Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in demanding applications, robustness to uncertainty remains an important challenge. Since Bayesian methods quantify uncertainty of the learning results, it is natural to incorporate these uncertainties into a robust design. In contrast to most state-of-the-art approaches that consider worst-case estimates, we leverage the learning method's posterior distribution in the controller synthesis. The result is a more informed and, thus, more efficient trade-off between performance and robustness. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin. The formulation is based on a recently proposed algorithm for linear quadratic control synthesis, which we extend by giving probabilistic robustness guarantees in the form of credibility bounds for the system's stability.Comparisons to existing methods based on worst-case and certainty-equivalence designs reveal superior performance and robustness properties of the proposed method.

Graph-to-text (G2T) generation and text-to-graph (T2G) triple extraction are two essential tasks for constructing and applying knowledge graphs. Existing unsupervised approaches turn out to be suitable candidates for jointly learning the two tasks due to their avoidance of using graph-text parallel data. However, they are composed of multiple modules and still require both entity information and relation type in the training process. To this end, we propose INFINITY, a simple yet effective unsupervised approach that does not require external annotation tools or additional parallel information. It achieves fully unsupervised graph-text mutual conversion for the first time. Specifically, INFINITY treats both G2T and T2G as a bidirectional sequence generation task by fine-tuning only one pretrained seq2seq model. A novel back-translation-based framework is then designed to automatically generate continuous synthetic parallel data. To obtain reasonable graph sequences with structural information from source texts, INFINITY employs reward-based training loss by leveraging the advantage of reward augmented maximum likelihood. As a fully unsupervised framework, INFINITY is empirically verified to outperform state-of-the-art baselines for G2T and T2G tasks.

We apply the technique of implicit differentiation to boost performance, reduce numerical error, and remove required user-tuning in the Marginal Unbiased Score Expansion (MUSE) algorithm for hierarchical Bayesian inference. We demonstrate these improvements on three representative inference problems: 1) an extended Neal's funnel 2) Bayesian neural networks, and 3) probabilistic principal component analysis. On our particular test cases, MUSE with implicit differentiation is faster than Hamiltonian Monte Carlo by factors of 155, 397, and 5, respectively, or factors of 65, 278, and 1 without implicit differentiation, and yields good approximate marginal posteriors. The Julia and Python MUSE packages have been updated to use implicit differentiation, and can solve problems defined by hand or with any of a number of popular probabilistic programming languages and automatic differentiation backends.

We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference distribution under a transport map, where the map is chosen via a maximum likelihood objective (equivalently, minimizing an empirical Kullback-Leibler loss) or a penalized version thereof. We establish concentration inequalities for a general class of penalized measure transport estimators, by combining techniques from M-estimation with analytical properties of the transport-based density representation. We then demonstrate the implications of our theory for the case of triangular Knothe-Rosenblatt (KR) transports on the $d$-dimensional unit cube, and show that both penalized and unpenalized versions of such estimators achieve minimax optimal convergence rates over H\"older classes of densities. Specifically, we establish optimal rates for unpenalized nonparametric maximum likelihood estimation over bounded H\"older-type balls, and then for certain Sobolev-penalized estimators and sieved wavelet estimators.

Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval typically does not contain the true outcome 90% of the time. This paper argues that calibration is important in practice and is easy to maintain by performing low-dimensional density estimation. We introduce a simple training procedure based on recalibration that yields calibrated models without sacrificing overall performance; unlike previous approaches, ours ensures the most general property of distribution calibration and applies to any model, including neural networks. We formally prove the correctness of our procedure assuming that we can estimate densities in low dimensions and we establish uniform convergence bounds. Our results yield empirical performance improvements on linear and deep Bayesian models and suggest that calibration should be increasingly leveraged across machine learning.

We present Bayesian Team Imitation Learner (BTIL), an imitation learning algorithm to model the behavior of teams performing sequential tasks in Markovian domains. In contrast to existing multi-agent imitation learning techniques, BTIL explicitly models and infers the time-varying mental states of team members, thereby enabling learning of decentralized team policies from demonstrations of suboptimal teamwork. Further, to allow for sample- and label-efficient policy learning from small datasets, BTIL employs a Bayesian perspective and is capable of learning from semi-supervised demonstrations. We demonstrate and benchmark the performance of BTIL on synthetic multi-agent tasks as well as a novel dataset of human-agent teamwork. Our experiments show that BTIL can successfully learn team policies from demonstrations despite the influence of team members' (time-varying and potentially misaligned) mental states on their behavior.

Multiple rigidly attached Inertial Measurement Unit (IMU) sensors provide a richer flow of data compared to a single IMU. State-of-the-art methods follow a probabilistic model of IMU measurements based on the random nature of errors combined under a Bayesian framework. However, affordable low-grade IMUs, in addition, suffer from systematic errors due to their imperfections not covered by their corresponding probabilistic model. In this paper, we propose a method, the Best Axes Composition (BAC) of combining Multiple IMU (MIMU) sensors data for accurate 3D-pose estimation that takes into account both random and systematic errors by dynamically choosing the best IMU axes from the set of all available axes. We evaluate our approach on our MIMU visual-inertial sensor and compare the performance of the method with a purely probabilistic state-of-the-art approach of MIMU data fusion. We show that BAC outperforms the latter and achieves up to 20% accuracy improvement for both orientation and position estimation in open loop, but needs proper treatment to keep the obtained gain.

Conventional frequentist FL schemes are known to yield overconfident decisions. Bayesian FL addresses this issue by allowing agents to process and exchange uncertainty information encoded in distributions over the model parameters. However, this comes at the cost of a larger per-iteration communication overhead. This letter investigates whether Bayesian FL can still provide advantages in terms of calibration when constraining communication bandwidth. We present compressed particle-based Bayesian FL protocols for FL and federated "unlearning" that apply quantization and sparsification across multiple particles. The experimental results confirm that the benefits of Bayesian FL are robust to bandwidth constraints.

Crowd sequential annotations can be an efficient and cost-effective way to build large datasets for sequence labeling. Different from tagging independent instances, for crowd sequential annotations the quality of label sequence relies on the expertise level of annotators in capturing internal dependencies for each token in the sequence. In this paper, we propose Modeling sequential annotation for sequence labeling with crowds (SA-SLC). First, a conditional probabilistic model is developed to jointly model sequential data and annotators' expertise, in which categorical distribution is introduced to estimate the reliability of each annotator in capturing local and non-local label dependency for sequential annotation. To accelerate the marginalization of the proposed model, a valid label sequence inference (VLSE) method is proposed to derive the valid ground-truth label sequences from crowd sequential annotations. VLSE derives possible ground-truth labels from the token-wise level and further prunes sub-paths in the forward inference for label sequence decoding. VLSE reduces the number of candidate label sequences and improves the quality of possible ground-truth label sequences. The experimental results on several sequence labeling tasks of Natural Language Processing show the effectiveness of the proposed model.

Although the no-u-turn sampler (NUTS) is a widely adopted method for performing Bayesian inference, it requires numerous posterior gradients which can be expensive to compute in practice. Recently, there has been a significant interest in physics-based machine learning of dynamical (or Hamiltonian) systems and Hamiltonian neural networks (HNNs) is a noteworthy architecture. But these types of architectures have not been applied to solve Bayesian inference problems efficiently. We propose the use of HNNs for performing Bayesian inference efficiently without requiring numerous posterior gradients. We introduce latent variable outputs to HNNs (L-HNNs) for improved expressivity and reduced integration errors. We integrate L-HNNs in NUTS and further propose an online error monitoring scheme to prevent sampling degeneracy in regions where L-HNNs may have little training data. We demonstrate L-HNNs in NUTS with online error monitoring considering several complex high-dimensional posterior densities and compare its performance to NUTS.