In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct an example to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.

Guided exploration with expert demonstrations improves data efficiency for reinforcement learning, but current algorithms often overuse expert information. We propose a novel algorithm to speed up Q-learning with the help of a limited amount of imperfect expert demonstrations. The algorithm avoids excessive reliance on expert data by relaxing the optimal expert assumption and gradually reducing the usage of uninformative expert data. Experimentally, we evaluate our approach on a sparse-reward chain environment and six more complicated Atari games with delayed rewards. With the proposed methods, we can achieve better results than Deep Q-learning from Demonstrations (Hester et al., 2017) in most environments.

This paper analyzes a popular loss function used in machine learning called the log-cosh loss function. A number of papers have been published using this loss function but, to date, no statistical analysis has been presented in the literature. In this paper, we present the distribution function from which the log-cosh loss arises. We compare it to a similar distribution, called the Cauchy distribution, and carry out various statistical procedures that characterize its properties. In particular, we examine its associated pdf, cdf, likelihood function and Fisher information. Side-by-side we consider the Cauchy and Cosh distributions as well as the MLE of the location parameter with asymptotic bias, asymptotic variance, and confidence intervals. We also provide a comparison of robust estimators from several other loss functions, including the Huber loss function and the rank dispersion function. Further, we examine the use of the log-cosh function for quantile regression. In particular, we identify a quantile distribution function from which a maximum likelihood estimator for quantile regression can be derived. Finally, we compare a quantile M-estimator based on log-cosh with robust monotonicity against another approach to quantile regression based on convolutional smoothing.

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared.

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems. However, the computation of Bayesian posteriors is typically an intractable problem, and has spawned a large literature on approximate Bayesian computation. Here, in the context of chance-constrained optimization, we focus on the question of statistical consistency (in an appropriate sense) of the optimal value, computed using an approximate posterior distribution. To this end, we rigorously prove a frequentist consistency result demonstrating the convergence of the optimal value to the optimal value of a fixed, parameterized constrained optimization problem. We augment this by also establishing a probabilistic rate of convergence of the optimal value. We also prove the convex feasibility of the approximate Bayesian stochastic optimization problem. Finally, we demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queueing model.

A wind turbines' power curve is easily accessible damage sensitive data, and as such is a key part of structural health monitoring in wind turbines. Power curve models can be constructed in a number of ways, but the authors argue that probabilistic methods carry inherent benefits in this use case, such as uncertainty quantification and allowing uncertainty propagation analysis. Many probabilistic power curve models have a key limitation in that they are not physically meaningful - they return mean and uncertainty predictions outside of what is physically possible (the maximum and minimum power outputs of the wind turbine). This paper investigates the use of two bounded Gaussian Processes in order to produce physically meaningful probabilistic power curve models. The first model investigated was a warped heteroscedastic Gaussian process, and was found to be ineffective due to specific shortcomings of the Gaussian Process in relation to the warping function. The second model - an approximated Gaussian Process with a Beta likelihood was highly successful and demonstrated that a working bounded probabilistic model results in better predictive uncertainty than a corresponding unbounded one without meaningful loss in predictive accuracy. Such a bounded model thus offers increased accuracy for performance monitoring and increased operator confidence in the model due to guaranteed physical plausibility.

Evaluating hypothetical statements about how the world would be had a different course of action been taken is arguably one key capability expected from modern AI systems. Counterfactual reasoning underpins discussions in fairness, the determination of blame and responsibility, credit assignment, and regret. In this paper, we study the evaluation of counterfactual statements through neural models. Specifically, we tackle two causal problems required to make such evaluations, i.e., counterfactual identification and estimation from an arbitrary combination of observational and experimental data. First, we show that neural causal models (NCMs) are expressive enough and encode the structural constraints necessary for performing counterfactual reasoning. Second, we develop an algorithm for simultaneously identifying and estimating counterfactual distributions. We show that this algorithm is sound and complete for deciding counterfactual identification in general settings. Third, considering the practical implications of these results, we introduce a new strategy for modeling NCMs using generative adversarial networks. Simulations corroborate with the proposed methodology.

Conditional language models are predominantly trained with maximum likelihood estimation (MLE), giving probability mass to sparsely observed target sequences. While MLE trained models assign high probability to plausible sequences given the context, the model probabilities often do not accurately rank-order generated sequences by quality. This has been empirically observed in beam search decoding as output quality degrading with large beam sizes, and decoding strategies benefiting from heuristics such as length normalization and repetition-blocking. In this work, we introduce sequence likelihood calibration (SLiC) where the likelihood of model generated sequences are calibrated to better align with reference sequences in the model's latent space. With SLiC, decoding heuristics become unnecessary and decoding candidates' quality significantly improves regardless of the decoding method. Furthermore, SLiC shows no sign of diminishing returns with model scale, and presents alternative ways to improve quality with limited training and inference budgets. With SLiC, we exceed or match SOTA results on a wide range of generation tasks spanning abstractive summarization, question generation, abstractive question answering and data-to-text generation, even with modest-sized models.

To discover new drugs is to seek and to prove causality. As an emerging approach leveraging human knowledge and creativity, data, and machine intelligence, causal inference holds the promise of reducing cognitive bias and improving decision making in drug discovery. While it has been applied across the value chain, the concepts and practice of causal inference remain obscure to many practitioners. This article offers a non-technical introduction to causal inference, reviews its recent applications, and discusses opportunities and challenges of adopting the causal language in drug discovery and development.

We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products of the latent positions. To balance posterior inference and computational scalability, we present a structured mean-field variational inference framework, where the time-dependent properties of the dynamic networks are exploited to facilitate computation and inference. Additionally, an easy-to-implement block coordinate ascent algorithm is developed with message-passing type updates in each block, whereas the complexity per iteration is linear with the number of nodes and time points. To facilitate learning of the pairwise latent distances, we adopt a Gamma prior for the transition variance different from the literature. To certify the optimality, we demonstrate that the variational risk of the proposed variational inference approach attains the minimax optimal rate under certain conditions. En route, we derive the minimax lower bound, which might be of independent interest. To best of our knowledge, this is the first such exercise for dynamic latent space models. Simulations and real data analysis demonstrate the efficacy of our methodology and the efficiency of our algorithm. Finally, our proposed methodology can be readily extended to the case where the scales of the latent nodes are learned in a nodewise manner.