Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. The encouraging results combined with advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). We contribute to this development by presenting a probabilistic VFM based on a Bayesian neural network. We consider homoscedastic and heteroscedastic measurement noise, and show how to train the models using maximum a posteriori estimation and variational inference. We study the methods by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where we achieve an average error of 5-6% and 9-13% for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. The difference in prediction performance and uncertainty on historical and future data is explored in detail, and the findings motivate the development of alternative strategies for data-driven VFM.

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a simple generalization of the adaptive interpolation method in Bayesian inference for linear regimes to sub-linear ones. A modification of the well-known approximate message passing algorithm to approach the MMSE fundamental limit is also proposed. Our results show that the traditional linear assumption between the signal dimension and number of observations in the replica and adaptive interpolation methods is not necessary for sparse signals. They also show how to modify the existing well-known AMP algorithms for linear regimes to sub-linear ones.

There is a clear need to involve patients in medical decisions. However, cognitive psychological research has highlighted the cognitive limitations of humans with respect to 1. Probabilistic assessment of the patient state and of potential outcomes of various decisions, 2. Elicitation of the patient utility function, and 3. Integration of the probabilistic knowledge and of patient preferences to determine the optimal strategy. Therefore, without adequate computational support, current shared decision models have severe ethical deficiencies. An informed consent model unfairly transfers the responsibility to a patient who does not have the necessary knowledge, nor the integration capability. A paternalistic model endows with exaggerated power a physician who might not be aware of the patient preferences, is prone to multiple cognitive biases, and whose computational integration capability is bounded. Recent progress in Artificial Intelligence suggests adding a third agent: a computer, in all deliberative medical decisions: Non emergency medical decisions in which more than one alternative exists, the patient preferences can be elicited, the therapeutic alternatives might be influenced by these preferences, medical knowledge exists regarding the likelihood of the decision outcomes, and there is sufficient decision time. Ethical physicians should exploit computational decision support technologies, neither making the decisions solely on their own, nor shirking their duty and shifting the responsibility to patients in the name of informed consent. The resulting three way (patient, care provider, computer) human machine model that we suggest emphasizes the patient preferences, the physician knowledge, and the computational integration of both aspects, does not diminish the physician role, but rather brings out the best in human and machine.

We present a framework for analysing agent incentives using causal influence diagrams. We establish that a well-known criterion for value of information is complete. We propose a new graphical criterion for value of control, establishing its soundness and completeness. We also introduce two new concepts for incentive analysis: response incentives indicate which changes in the environment affect an optimal decision, while instrumental control incentives establish whether an agent can influence its utility via a variable X. For both new concepts, we provide sound and complete graphical criteria. We show by example how these results can help with evaluating the safety and fairness of an AI system.

The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would otherwise remain unknown. However, these algorithms are less effective when the input data are limited in terms of sample size, which is often the case when working with real data. This paper focuses on purely machine learned and purely knowledge-based BNs and investigates their differences in terms of graphical structure and how well the implied statistical models explain the data. The tests are based on four previous case studies whose BN structure was determined by domain knowledge. Using various metrics, we compare the knowledge-based graphs to the machine learned graphs generated from various algorithms implemented in TETRAD spanning all three classes of learning. The results show that, while the algorithms produce graphs with much higher model selection score, the knowledge-based graphs are more accurate predictors of variables of interest. Maximising score fitting is ineffective in the presence of limited sample size because the fitting becomes increasingly distorted with limited data, guiding algorithms towards graphical patterns that share higher fitting scores and yet deviate considerably from the true graph. This highlights the value of causal knowledge in these cases, as well as the need for more appropriate fitting scores suitable for limited data. Lastly, the experiments also provide new evidence that support the notion that results from simulated data tell us little about actual real-world performance.

Combination and aggregation techniques can improve forecast accuracy substantially. This also holds for probabilistic forecasting methods where full predictive distributions are combined. There are several time-varying and adaptive weighting schemes like Bayesian model averaging (BMA). However, the performance of different forecasters may vary not only over time but also in parts of the distribution. So one may be more accurate in the center of the distributions, and other ones perform better in predicting the distribution's tails. Consequently, we introduce a new weighting procedure that considers both varying performance across time and the distribution. We discuss pointwise online aggregation algorithms that optimize with respect to the continuous ranked probability score (CRPS). After analyzing the theoretical properties of a fully adaptive Bernstein online aggregation (BOA) method, we introduce smoothing procedures for pointwise CRPS learning. The properties are confirmed and discussed using simulation studies. Additionally, we illustrate the performance in a forecasting study for carbon markets. In detail, we predict the distribution of European emission allowance prices.

We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the $E_\gamma$-divergence. We then use this equivalent formula to express LDP guarantees of privacy mechanisms in terms of contraction coefficients of arbitrary $f$-divergences. When combined with standard estimation-theoretic tools (such as Le Cam's and Fano's converse methods), this result allows us to study the trade-off between privacy and utility in several testing and minimax and Bayesian estimation problems.

We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine learning via Bayesian Additive Regression Trees (BART). Error terms and their distribution are inferred using Dirichlet Process mixtures. Simulated and real examples show that when the true functions are linear, little is lost. But when nonlinearities are present, dramatic improvements are obtained with virtually no manual tuning.

This idea was further extended in (Xie et al., 2017), where Symmetric positive definite (SPD) matrices are widely used sub-manifold learning for dimension reduction is used before data structures in many disciplines, e.g. in medical imaging the tangent space approximation. However, the first-order approximations (Penne et al., 2006) and computer vision as covariance region can lead to undesirable distortion, especially in descriptors (Tuzel et al., 2006; Jayasumana et al., 2015), regions far from the tangent space origin (Tuzel et al., 2008; as well as in brain-computer interface (BCI) (Congedo et al., Jayasumana et al., 2015). The mean of the SPD matrices is a 2017), etc. Endowed with an appropriate metric, SPD matrices frequently used candidate for the tangent space origin, however, form a curved Riemannian manifold. Consequently, many popular no theoretical proof exists to guarantee the mean yields the best machine learning algorithms such as linear discriminant tangent space approximation for the data (Tuzel et al., 2008).

Medical toxicology is the clinical specialty that treats the toxic effects of substances, be it an overdose, a medication error, or a scorpion sting. The volume of toxicological knowledge and research has, as with other medical specialties, outstripped the ability of the individual clinician to entirely master and stay current with it. The application of machine learning techniques to medical toxicology is challenging because initial treatment decisions are often based on a few pieces of textual data and rely heavily on prior knowledge. ML techniques often do not represent knowledge in a way that is transparent for the physician, raising barriers to usability. Rule-based systems and decision tree learning are more transparent approaches, but often generalize poorly and require expert curation to implement and maintain. Here, we construct a probabilistic logic network to represent a portion of the knowledge base of a medical toxicologist. Our approach transparently mimics the knowledge representation and clinical decision-making of practicing clinicians. The software, dubbed Tak, performs comparably to humans on straightforward cases and intermediate difficulty cases, but is outperformed by humans on challenging clinical cases. Tak outperforms a decision tree classifier at all levels of difficulty. Probabilistic logic provides one form of explainable artificial intelligence that may be more acceptable for use in healthcare, if it can achieve acceptable levels of performance.