We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of the Bayesian model averaging for improving the uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

Most predictive models assume that training and test data are generated from a stationary process. However, this assumption does not hold true in practice. In this paper, we consider the scenario of a gradual concept drift due to the underlying non-stationarity of the data source. While previous work has investigated this scenario under a supervised-learning and adaption conditions, few have addressed the common, real-world scenario when labels are only available during training. We propose a novel, iterative algorithm for unsupervised adaptation of predictive models. We show that the performance of our batch adapted prediction algorithm is better than that of its corresponding unadapted version. The proposed algorithm provides similar (or better, in most cases) performance within significantly less run time compared to other state of the art methods.

We discuss the problem of performing similarity search over function spaces. To perform search over such spaces in a reasonable amount of time, we use {\it locality-sensitive hashing} (LSH). We present two methods that allow LSH functions on $\mathbb{R}^N$ to be extended to $L^p$ spaces: one using function approximation in an orthonormal basis, and another using (quasi-)Monte Carlo-style techniques. We use the presented hashing schemes to construct an LSH family for Wasserstein distance over one-dimensional, continuous probability distributions.

Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a classifier to distinguish between pairs of parameter-observation samples generated using the simulator and pairs sampled from some reference distribution, which implicitly learns a density ratio proportional to the likelihood. Another popular class of methods fits a conditional distribution to the parameter posterior directly, and a particular recent variant allows for the use of flexible neural density estimators for this task. In this work, we show that both of these approaches can be unified under a general contrastive learning scheme, and clarify how they should be run and compared.

With the overwhelming online products available in recent years, there is an increasing need to filter and deliver relevant personalized advice for users. Recommender systems solve this problem by modeling and predicting individual preferences for a great variety of items such as movies, books or research articles. In this chapter, we explore rigorous network-based models that outperform leading approaches for recommendation. The network models we consider are based on the explicit assumption that there are groups of individuals and of items, and that the preferences of an individual for an item are determined only by their group memberships. The accurate prediction of individual user preferences over items can be accomplished by different methodologies, such as Monte Carlo sampling or Expectation-Maximization methods, the latter resulting in a scalable algorithm which is suitable for large datasets.

We present a new operator-free, measure-theoretic definition of the conditional mean embedding as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of marginal distributions has been defined rigorously, the existing operator-based approach of the conditional version lacks a rigorous definition, and depends on strong assumptions that hinder its analysis. Our definition does not impose any of the assumptions that the operator-based counterpart requires. We derive a natural regression interpretation to obtain empirical estimates, and provide a thorough analysis of its properties, including universal consistency. As natural by-products, we obtain the conditional analogues of the Maximum Mean Discrepancy and Hilbert-Schmidt Independence Criterion, and demonstrate their behaviour via simulations.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate that the {\sc BregmanTron} substantially outperforms the {\sc SLIsotron}, and that the loss it learns can be minimized by other algorithms for different tasks, thereby opening the interesting problem of \textit{loss transfer} between domains.

Tidy-up tasks by service robots in home environments are challenging in the application of robotics because they involve various interactions with the environment. In particular, robots are required not only to grasp, move, and release various home objects, but also plan the order and positions where to put them away. In this paper, we propose a novel planning method that can efficiently estimate the order and positions of the objects to be tidied up based on the learning of the parameters of a probabilistic generative model. The model allows the robot to learn the distributions of co-occurrence probability of objects and places to tidy up by using multimodal sensor information collected in a tidied environment. Additionally, we develop an autonomous robotic system to perform the tidy-up operation. We evaluate the effectiveness of the proposed method in an experimental simulation that reproduces the conditions of the Tidy Up Here task of the World Robot Summit international robotics competition. The simulation results showed that the proposed method enables the robot to successively tidy up several objects and achieves the best task score compared to baseline tidy-up methods.

Data gathered from multiple sensors can be effectively fused for accurate monitoring of many engineering applications. In the last few years, one of the most sought after applications for multi sensor fusion has been fault diagnosis. Dempster-Shafer Theory of Evidence along with Dempsters Combination Rule is a very popular method for multi sensor fusion which can be successfully applied to fault diagnosis. But if the information obtained from the different sensors shows high conflict, the classical Dempsters Combination Rule may produce counter-intuitive result. To overcome this shortcoming, this paper proposes an improved combination rule for multi sensor data fusion. Numerical examples have been put forward to show the effectiveness of the proposed method. Comparative analysis has also been carried out with existing methods to show the superiority of the proposed method in multi sensor fault diagnosis.

The curse of dimensionality is a critical challenge in Bayesian inference for high dimensional parameters. In this work, we address this challenge by developing a projected Stein variational gradient descent (pSVGD) method, which projects the parameters into a subspace that is adaptively constructed using the gradient of the log-likelihood, and applies SVGD for the much lower-dimensional coefficients of the projection. We provide an upper bound for the projection error with respect to the posterior and demonstrate the accuracy (compared to SVGD) and scalability of pSVGD with respect to the number of parameters, samples, data points, and processor cores.