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In autonomous robotic decision-making under uncertainty, the tradeoff between exploitation and exploration of available options must be considered. If secondary information associated with options can be utilized, such decision-making problems can often be formulated as a contextual multi-armed bandits (CMABs). In this study, we apply active inference, which has been actively studied in the field of neuroscience in recent years, as an alternative action selection strategy for CMABs. Unlike conventional action selection strategies, it is possible to rigorously evaluate the uncertainty of each option when calculating the expected free energy (EFE) associated with the decision agent's probabilistic model, as derived from the free-energy principle. We specifically address the case where a categorical observation likelihood function is used, such that EFE values are analytically intractable. We introduce new approximation methods for computing the EFE based on variational and Laplace approximations. Extensive simulation study results demonstrate that, compared to other strategies, active inference generally requires far fewer iterations to identify optimal options and generally achieves superior cumulative regret, for relatively low extra computational cost.

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the reliability of probabilistic predictions but their estimators are usually biased and inconsistent. In this work, we introduce the framework of proper calibration errors, which relates every calibration error to a proper score and provides a respective upper bound with optimal estimation properties. This relationship can be used to reliably quantify the model calibration improvement. We theoretically and empirically demonstrate the shortcomings of commonly used estimators compared to our approach. Due to the wide applicability of proper scores, this gives a natural extension of recalibration beyond classification.

Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications in practice. However, due to the computational intractability of BSGS in high-dimensional settings, developing efficient algorithms for solving BSGS remains a research hotspot. In this paper,we propose a group-splicing algorithm that iteratively detects the relevant groups and excludes the irrelevant ones. Moreover, coupled with a novel group information criterion, we develop an adaptive algorithm to determine the optimal model size. Under mild conditions, it is certifiable that our algorithm can identify the optimal subset of groups in polynomial time with high probability. Finally, we demonstrate the efficiency and accuracy of our methods by comparing them with several state-of-the-art algorithms on both synthetic and real-world datasets.

Binary stars undergo a variety of interactions and evolutionary phases, critical for predicting and explaining observed properties. Binary population synthesis with full stellar-structure and evolution simulations are computationally expensive requiring a large number of mass-transfer sequences. The recently developed binary population synthesis code POSYDON incorporates grids of MESA binary star simulations which are then interpolated to model large-scale populations of massive binaries. The traditional method of computing a high-density rectilinear grid of simulations is not scalable for higher-dimension grids, accounting for a range of metallicities, rotation, and eccentricity. We present a new active learning algorithm, psy-cris, which uses machine learning in the data-gathering process to adaptively and iteratively select targeted simulations to run, resulting in a custom, high-performance training set. We test psy-cris on a toy problem and find the resulting training sets require fewer simulations for accurate classification and regression than either regular or randomly sampled grids. We further apply psy-cris to the target problem of building a dynamic grid of MESA simulations, and we demonstrate that, even without fine tuning, a simulation set of only $\sim 1/4$ the size of a rectilinear grid is sufficient to achieve the same classification accuracy. We anticipate further gains when algorithmic parameters are optimized for the targeted application. We find that optimizing for classification only may lead to performance losses in regression, and vice versa. Lowering the computational cost of producing grids will enable future versions of POSYDON to cover more input parameters while preserving interpolation accuracies.

Evolutionary Algorithms (EAs) and Deep Reinforcement Learning (DRL) have recently been integrated to take the advantage of the both methods for better exploration and exploitation.The evolutionary part in these hybrid methods maintains a population of policy networks.However, existing methods focus on optimizing the parameters of policy network, which is usually high-dimensional and tricky for EA.In this paper, we shift the target of evolution from high-dimensional parameter space to low-dimensional action space.We propose Evolutionary Action Selection-Twin Delayed Deep Deterministic Policy Gradient (EAS-TD3), a novel hybrid method of EA and DRL.In EAS, we focus on optimizing the action chosen by the policy network and attempt to obtain high-quality actions to promote policy learning through an evolutionary algorithm. We conduct several experiments on challenging continuous control tasks.The result shows that EAS-TD3 shows superior performance over other state-of-art methods.

Finding the optimal design of a hydrodynamic or aerodynamic surface is often impossible due to the expense of evaluating the cost functions (say, with computational fluid dynamics) needed to determine the performances of the flows that the surface controls. In addition, inherent limitations of the design space itself due to imposed geometric constraints, conventional parameterization methods, and user bias can restrict {\it all} of the designs within a chosen design space regardless of whether traditional optimization methods or newer, data-driven design algorithms with machine learning are used to search the design space. We present a 2-pronged attack to address these difficulties: we propose (1) a methodology to create the design space using morphing that we call {\it Design-by-Morphing} (DbM); and (2) an optimization algorithm to search that space that uses a novel Bayesian Optimization (BO) strategy that we call {\it Mixed variable, Multi-Objective Bayesian Optimization} (MixMOBO). We apply this shape optimization strategy to maximize the power output of a hydrokinetic turbine. Applying these two strategies in tandem, we demonstrate that we can create a novel, geometrically-unconstrained, design space of a draft tube and hub shape and then optimize them simultaneously with a {\it minimum} number of cost function calls. Our framework is versatile and can be applied to the shape optimization of a variety of fluid problems.

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm regularizer is proposed to estimate the matrix parameter. Then under the (near) low-rank assumption, we analyse statistical and computational theoretical properties of global solutions of the nonconvex regularized estimator from a general point of view. In the statistical aspect, we establish the nonasymptotic recovery bound for any global solution of the nonconvex estimator, under restricted strong convexity on the loss function. In the computational aspect, we solve the nonconvex optimization problem via the proximal gradient method. The algorithm is proved to converge to a near-global solution and achieve a linear convergence rate. In addition, we also verify sufficient conditions for the general results to be held, in order to obtain probabilistic consequences for specific types of measurement errors, including the additive noise and missing data. Finally, theoretical consequences are demonstrated by several numerical experiments on corrupted errors-in-variables multi-response regression models. Simulation results reveal excellent consistency with our theory under high-dimensional scaling.

Mendelian randomization is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. Here, we focus on two-sample summary-data Mendelian randomization analyses with many correlated variants from a single gene region, and particularly on cis-Mendelian randomization studies which use protein expression as a risk factor. Such studies must rely on a small, curated set of variants from the studied region; using all variants in the region requires inverting an ill-conditioned genetic correlation matrix and results in numerically unstable causal effect estimates. We review methods for variable selection and estimation in cis-Mendelian randomization with summary-level data, ranging from stepwise pruning and conditional analysis to principal components analysis, factor analysis and Bayesian variable selection. In a simulation study, we show that the various methods have a comparable performance in analyses with large sample sizes and strong genetic instruments. However, when weak instrument bias is suspected, factor analysis and Bayesian variable selection produce more reliable inferences than simple pruning approaches, which are often used in practice. We conclude by examining two case studies, assessing the effects of LDL-cholesterol and serum testosterone on coronary heart disease risk using variants in the HMGCR and SHBG gene regions respectively.

Variational Bayesian posterior inference often requires simplifying approximations such as mean-field parametrisation to ensure tractability. However, prior work has associated the variational mean-field approximation for Bayesian neural networks with underfitting in the case of small datasets or large model sizes. In this work, we show that invariances in the likelihood function of over-parametrised models contribute to this phenomenon because these invariances complicate the structure of the posterior by introducing discrete and/or continuous modes which cannot be well approximated by Gaussian mean-field distributions. In particular, we show that the mean-field approximation has an additional gap in the evidence lower bound compared to a purpose-built posterior that takes into account the known invariances. Importantly, this invariance gap is not constant; it vanishes as the approximation reverts to the prior. We proceed by first considering translation invariances in a linear model with a single data point in detail. We show that, while the true posterior can be constructed from a mean-field parametrisation, this is achieved only if the objective function takes into account the invariance gap. Then, we transfer our analysis of the linear model to neural networks. Our analysis provides a framework for future work to explore solutions to the invariance problem.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.