Editor: John Shawe-Taylor We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization networks, are extended to the case of multi-task learning. Our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi-task kernel functions we define is used. These kernels model relations among the tasks and are derived from a novel form of regularizers. Specific kernels that can be used for multi-task learning are provided and experimentally tested on two real data sets. In agreement with past empirical work on multi-task learning, the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single-task learning particularly when there are many related tasks but few data per task.

1Open source R and Stata software to implement the methods described herein (called CEM) is available

Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last half-decade become common in American politics and political behavior. Scholars in this subset of political science have thus increasingly avoided the biases and inefficiencies caused by ad hoc methods like listwise deletion and best guess imputation. However, researchers in much of comparative politics and international relations, and others with similar data, have been unable to do the same because the best available imputation methods work poorly with the time-series cross section data structures common in these fields. Weattempttorectify this situation with three related developments. First, we build a multiple imputation model that allows smooth time trends, shifts across cross-sectional units, and correlations over time and space, resulting in far more accurate imputations. Second, we enable analysts to incorporate knowledge from area studies experts via priors on individual missing cell values, rather than on difficult-to-interpret model parameters. Third, because these tasks could not be accomplished within existing imputation algorithms, in that they cannot handle as many variables as needed even in the simpler cross-sectional data for which they were designed, we also develop a new algorithm that substantially expands the range of computationally feasible data types and sizes for which multiple imputation can be used. These developments also make it possible to implement the methods introduced here in freely available open source software that is considerably more reliable than existing algorithms. We develop an approach to analyzing data with

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Behavioral game theory experiments consistently reveal that individuals deviate from theoretically optimal (Nash equilibrium) strategies even in simple games. The α-beauty contest is among the simplest games that elicit such non-optimal behavior; accordingly, there is substantial interest in formally characterizing the observed play for this game. Contributing to such an effort, and building on earlier work by Stahl and Wilson (1995, 1994) and Nagel (1995), Camerer et al. (2004) introduce an intuitively appealing and formally elegant cognitive hierarchy (CH) model of strategic reasoning. Under their model the player population is partitioned according to a Poisson distribution (CH-P) and the resulting subgroups are hierarchically ordered in terms of how many steps of iterated reasoning they perform when strategizing. Though the analytic properties of this model provide easily interpretable parameters, we are able to show that the data do not strongly support such a model, at least in the case of the α-beauty contest. In fact, we find no evidence of cognitive hierarchy structure at all. We arrive at this result by developing a rigorous testing methodology consisting of three key components. First, we generalize CH-P by developing a flexible semiparametric (SP) CH model which nests many common CH variants. Second, we describe an experiment to collect data specifically tailored to test key assumptions of the CH framework. Finally, we describe an appropriate null model against which to evaluate the ability of CH models to characterize our experimental data. Some key words: behavioral game theory, cognitive hierarchy models, model assessment, bounded rationality. 2 1

This paper introduces a new framework for modelling the joint development over time of mortality rates in a pair of related populations with the primary aim of producing consistent mortality forecasts for the two populations. The primary aim is achieved by combining a number of recent and novel developments in stochastic mortality modelling, but these, additionally, provide us with a number of side benefits and insights for stochastic mortality modelling. By way of example, we propose an Age-Period-Cohort model which incorporates a mean-reverting stochastic spread that allows for different trends in mortality improvement rates in the short-run, but parallel improvements in the long run. Second, we fit the model using a Bayesian framework that allows us to combine estimation of the unobservable state variables and the parameters of the stochastic processes driving them into a single procedure. Key benefits of this include dampening down of the impact of Poisson variation in death counts, full allowance for paramater uncertainty, and the flexibility to deal with missing data. The framework is designed for large populations coupled with a small sub-population and is applied to the England & Wales national and Continuous Mortality Investigation assured lives males populations. We compare and contrast results based on the two-population approach with single-population results.

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In this paper, we model self-assessed health, and quantify its uncertainty through a stochastic approach based on the framework from Lee and Carter (1992). We combine explanatory and extrapolative approaches by including macroeconomic factors (GDP and unemployment rate), and life-style related factors (alcohol and tobacco consumption) into the stochastic model for health dynamics. This leads to a significant improvement in the model fit, where a large part of the time trend in health can be attributed to the trends in the observed variables. These observed variables affect separate age groups differently. The backtesting analysis suggests that this approach is successful in terms of forecasting, especially when combining the latent variable and macroeconomic fluctuations. As one of the applications, this paper estimates and predicts life expectancy (LE) and healthy life expectancy (HLE), and quantifies (healthy) longevity risk. Keywords: Health stochastic process, Lee-Carter model, Lee-Carter model with observed variables, Health forecast 1

Preston, and Jason Schnittker for helpful comments and suggestions. An earlier version of this paper