Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single point solution and propose a probabilistic paradigm to estimate a diverse set of counterfactuals. Specifically, we treat the perturbations as random variables endowed with prior distribution functions. This allows sampling multiple counterfactuals from the posterior density, with the added benefit of incorporating inductive biases, preserving domain specific constraints and quantifying uncertainty in estimates. More importantly, we leverage Bayesian hierarchical modeling to share information across different subgroups of a population, which can both improve robustness and measure fairness. A gradient based sampler with superior convergence characteristics efficiently computes the posterior samples. Experiments across several datasets demonstrate that the counterfactuals estimated using our approach are valid, sparse, diverse and feasible.

This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden Markov model with stochastic dynamics. We then analyze this objective function in the context of several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that our proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics' origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach can identify accurate and generalizable models even when there are more parameters than data or when the underlying system exhibits chaotic behavior.

Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random variables. However, directed cycles can naturally arise when cross-dependencies between random variables exist, e.g., for modeling feedback loops. Existing methods to deal with such cross-dependencies usually rely on reductions to BNs without cycles. These approaches are fragile to generalize, since their justifications are intermingled with additional knowledge about the application context. In this paper, we present a foundational study regarding semantics for cyclic BNs that are generic and conservatively extend the cycle-free setting. First, we propose constraint-based semantics that specify requirements for full joint distributions over a BN to be consistent with the local conditional probabilities and independencies. Second, two kinds of limit semantics that formalize infinite unfolding approaches are introduced and shown to be computable by a Markov chain construction.

Understanding and predicting highway lane-change maneuvers is essential for driving modeling and its automation. The development of data-based lane-changing decision-making algorithms is nowadays in full expansion. We compare empirically in this article different machine and ensemble learning classification techniques to the MOBIL rule-based model using trajectory data of European two-lane highways. The analysis relies on instantaneous measurements of up to twenty-four spatial-temporal variables with the four neighboring vehicles on current and adjacent lanes. Preliminary descriptive investigations by principal component and logistic analyses allow identifying main variables intending a driver to change lanes. We predict two types of discretionary lane-change maneuvers: overtaking (from the slow to the fast lane) and fold-down (from the fast to the slow lane). The prediction accuracy is quantified using total, lane-changing and lane-keeping errors and associated receiver operating characteristic curves. The benchmark analysis includes logistic model, linear discriminant, decision tree, na\"ive Bayes classifier, support vector machine, neural network machine learning algorithms, and up to ten bagging and stacking ensemble learning meta-heuristics. If the rule-based model provides limited predicting accuracy, the data-based algorithms, devoid of modeling bias, allow significant prediction improvements. Cross validations show that selected neural networks and stacking algorithms allow predicting from a single observation both fold-down and overtaking maneuvers up to four seconds in advance with high accuracy.

We propose a novel online and adaptive truncation method for differentially private Bayesian online estimation of a static parameter regarding a population. We assume that sensitive information from individuals is collected sequentially and the inferential aim is to estimate, on-the-fly, a static parameter regarding the population to which those individuals belong. We propose sequential Monte Carlo to perform online Bayesian estimation. When individuals provide sensitive information in response to a query, it is necessary to perturb it with privacy-preserving noise to ensure the privacy of those individuals. The amount of perturbation is proportional to the sensitivity of the query, which is determined usually by the range of the queried information. The truncation technique we propose adapts to the previously collected observations to adjust the query range for the next individual. The idea is that, based on previous observations, we can carefully arrange the interval into which the next individual's information is to be truncated before being perturbed with privacy-preserving noise. In this way, we aim to design predictive queries with small sensitivity, hence small privacy-preserving noise, enabling more accurate estimation while maintaining the same level of privacy. To decide on the location and the width of the interval, we use an exploration-exploitation approach a la Thompson sampling with an objective function based on the Fisher information of the generated observation. We show the merits of our methodology with numerical examples.

We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for different classes of prior distributions, including Gaussian process priors. We show that fractional posterior credible sets can provide reliable semiparametric uncertainty quantification, but have inflated size. To remedy this, we further propose a \textit{shifted-and-rescaled} fractional posterior set that is an efficient confidence set having optimal size under regularity conditions. As part of our proofs, we also refine existing contraction rate results for fractional posteriors by sharpening the dependence of the rate on the fractional exponent.

Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations remains still a challenging endeavour. Existing approaches focus either on the temporal structure of the observations by relying on conditional expectations, discarding thereby information ingrained in the geometry of the system's invariant density; or employ geometric approximations of the invariant density, which are nevertheless restricted to systems with conservative forces. Here we propose a method that reconciles these two paradigms. We introduce a new data-driven path augmentation scheme that takes the local observation geometry into account. By employing non-parametric inference on the augmented paths, we can efficiently identify the deterministic driving forces of the underlying system for systems observed at low sampling rates.

Machine learning currently plays an increasingly important role in people's lives in areas such as credit scoring, auto-driving, disease diagnosing, and insurance quoting. However, in many of these areas, machine learning models have performed unfair behaviors against some sub-populations, such as some particular groups of race, sex, and age. These unfair behaviors can be on account of the pre-existing bias in the training dataset due to historical and social factors. In this paper, we focus on a real-world application of credit scoring and construct a fair prediction model by introducing latent variables to remove the correlation between protected attributes, such as sex and age, with the observable feature inputs, including house and job. For detailed implementation, we apply Bayesian approaches, including the Markov Chain Monte Carlo simulation, to estimate our proposed fair model.

Since the meaning representations are detailed and accurate annotations which express fine-grained sequence-level semtantics, it is usually hard to train discriminative semantic parsers via Maximum Likelihood Estimation (MLE) in an autoregressive fashion. In this paper, we propose a semantic-aware contrastive learning algorithm, which can learn to distinguish fine-grained meaning representations and take the overall sequence-level semantic into consideration. Specifically, a multi-level online sampling algorithm is proposed to sample confusing and diverse instances. Three semantic-aware similarity functions are designed to accurately measure the distance between meaning representations as a whole. And a ranked contrastive loss is proposed to pull the representations of the semantic-identical instances together and push negative instances away. Experiments on two standard datasets show that our approach achieves significant improvements over MLE baselines and gets state-of-the-art performances by simply applying semantic-aware contrastive learning on a vanilla Seq2Seq model.

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the posterior distribution not only for one instance of data, but a distribution of data pertaining to a specific inverse problem. During inference, the neural network -- in our case a conditional normalizing flow -- provides posterior samples at virtually no cost. However, the accuracy of amortized variational inference relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems due to the Earth's heterogeneity. In addition, the network is prone to errors if evaluated over out-of-distribution data. As such, we propose to increase the resilience of amortized variational inference in the presence of moderate data distribution shifts. We achieve this via a correction to the latent distribution that improves the posterior distribution approximation for the data at hand. The correction involves relaxing the standard Gaussian assumption on the latent distribution and parameterizing it via a Gaussian distribution with an unknown mean and (diagonal) covariance. These unknowns are then estimated by minimizing the Kullback-Leibler divergence between the corrected and the (physics-based) true posterior distributions. While generic and applicable to other inverse problems, by means of a linearized seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in the number of seismic sources, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty at approximately the same cost as five reverse-time migrations.