Fast conditional density estimation for quantitative structure-activity relationships

Many methods for quantitative structure-activity relationships (QSARs) deliver point estimates only, without quantifying the uncertainty inherent in the prediction. One way to quantify the uncertainy of a QSAR prediction is to predict the conditional density of the activity given the structure instead of a point estimate. If a conditional density estimate is available, it is easy to derive prediction intervals of activities. In this paper, we experimentally evaluate and compare three methods for conditional density estimation for their suitability in QSAR modeling. In contrast to traditional methods for conditional density estimation, they are based on generic machine learning schemes, more specifically, class probability estimators. Our experiments show that a kernel estimator based on class probability estimates from a random forest classifier is highly competitive with Gaussian process regression, while taking only a fraction of the time for training. Therefore, generic machine-learning based methods for conditional density estimation may be a good and fast option for quantifying uncertainty in QSAR modeling.http://www.aaai.org/ocs/index.php/AAAI/AAAI10/paper/view/181

Targeted Maximum Likelihood Estimation using Exponential Families

Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We investigate the use of exponential families to define the parametric submodel. This implementation of TMLE gives a general approach for estimating any smooth parameter in the nonparametric model. A computational advantage of this approach is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate the method in three estimation problems, involving the mean of an outcome missing at random, the parameter of a median regression model, and the causal effect of a continuous exposure, respectively. We conduct a simulation study comparing different choices for the parametric submodel, focusing on the first of these problems. To the best of our knowledge, this is the first study investigating robustness of TMLE to different specifications of the parametric submodel. We find that the choice of submodel can have an important impact on the behavior of the estimator in finite samples

Efficient prediction for linear and nonlinear autoregressive models

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference on Counterfactual Distributions

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States. As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the \textit{entire} conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional results available from the authors' web site