Implicit Processes (IPs) are flexible priors that can describe models such as Bayesian neural networks, neural samplers and data generators. IPs allow for approximate inference in function-space. This avoids some degenerate problems of parameter-space approximate inference due to the high number of parameters and strong dependencies. For this, an extra IP is often used to approximate the posterior of the prior IP. However, simultaneously adjusting the parameters of the prior IP and the approximate posterior IP is a challenging task. Existing methods that can tune the prior IP result in a Gaussian predictive distribution, which fails to capture important data patterns. By contrast, methods producing flexible predictive distributions by using another IP to approximate the posterior process cannot fit the prior IP to the observed data. We propose here a method that can carry out both tasks. For this, we rely on an inducing-point representation of the prior IP, as often done in the context of sparse Gaussian processes. The result is a scalable method for approximate inference with IPs that can tune the prior IP parameters to the data, and that provides accurate non-Gaussian predictive distributions.

We present extensive empirical evidence showing that current Bayesian simulation-based inference algorithms are inadequate for the falsificationist methodology of scientific inquiry. Our results collected through months of experimental computations show that all benchmarked algorithms -- (S)NPE, (S)NRE, SNL and variants of ABC -- may produce overconfident posterior approximations, which makes them demonstrably unreliable and dangerous if one's scientific goal is to constrain parameters of interest. We believe that failing to address this issue will lead to a well-founded trust crisis in simulation-based inference. For this reason, we argue that research efforts should now consider theoretical and methodological developments of conservative approximate inference algorithms and present research directions towards this objective. In this regard, we show empirical evidence that ensembles are consistently more reliable.

Interpretable, highly accurate segmentation models have the potential to provide substantial benefit for automated clinical workflows. Estimating the uncertainty in a model's prediction (predictive uncertainty) can help clinicians quantify, visualize, and communicate model performance. Variational inference, Monte Carlo dropout, and ensembles are reliable methods to estimate predictive uncertainty. Interpretable artificial intelligence is key for clinical translation of this technology. Artificial intelligence (AI) has seen a resurgence in popularity since the development of deep learning (DL), a method to learn representations within data with multiple levels of abstraction (1). DL frameworks have been widely successful for a variety of applications, including image object recognition and detection tasks where there is a particular interest in applying this technology to interpret complex medical images (2). As modern DL frameworks are structured through multiple hidden layers of network weights, these networks are coined as black box models.

Autonomous cyber-physical systems (CPS) can improve safety and efficiency for safety-critical applications, but require rigorous testing before deployment. The complexity of these systems often precludes the use of formal verification and real-world testing can be too dangerous during development. Therefore, simulation-based techniques have been developed that treat the system under test as a black box operating in a simulated environment. Safety validation tasks include finding disturbances in the environment that cause the system to fail (falsification), finding the most-likely failure, and estimating the probability that the system fails. Motivated by the prevalence of safety-critical artificial intelligence, this work provides a survey of state-of-the-art safety validation techniques for CPS with a focus on applied algorithms and their modifications for the safety validation problem. We present and discuss algorithms in the domains of optimization, path planning, reinforcement learning, and importance sampling. Problem decomposition techniques are presented to help scale algorithms to large state spaces, which are common for CPS. A brief overview of safety-critical applications is given, including autonomous vehicles and aircraft collision avoidance systems. Finally, we present a survey of existing academic and commercially available safety validation tools.

As the primary cause of software defects, human error is the key to understanding, and perhaps to predicting and avoiding them. Little research has been done to predict defects on the basis of the cognitive errors that cause them. This paper proposes an approach to predicting software defects through knowledge about the cognitive mechanisms of human errors. Our theory is that the main process behind a software defect is that an error-prone scenario triggers human error modes, which psychologists have observed to recur across diverse activities. Software defects can then be predicted by identifying such scenarios, guided by this knowledge of typical error modes. The proposed idea emphasizes predicting the exact location and form of a possible defect. We conducted two case studies to demonstrate and validate this approach, with 55 programmers in a programming competition and 5 analysts serving as the users of the approach. We found it impressive that the approach was able to predict, at the requirement phase, the exact locations and forms of 7 out of the 22 (31.8%) specific types of defects that were found in the code. The defects predicted tended to be common defects: their occurrences constituted 75.7% of the total number of defects in the 55 developed programs; each of them was introduced by at least two persons. The fraction of the defects introduced by a programmer that were predicted was on average (over all programmers) 75%. Furthermore, these predicted defects were highly persistent through the debugging process. If the prediction had been used to successfully prevent these defects, this could have saved 46.2% of the debugging iterations. This excellent capability of forecasting the exact locations and forms of possible defects at the early phases of software development recommends the approach for substantial benefits to defect prevention and early detection.

POI recommendation is a key task in tourism information systems. However, in contrast to conventional point of interest (POI) recommender systems, the available data is extremely sparse; most tourist visit a few sightseeing spots once and most of these spots have no check-in data from new tourists. Most conventional systems rank sightseeing spots based on their popularity, reputations, and category-based similarities with users' preferences. They do not clarify what users can experience in these spots, which makes it difficult to meet diverse tourism needs. To this end, in this work, we propose a mechanism to recommend POIs to tourists. Our mechanism include two components: one is a probabilistic model that reveals the user behaviors in tourism; the other is a pseudo rating mechanism to handle the cold-start issue in POIs recommendations. We carried out extensive experiments with two datasets collected from Flickr. The experimental results demonstrate that our methods are superior to the state-of-the-art methods in both the recommendation performances (precision, recall and F-measure) and fairness. The experimental results also validate the robustness of the proposed methods, i.e., our methods can handle well the issue of data sparsity.

After deploying a clinical prediction model, subsequently collected data can be used to fine-tune its predictions and adapt to temporal shifts. Because model updating carries risks of over-updating/fitting, we study online methods with performance guarantees. We introduce two procedures for continual recalibration or revision of an underlying prediction model: Bayesian logistic regression (BLR) and a Markov variant that explicitly models distribution shifts (MarBLR). We perform empirical evaluation via simulations and a real-world study predicting COPD risk. We derive "Type I and II" regret bounds, which guarantee the procedures are non-inferior to a static model and competitive with an oracle logistic reviser in terms of the average loss. Both procedures consistently outperformed the static model and other online logistic revision methods. In simulations, the average estimated calibration index (aECI) of the original model was 0.828 (95%CI 0.818-0.938). Online recalibration using BLR and MarBLR improved the aECI, attaining 0.265 (95%CI 0.230-0.300) and 0.241 (95%CI 0.216-0.266), respectively. When performing more extensive logistic model revisions, BLR and MarBLR increased the average AUC (aAUC) from 0.767 (95%CI 0.765-0.769) to 0.800 (95%CI 0.798-0.802) and 0.799 (95%CI 0.797-0.801), respectively, in stationary settings and protected against substantial model decay. In the COPD study, BLR and MarBLR dynamically combined the original model with a continually-refitted gradient boosted tree to achieve aAUCs of 0.924 (95%CI 0.913-0.935) and 0.925 (95%CI 0.914-0.935), compared to the static model's aAUC of 0.904 (95%CI 0.892-0.916). Despite its simplicity, BLR is highly competitive with MarBLR. MarBLR outperforms BLR when its prior better reflects the data. BLR and MarBLR can improve the transportability of clinical prediction models and maintain their performance over time.

The need to avoid confident predictions on unfamiliar data has sparked interest in out-of-distribution (OOD) detection. It is widely assumed that Bayesian neural networks (BNNs) are well suited for this task, as the endowed epistemic uncertainty should lead to disagreement in predictions on outliers. In this paper, we question this assumption and show that proper Bayesian inference with function space priors induced by neural networks does not necessarily lead to good OOD detection. To circumvent the use of approximate inference, we start by studying the infinite-width case, where Bayesian inference can be exact due to the correspondence with Gaussian processes. Strikingly, the kernels induced under common architectural choices lead to uncertainties that do not reflect the underlying data generating process and are therefore unsuited for OOD detection. Importantly, we find this OOD behavior to be consistent with the corresponding finite-width networks. Desirable function space properties can be encoded in the prior in weight space, however, this currently only applies to a specified subset of the domain and thus does not inherently extend to OOD data. Finally, we argue that a trade-off between generalization and OOD capabilities might render the application of BNNs for OOD detection undesirable in practice. Overall, our study discloses fundamental problems when naively using BNNs for OOD detection and opens interesting avenues for future research.

This paper managed to induce probability theory (sigma system) and possibility theory (max system) respectively from randomness and fuzziness, through which the premature theory of possibility is expected to be well founded. Such an objective is achieved by addressing three open key issues: a) the lack of clear mathematical definitions of randomness and fuzziness; b) the lack of intuitive mathematical definition of possibility; c) the lack of abstraction procedure of the axiomatic definitions of probability/possibility from their intuitive definitions. Especially, the last issue involves the question why the key axiom of "maxitivity" is adopted for possibility measure. By taking advantage of properties of the well-defined randomness and fuzziness, we derived the important conclusion that "max" is the only but un-strict disjunctive operator that is applicable across the fuzzy event space, and is an exact operator for fuzzy feature extraction that assures the max inference is an exact mechanism. It is fair to claim that the long-standing problem of lack of consensus to the foundation of possibility theory is well resolved, which would facilitate wider adoption of possibility theory in practice and promote cross prosperity of the two uncertainty theories of probability and possibility. Randomness and fuzziness are well recognized as two kinds of fundamental uncertainties of this world. It remains as an open topic on how to correctly comprehend these uncertainties and effectively handle them in practice. For modeling of random uncertainty, probability theory and the derivative subjects of statistics and stochastic process are no doubt the classic tool set. Probability theory, which satisfies the key axiom of "additivity" [18,23], has grown up to be mature, upon which nearly the whole building of information sciences is based and applications of which could be found over a great diversity of communities [22, 29,41,42,52,53].

We study the model-based reward-free reinforcement learning with linear function approximation for episodic Markov decision processes (MDPs). In this setting, the agent works in two phases. In the exploration phase, the agent interacts with the environment and collects samples without the reward. In the planning phase, the agent is given a specific reward function and uses samples collected from the exploration phase to learn a good policy. We propose a new provably efficient algorithm, called UCRL-RFE under the Linear Mixture MDP assumption, where the transition probability kernel of the MDP can be parameterized by a linear function over certain feature mappings defined on the triplet of state, action, and next state. We show that to obtain an $\epsilon$-optimal policy for arbitrary reward function, UCRL-RFE needs to sample at most $\tilde O(H^5d^2\epsilon^{-2})$ episodes during the exploration phase. Here, $H$ is the length of the episode, $d$ is the dimension of the feature mapping. We also propose a variant of UCRL-RFE using Bernstein-type bonus and show that it needs to sample at most $\tilde O(H^4d(H + d)\epsilon^{-2})$ to achieve an $\epsilon$-optimal policy. By constructing a special class of linear Mixture MDPs, we also prove that for any reward-free algorithm, it needs to sample at least $\tilde \Omega(H^2d\epsilon^{-2})$ episodes to obtain an $\epsilon$-optimal policy. Our upper bound matches the lower bound in terms of the dependence on $\epsilon$ and the dependence on $d$ if $H \ge d$.