Ithaca is a Fuzzy Logic (FL) plugin for developing artificial intelligence systems within the Unity game engine. Its goal is to provide an intuitive and natural way to build advanced artificial intelligence systems, making the implementation of such a system faster and more affordable. The software is made up by a C\# framework and an Application Programming Interface (API) for writing inference systems, as well as a set of tools for graphic development and debugging. Additionally, a Fuzzy Control Language (FCL) parser is provided in order to import systems previously defined using this standard.

This paper concerns realizing highly efficient information-theoretic robot exploration with desired performance in complex scenes. We build a continuous lightweight inference model to predict the mutual information (MI) and the associated prediction confidence of the robot's candidate actions which have not been evaluated explicitly. This allows the decision-making stage in robot exploration to run with a logarithmic complexity approximately, this will also benefit online exploration in large unstructured, and cluttered places that need more spatial samples to assess and decide. We also develop an objective function to balance the local optimal action with the highest MI value and the global choice with high prediction variance. Extensive numerical and dataset simulations show the desired efficiency of our proposed method without losing exploration performance in different environments. We also provide our open-source implementation codes released on GitHub for the robot community.

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its asymptotic behavior in a non-asymptotic fashion. An important feature of our bound is that its dimension dependency is captured by the effective dimension $\unicode{x2013}$ the trace of the limiting sandwich covariance $\unicode{x2013}$ which can be much smaller than the parameter dimension in some regimes. We then illustrate how the bound can be used to obtain a confidence set whose shape is adapted to the optimization landscape induced by the loss function. Unlike previous works that rely heavily on the strong convexity of the loss function, we only assume the Hessian is lower bounded at optimum and allow it to gradually becomes degenerate. This property is formalized by the notion of generalized self-concordance which originated from convex optimization. Moreover, we demonstrate how the effective dimension can be estimated from data and characterize its estimation accuracy. We apply our results to maximum likelihood estimation with generalized linear models, score matching with exponential families, and hypothesis testing with Rao's score test.

Multi-fidelity Kriging model is a promising technique in surrogate-based design as it can balance the model accuracy and cost of sample preparation by fusing low- and high-fidelity data. However, the cost for building a multi-fidelity Kriging model increases significantly with the increase of the problem dimension. To attack this issue, an efficient Hierarchical Kriging modeling method is proposed. In building the low-fidelity model, the maximal information coefficient is utilized to calculate the relative value of the hyperparameter. With this, the maximum likelihood estimation problem for determining the hyperparameters is transformed as a one-dimension optimization problem, which can be solved in an efficient manner and thus improve the modeling efficiency significantly. A local search is involved further to exploit the search space of hyperparameters to improve the model accuracy. The high-fidelity model is built in a similar manner with the hyperparameter of the low-fidelity model served as the relative value of the hyperparameter for high-fidelity model. The performance of the proposed method is compared with the conventional tuning strategy, by testing them over ten analytic problems and an engineering problem of modeling the isentropic efficiency of a compressor rotor. The empirical results demonstrate that the modeling time of the proposed method is reduced significantly without sacrificing the model accuracy. For the modeling of the isentropic efficiency of the compressor rotor, the cost saving associated with the proposed method is about 90% compared with the conventional strategy. Meanwhile, the proposed method achieves higher accuracy.

Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. It is therefore of paramount importance to quantify the uncertainties associated to the inversion process to ease the subsequent interpretation and decision making processes. Within this framework of reference, sampling from a target posterior provides a fundamental approach to quantifying the uncertainty in seismic inversion. However, selecting appropriate prior information in a probabilistic inversion is crucial, yet non-trivial, as it influences the ability of a sampling-based inference in providing geological realism in the posterior samples. To overcome such limitations, we present a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a CNN-based denoiser by means of the Plug-and-Play methods. We call this new algorithm Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) and demonstrate its ability in producing high-resolution, trustworthy samples representative of the subsurface structures, which we argue could be used for post-inference tasks such as reservoir modelling and history matching. To validate the proposed method, numerical tests are performed on both synthetic and field post-stack seismic data.

We consider the problem of constructing minimax rate-optimal estimators for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. Minimax rate-optimal estimators for such functionals are typically constructed through higher-order bias corrections of plug-in and one-step type estimators and, in turn, depend on estimators of nuisance functions. In this paper, we consider a parallel question of interest regarding the optimality and/or sub-optimality of plug-in and one-step bias-corrected estimators for the specific doubly robust functional of interest. Specifically, we verify that by using undersmoothing and sample splitting techniques when constructing nuisance function estimators, one can achieve minimax rates of convergence in all H\"older smoothness classes of the nuisance functions (i.e. the propensity score and outcome regression) provided that the marginal density of the covariates is sufficiently regular. Additionally, by demonstrating suitable lower bounds on these classes of estimators, we demonstrate the necessity to undersmooth the nuisance function estimators to obtain minimax optimal rates of convergence.

In this paper, we consider the problem of adjusting the exploration rate when using value-of-information-based exploration. We do this by converting the value-of-information optimization into a problem of finding equilibria of a flow for a changing exploration rate. We then develop an efficient path-following scheme for converging to these equilibria and hence uncovering optimal action-selection policies. Under this scheme, the exploration rate is automatically adapted according to the agent's experiences. Global convergence is theoretically assured. We first evaluate our exploration-rate adaptation on the Nintendo GameBoy games Centipede and Millipede. We demonstrate aspects of the search process, like that it yields a hierarchy of state abstractions. We also show that our approach returns better policies in fewer episodes than conventional search strategies relying on heuristic, annealing-based exploration-rate adjustments. We then illustrate that these trends hold for deep, value-of-information-based agents that learn to play ten simple games and over forty more complicated games for the Nintendo GameBoy system. Performance either near or well above the level of human play is observed.

Objective: Convolutional neural networks (CNNs) have demonstrated promise in automated cardiac magnetic resonance image segmentation. However, when using CNNs in a large real-world dataset, it is important to quantify segmentation uncertainty and identify segmentations which could be problematic. In this work, we performed a systematic study of Bayesian and non-Bayesian methods for estimating uncertainty in segmentation neural networks. Methods: We evaluated Bayes by Backprop, Monte Carlo Dropout, Deep Ensembles, and Stochastic Segmentation Networks in terms of segmentation accuracy, probability calibration, uncertainty on out-of-distribution images, and segmentation quality control. Results: We observed that Deep Ensembles outperformed the other methods except for images with heavy noise and blurring distortions. We showed that Bayes by Backprop is more robust to noise distortions while Stochastic Segmentation Networks are more resistant to blurring distortions. For segmentation quality control, we showed that segmentation uncertainty is correlated with segmentation accuracy for all the methods. With the incorporation of uncertainty estimates, we were able to reduce the percentage of poor segmentation to 5% by flagging 31--48% of the most uncertain segmentations for manual review, substantially lower than random review without using neural network uncertainty (reviewing 75--78% of all images). Conclusion: This work provides a comprehensive evaluation of uncertainty estimation methods and showed that Deep Ensembles outperformed other methods in most cases. Significance: Neural network uncertainty measures can help identify potentially inaccurate segmentations and alert users for manual review.

The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the quantity to be estimated depend on the estimate of its current value. This type of estimation problems has been formulated as the dynamic inference problem. In this work, we formulate the Bayesian learning problem for dynamic inference, where the unknown quantity-generation model is assumed to be randomly drawn according to a random model parameter. We derive the optimal Bayesian learning rules, both offline and online, to minimize the inference loss. Moreover, learning for dynamic inference can serve as a meta problem, such that all familiar machine learning problems, including supervised learning, imitation learning and reinforcement learning, can be cast as its special cases or variants. Gaining a good understanding of this unifying meta problem thus sheds light on a broad spectrum of machine learning problems as well.

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.