial quantiles. We provide estimators, associated rates of convergence, and asymptotic distributions that hold uniformly over a continuum of quantile indices. Furthermore, we provide procedures that can restore monotonicity properties that might have been disturbed by estimation error, establish computational complexity bounds, and point out a concentration of measure phenomenon (the latter under independence and the componentwise natural order). Finally, we illustrate the concepts by discussing several theoretical examples and simulations. Empirical applications to compare intake nutrients within diets, to evaluate the performance of investment funds, and to study the impact of policies on tobacco awareness are also presented to illustrate the concepts and their use.Comment: Published in at http://dx.doi.org/10.1214/10-AOS863 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Genetic algorithms: a tool for optimization in econometrics - basic concept and an example for empirical applications

This paper discusses a tool for optimization of econometric models based on genetic algorithms. First, we briefly describe the concept of this optimization technique. Then, we explain the design of a specifically developed algorithm and apply it to a difficult econometric problem, the semiparametric estimation of a censored regression model. We carry out some Monte Carlo simulations and compare the genetic algorithm with another technique, the iterative linear programming algorithm, to run the censored least absolute deviation estimator. It turns out that both algorithms lead to similar results in this case, but that the proposed method is computationally more stable than its competitor. --Genetic Algorithm,Semiparametrics,Monte Carlo Simulation

A Quantile Variant of the EM Algorithm and Its Applications to Parameter Estimation with Interval Data

The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the expectation in each E-step and the maximization in each M-step are straightforward. A difficulty with the implementation of the EM algorithm is that each E-step requires the integration of the log-likelihood function in closed form. The explicit integration can be avoided by using what is known as the Monte Carlo EM (MCEM) algorithm. The MCEM uses a random sample to estimate the integral at each E-step. However, the problem with the MCEM is that it often converges to the integral quite slowly and the convergence behavior can also be unstable, which causes a computational burden. In this paper, we propose what we refer to as the quantile variant of the EM (QEM) algorithm. We prove that the proposed QEM method has an accuracy of $O(1/K^2)$ while the MCEM method has an accuracy of $O_p(1/\sqrt{K})$. Thus, the proposed QEM method possesses faster and more stable convergence properties when compared with the MCEM algorithm. The improved performance is illustrated through the numerical studies. Several practical examples illustrating its use in interval-censored data problems are also provided