Model selection and local geometry

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases---including common classes of causal or graphical models, as well as time series models---distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametric $n^{-1/2}$ (typically we will require $n^{-1/4}$ or slower); in other words, to distinguish between the models we need large effect sizes or very large sample sizes. Second, we show that under even weaker conditions on their tangent cones, models in these classes cannot be made simultaneously convex by a reparameterization. This shows that Bayesian network models, amongst others, cannot be learned directly with a convex method similar to the graphical lasso. However, we are able to use our results to suggest methods for model selection that learn the tangent space directly, rather than the model itself. In particular, we give a generic algorithm for learning Bayesian network models

Local Search Techniques for Constrained Portfolio Selection Problems

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the cardinality of the portfolio and on the quantity of individual shares. Such constraints better capture the real-world trading system, but make the problem more difficult to be solved with exact methods. We explore the use of local search techniques, mainly tabu search, for the portfolio selection problem. We compare and combine previous work on portfolio selection that makes use of the local search approach and we propose new algorithms that combine different neighborhood relations. In addition, we show how the use of randomization and of a simple form of adaptiveness simplifies the setting of a large number of critical parameters. Finally, we show how our techniques perform on public benchmarks.Comment: 22 pages, 3 figure

Policy Learning with Hypothesis based Local Action Selection

For robots to be able to manipulate in unknown and unstructured environments the robot should be capable of operating under partial observability of the environment. Object occlusions and unmodeled environments are some of the factors that result in partial observability. A common scenario where this is encountered is manipulation in clutter. In the case that the robot needs to locate an object of interest and manipulate it, it needs to perform a series of decluttering actions to accurately detect the object of interest. To perform such a series of actions, the robot also needs to account for the dynamics of objects in the environment and how they react to contact. This is a non trivial problem since one needs to reason not only about robot-object interactions but also object-object interactions in the presence of contact. In the example scenario of manipulation in clutter, the state vector would have to account for the pose of the object of interest and the structure of the surrounding environment. The process model would have to account for all the aforementioned robot-object, object-object interactions. The complexity of the process model grows exponentially as the number of objects in the scene increases. This is commonly the case in unstructured environments. Hence it is not reasonable to attempt to model all object-object and robot-object interactions explicitly. Under this setting we propose a hypothesis based action selection algorithm where we construct a hypothesis set of the possible poses of an object of interest given the current evidence in the scene and select actions based on our current set of hypothesis. This hypothesis set tends to represent the belief about the structure of the environment and the number of poses the object of interest can take. The agent's only stopping criterion is when the uncertainty regarding the pose of the object is fully resolved.Comment: RLDM abstrac

Bidirectional branch and bound for controlled variable selection. Part III: local average loss minimization

The selection of controlled variables (CVs) from available measurements through exhaustive search is computationally forbidding for large-scale processes. We have recently proposed novel bidirectional branch and bound (B-3) approaches for CV selection using the minimum singular value (MSV) rule and the local worst- case loss criterion in the framework of self-optimizing control. However, the MSV rule is approximate and worst-case scenario may not occur frequently in practice. Thus, CV selection by minimizing local average loss can be deemed as most reliable. In this work, the B-3 approach is extended to CV selection based on local average loss metric. Lower bounds on local average loss and, fast pruning and branching algorithms are derived for the efficient B-3 algorithm. Random matrices and binary distillation column case study are used to demonstrate the computational efficiency of the proposed method

Perturbation selection and influence measures in local influence analysis

Cook's [J. Roy. Statist. Soc. Ser. B 48 (1986) 133--169] local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model. However, no rigorous approach has been developed to address two fundamental issues: the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative. The aim of this paper is to develop a differential--geometrical framework of a perturbation model (called the perturbation manifold) and utilize associated metric tensor and affine curvatures to resolve these issues. We will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model. Moreover, we will introduce new influence measures that are applicable to objective functions at any point. Examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations.Comment: Published in at http://dx.doi.org/10.1214/009053607000000343 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Self-selection and Earnings of Migrants: Evidence from Rural China

Using data from a rural household survey in China, this paper explores the link between employment choice (nonworking, local farm work, local nonfarm work and migratory work) and migrant earnings. We find significant self-selection in migration. Youths, males, better-educated individuals and those in good health are more likely to migrate. In terms of unobserved characteristics, we find positive selection in migration as related to the alternatives of not working and local farm work, and insignificant self-selection as related to local nonfarm work. Controlling for self-selection, the wage returns to gender (male), education and health are lower than those obtained from simple ordinary least squares (OLS), and the returns to experience are higher. More importantly, we find different self-selection between individuals who have moved as pioneers and migrants from households in which other members have already migrated.Migration, Self-selection, Pioneer migrants

The left intraparietal sulcus modulates the selection of low salient stimuli

Neuropsychological and functional imaging studies have suggested a general right hemisphere advantage for processing global visual information and a left hemisphere advantage for processing local information. In contrast, a recent transcranial magnetic stimulation study [Mevorach, C., Humphreys, G. W., & Shalev, L. Opposite biases in salience-based selection for the left and right posterior parietal cortex. Nature Neuroscience, 9, 740-742, 2006b] demonstrated that functional lateralization of selection in the parietal cortices on the basis of the relative salience of stimuli might provide an alternative explanation for previous results. In the present study, we applied a whole-brain analysis of the functional magnetic resonance signal when participants responded to either the local or the global levels of hierarchical figures. The task (respond to local or global) was crossed with the saliency of the target level (local salient, global salient) to provide, for the first time, a direct contrast between brain activation related to the stimulus level and that related to relative saliency. We found evidence for lateralization of salience-based selection but not for selection based on the level of processing. Activation along the left intraparietal sulcus (IPS) was found when a low saliency stimulus had to be selected irrespective of its level. A control task showed that this was not simply an effect of task difficulty. The data suggest a specific role for regions along the left IPS in salience-based selection, supporting the argument that previous reports of lateralized responses to local and global stimuli were contaminated by effects of saliency

Recovery and sanitary selection of local vines of the Sardinia

A study was made on the recovery genotypes local grapevine with the aim to conserve them and to evaluate their health status and thus to improve the quality of the propagation material. Clone accessions of 61 vines were grafted and placed in a germoplasma field. The varieties that were considered enologically valuable were subjected to sanitary selection. Some vines showed indubitable healthy qualities, and should be immediately evaluated from an economical point view and then certificated. Possible sanitation treatments were also evaluated, with the aim of extending the number clone accessions to be included in experimental trials to access their yield