In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. In particular, with the bound derived in this paper relates future average prediction errors with the prediction error generated by the model on the data used for learning. In turn, this allows us to provide finite-sample error bounds for a wide class of learning/system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

Learning a generalizable object manipulation policy is vital for an embodied agent to work in complex real-world scenes. Parts, as the shared components in different object categories, have the potential to increase the generalization ability of the manipulation policy and achieve cross-category object manipulation. In this work, we build the first large-scale, part-based cross-category object manipulation benchmark, PartManip, which is composed of 11 object categories, 494 objects, and 1432 tasks in 6 task classes. Compared to previous work, our benchmark is also more diverse and realistic, i.e., having more objects and using sparse-view point cloud as input without oracle information like part segmentation. To tackle the difficulties of vision-based policy learning, we first train a state-based expert with our proposed part-based canonicalization and part-aware rewards, and then distill the knowledge to a vision-based student. We also find an expressive backbone is essential to overcome the large diversity of different objects. For cross-category generalization, we introduce domain adversarial learning for domain-invariant feature extraction. Extensive experiments in simulation show that our learned policy can outperform other methods by a large margin, especially on unseen object categories. We also demonstrate our method can successfully manipulate novel objects in the real world.

The mixed multinomial logit model assumes constant preference parameters of a decision-maker throughout different choice situations, which may be considered too strong for certain choice modelling applications. This paper proposes an effective approach to model context-dependent intra-respondent heterogeneity, thereby introducing the concept of the Context-aware Bayesian mixed multinomial logit model, where a neural network maps contextual information to interpretable shifts in the preference parameters of each individual in each choice occasion. The proposed model offers several key advantages. First, it supports both continuous and discrete variables, as well as complex non-linear interactions between both types of variables. Secondly, each context specification is considered jointly as a whole by the neural network rather than each variable being considered independently. Finally, since the neural network parameters are shared across all decision-makers, it can leverage information from other decision-makers to infer the effect of a particular context on a particular decision-maker. Even though the context-aware Bayesian mixed multinomial logit model allows for flexible interactions between attributes, the increase in computational complexity is minor, compared to the mixed multinomial logit model. We illustrate the concept and interpretation of the proposed model in a simulation study. We furthermore present a real-world case study from the travel behaviour domain - a bicycle route choice model, based on a large-scale, crowdsourced dataset of GPS trajectories including 119,448 trips made by 8,555 cyclists.

Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models called mixtures of all trees: that is, a mixture over all possible ($n^{n-2}$) tree-shaped graphical models over $n$ variables. We show that it is possible to parameterize this Mixture of All Trees (MoAT) model compactly (using a polynomial-size representation) in a way that allows for tractable likelihood computation and optimization via stochastic gradient descent. Furthermore, by leveraging the tractability of tree-shaped models, we devise fast-converging conditional sampling algorithms for approximate inference, even though our theoretical analysis suggests that exact computation of marginals in the MoAT model is NP-hard. Empirically, MoAT achieves state-of-the-art performance on density estimation benchmarks when compared against powerful probabilistic models including hidden Chow-Liu Trees.

The process of training feedforward neural networks (FFNNs) can benefit from an automated process where the best heuristic to train the network is sought out automatically by means of a high-level probabilistic-based heuristic. This research introduces a novel population-based Bayesian hyper-heuristic (BHH) that is used to train feedforward neural networks (FFNNs). The performance of the BHH is compared to that of ten popular low-level heuristics, each with different search behaviours. The chosen heuristic pool consists of classic gradient-based heuristics as well as meta-heuristics (MHs). The empirical process is executed on fourteen datasets consisting of classification and regression problems with varying characteristics. The BHH is shown to be able to train FFNNs well and provide an automated method for finding the best heuristic to train the FFNNs at various stages of the training process.

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed hyper-parameters to enforce joint sparsity. The resulting joint-sparsity-promoting priors are combined with existing Bayesian inference methods to generate a new family of algorithms. Our numerical experiments, which include a multi-coil magnetic resonance imaging application, demonstrate that our new approach consistently outperforms commonly used hierarchical Bayesian methods.

We present a novel approach for efficient and reliable goal-directed long-horizon navigation for a multi-robot team in a structured, unknown environment by predicting statistics of unknown space. Building on recent work in learning-augmented model based planning under uncertainty, we introduce a high-level state and action abstraction that lets us approximate the challenging Dec-POMDP into a tractable stochastic MDP. Our Multi-Robot Learning over Subgoals Planner (MR-LSP) guides agents towards coordinated exploration of regions more likely to reach the unseen goal. We demonstrate improvement in cost against other multi-robot strategies; in simulated office-like environments, we show that our approach saves 13.29% (2 robot) and 4.6% (3 robot) average cost versus standard non-learned optimistic planning and a learning-informed baseline.

In this paper, we consider the problem of probabilistic stability analysis of a subclass of Stochastic Hybrid Systems, namely, Polyhedral Probabilistic Hybrid Systems (PPHS), where the flow dynamics is given by a polyhedral inclusion, the discrete switching between modes happens probabilistically at the boundaries of their invariant regions and the continuous state is not reset during switching. We present an abstraction-based analysis framework that consists of constructing a finite Markov Decision Processes (MDP) such that verification of certain property on the finite MDP ensures the satisfaction of probabilistic stability on the PPHS. Further, we present a polynomial-time algorithm for verifying the corresponding property on the MDP. Our experimental analysis demonstrates the feasibility of the approach in successfully verifying probabilistic stability on PPHS of various dimensions and sizes.

This paper presents a white-box intention-aware decision-making for the handling of interactions between a pedestrian and an automated vehicle (AV) in an unsignalized street crossing scenario. Moreover, a design framework has been developed, which enables automated parameterization of the decision-making. This decision-making is designed in such a manner that it can understand pedestrians in urban traffic and can react accordingly to their intentions. That way, a human-like response to the actions of the pedestrian is ensured, leading to a higher acceptance of AVs. The core notion of this paper is that the intention prediction of the pedestrian to cross the street and decision-making are divided into two subsystems. On the one hand, the intention detection is a data-driven, black-box model. Thus, it can model the complex behavior of the pedestrians. On the other hand, the decision-making is a white-box model to ensure traceability and to enable a rapid verification and validation of AVs. This white-box decision-making provides human-like behavior and a guaranteed prevention of deadlocks. An additional benefit is that the proposed decision-making requires low computational resources only enabling real world usage. The automated parameterization uses a particle swarm optimization and compares two different models of the pedestrian: The social force model and the Markov decision process model. Consequently, a rapid design of the decision-making is possible and different pedestrian behaviors can be taken into account. The results reinforce the applicability of the proposed intention-aware decision-making.

This paper revisits classical works of Rauch (1963, et al. 1965) and develops a novel method for maximum likelihood (ML) smoothing estimation from incomplete information/data of stochastic state-space systems. Score function and conditional observed information matrices of incomplete data are introduced and their distributional identities are established. Using these identities, the ML smoother $\widehat{x}_{k\vert n}^s =\argmax_{x_k} \log f(x_k,\widehat{x}_{k+1\vert n}^s, y_{0:n}\vert\theta)$, $k\leq n-1$, is presented. The result shows that the ML smoother gives an estimate of state $x_k$ with more adherence of loglikehood having less standard errors than that of the ML state estimator $\widehat{x}_k=\argmax_{x_k} \log f(x_k,y_{0:k}\vert\theta)$, with $\widehat{x}_{n\vert n}^s=\widehat{x}_n$. Recursive estimation is given in terms of an EM-gradient-particle algorithm which extends the work of \cite{Lange} for ML smoothing estimation. The algorithm has an explicit iteration update which lacks in (\cite{Ramadan}) EM-algorithm for smoothing. A sequential Monte Carlo method is developed for valuation of the score function and observed information matrices. A recursive equation for the covariance matrix of estimation error is developed to calculate the standard errors. In the case of linear systems, the method shows that the Rauch-Tung-Striebel (RTS) smoother is a fully efficient smoothing state-estimator whose covariance matrix coincides with the Cram\'er-Rao lower bound, the inverse of expected information matrix. Furthermore, the RTS smoother coincides with the Kalman filter having less covariance matrix. Numerical studies are performed, confirming the accuracy of the main results.