A hybrid Bayesian/ frequentist approach is presented for the Simultaneous Localization and Mapping Problem (SLAM). A frequentist approach is proposed for mapping with time varying robotic poses and is generalized to the case when the robotic pose is both time varying and uncertain. The SLAM problem is then solved in two steps: 1) the robot is localized with respect to a sparse set of landmarks ...

Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such est...

Bayes estimators are well known to provide a means incorporate prior knowledge that can be expressed in terms of single distribution. However, when this is too vague express with prior, an alternative approach needed. Gamma-minimax such approach. These minimize the worst-case risk over set Γ distributions compatible available knowledge. Traditionally, Gamma-minimaxity defined for parametric mod...

Quantification learning is the task of prevalence estimation for a test population using predictions from classifier trained on different population. methods assume that sensitivities and specificities are either perfect or transportable training to These assumptions inappropriate in presence dataset shift, when misclassification rates not representative those under shift has been addressed onl...

The possibility of employing explicitly defined functions of the observations as estimators of parametric functions in nonlinear regression analysis is explored. A general theory of best average mean square error estimation leading to explicit estimators is set forth. Such estimators are given a Bayesian interpretation as Fourier expansions of the estimator which minimizes expected posterior sq...

We consider finite-horizon fitted Q-iteration with linear function approximation to learn a policy from a training set of trajectories. We show that fitted Q-iteration can give biased estimates and invalid confidence intervals for the parameters that feature in the policy. We propose a regularized estimator called soft-threshold estimator, derive it as an approximate empirical Bayes estimator, ...

Summary Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification uncertainty estimated clusters is a disadvantage. Model-based based on mixture models provides an alternative approach, but methods face computational problems highly sensitive to choice kernel. In this article we propose generalized Bayes f...

We propose an adaptive shrinkage estimator for use in regression problems charaterized by many predictors, such as wavelet estimation. Adaptive estimators perform well over a variety of circumstances, such as regression models in which few, some or many coefficients are zero. Our estimator, PolyShrink, adaptively varies the amount of shrinkage to suit the estimation task. Whereas hard threshold...