Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.Comment: 9 pages, 7 figures, International Conference on Machine Learning 201

A sparse multinomial probit model for classification

A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method

Sequential stopping for high-throughput experiments

In high-throughput experiments, the sample size is typically chosen informally. Most formal sample-size calculations depend critically on prior knowledge. We propose a sequential strategy that, by updating knowledge when new data are available, depends less critically on prior assumptions. Experiments are stopped or continued based on the potential benefits in obtaining additional data. The underlying decision-theoretic framework guarantees the design to proceed in a coherent fashion. We propose intuitively appealing, easy-to-implement utility functions. As in most sequential design problems, an exact solution is prohibitive. We propose a simulation-based approximation that uses decision boundaries. We apply the method to RNA-seq, microarray, and reverse-phase protein array studies and show its potential advantages. The approach has been added to the Bioconductor package gaga

An Evaluation of the Exchange Rate Forecasting Performance of the New Keynesian Model

This paper evaluates the dynamic out of sample nominal exchange rate forecasting performance of the canonical New Keynesian model of a small open economy. A novel Bayesian procedure for jointly estimating the hyperparameters and trend components of a state space representation of an approximate linear panel unobserved components representation of this New Keynesian model, conditional on prior information concerning the values of hyperparameters and trend components, is developed and applied for this purpose. In agreement with the existing empirical literature, we find that nominal exchange rate movements are difficult to forecast, with a random walk generally dominating the canonical New Keynesian model of a small open economy in terms of predictive accuracy at all horizons. Nevertheless, we find empirical support for the common practice in the theoretical open economy macroeconomics literature of imposing deterministic equality restrictions on deep structural parameters across economies, both in sample and out of sample.Exchange rate forecasting; New Keynesian model; Small open economy

Family Capitalism Corporate Governance Theory

Family firms, which are prevalent around the world both for small organizations and large corporations, are usually more performant than other types of firms. This paper draws on altruism and on the theory of incentives contracting to explain why family firms perform better. Assuming that altruism only exists in family firms, we show that the strength of family ties has an impact on the optimal contract only under asymmetric information. Then, we extend the analysis to the principal-agent supervisor setting and prove that the recruitment of family members may be seen as a device against collusion within a three-tier hierarchy.Family Capitalism; Altruism; Family Ties ;Asymmetric Information;Supervisor Agent Principal; Collusion

Dynamic Control of Explore/Exploit Trade-Off In Bayesian Optimization

Bayesian optimization offers the possibility of optimizing black-box operations not accessible through traditional techniques. The success of Bayesian optimization methods such as Expected Improvement (EI) are significantly affected by the degree of trade-off between exploration and exploitation. Too much exploration can lead to inefficient optimization protocols, whilst too much exploitation leaves the protocol open to strong initial biases, and a high chance of getting stuck in a local minimum. Typically, a constant margin is used to control this trade-off, which results in yet another hyper-parameter to be optimized. We propose contextual improvement as a simple, yet effective heuristic to counter this - achieving a one-shot optimization strategy. Our proposed heuristic can be swiftly calculated and improves both the speed and robustness of discovery of optimal solutions. We demonstrate its effectiveness on both synthetic and real world problems and explore the unaccounted for uncertainty in the pre-determination of search hyperparameters controlling explore-exploit trade-off.Comment: Accepted for publication in the proceedings of 2018 Computing Conferenc

A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences