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.

We describe a method and new no-code software tools enabling domain experts to build custom structured, labeled datasets from the unstructured text of documents and build niche machine learning text classification models traceable to expert-written rules. The Context Rule Assisted Machine Learning (CRAML) method allows accurate and reproducible labeling of massive volumes of unstructured text. CRAML enables domain experts to access uncommon constructs buried within a document corpus, and avoids limitations of current computational approaches that often lack context, transparency, and interpetability. In this research methods paper, we present three use cases for CRAML: we analyze recent management literature that draws from text data, describe and release new machine learning models from an analysis of proprietary job advertisement text, and present findings of social and economic interest from a public corpus of franchise documents. CRAML produces document-level coded tabular datasets that can be used for quantitative academic research, and allows qualitative researchers to scale niche classification schemes over massive text data. CRAML is a low-resource, flexible, and scalable methodology for building training data for supervised ML. We make available as open-source resources: the software, job advertisement text classifiers, a novel corpus of franchise documents, and a fully replicable start-to-finish trained example in the context of no poach clauses.

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.

In this paper, I try to tame "Basu's elephants" (data with extreme selection on observables). I propose new practical large-sample and finite-sample methods for estimating and inferring heterogeneous causal effects (under unconfoundedness) in the empirically relevant context of limited overlap. I develop a general principle called "Stable Probability Weighting" (SPW) that can be used as an alternative to the widely used Inverse Probability Weighting (IPW) technique, which relies on strong overlap. I show that IPW (or its augmented version), when valid, is a special case of the more general SPW (or its doubly robust version), which adjusts for the extremeness of the conditional probabilities of the treatment states. The SPW principle can be implemented using several existing large-sample parametric, semiparametric, and nonparametric procedures for conditional moment models. In addition, I provide new finite-sample results that apply when unconfoundedness is plausible within fine strata. Since IPW estimation relies on the problematic reciprocal of the estimated propensity score, I develop a "Finite-Sample Stable Probability Weighting" (FPW) set-estimator that is unbiased in a sense. I also propose new finite-sample inference methods for testing a general class of weak null hypotheses. The associated computationally convenient methods, which can be used to construct valid confidence sets and to bound the finite-sample confidence distribution, are of independent interest. My large-sample and finite-sample frameworks extend to the setting of multivalued treatments.

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.

This paper introduces a novel Learning from Demonstration framework to learn robotic skills with keyframe demonstrations using a Dynamic Bayesian Network (DBN) and a Bayesian Optimized Policy Search approach to improve the learned skills. DBN learns the robot motion, perceptual change in the object of interest (aka skill sub-goals) and the relation between them. The rewards are also learned from the perceptual part of the DBN. The policy search part is a semiblack box algorithm, which we call BO-PI2 . It utilizes the action-perception relation to focus the high-level exploration, uses Gaussian Processes to model the expected-return and performs Upper Confidence Bound type low-level exploration for sampling the rollouts. BO-PI2 is compared against a stateof-the-art method on three different skills in a real robot setting with expert and naive user demonstrations. The results show that our approach successfully focuses the exploration on the failed sub-goals and the addition of reward-predictive exploration outperforms the state-of-the-art approach on cumulative reward, skill success, and termination time metrics.

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.