In tracking multiple objects, it is often assumed that each observation (measurement) is originated from one and only one object. However, we may encounter a situation that each measurement may or may not be associated with multiple objects at each time step --spawning. Therefore, the association of each measurement to multiple objects is a crucial task to perform in order to track multiple objects with birth and death. In this paper, we introduce a novel Bayesian nonparametric approach that models a scenario where each observation may be drawn from an unknown number of objects for which it provides a tractable Markov chain Monte Carlo (MCMC) approach to sample from the posterior distribution. The number of objects at each time step, itself, is also assumed to be unknown. We, then, show through experiments the advantage of nonparametric modeling to scenarios with spawning events. Our experiment results also demonstrate the advantages of our framework over the existing methods.

Active inference is a mathematical framework which originated in computational neuroscience as a theory of how the brain implements action, perception and learning. Recently, it has been shown to be a promising approach to the problems of state-estimation and control under uncertainty, as well as a foundation for the construction of goal-driven behaviours in robotics and artificial agents in general. Here, we review the state-of-the-art theory and implementations of active inference for state-estimation, control, planning and learning; describing current achievements with a particular focus on robotics. We showcase relevant experiments that illustrate its potential in terms of adaptation, generalization and robustness. Furthermore, we connect this approach with other frameworks and discuss its expected benefits and challenges: a unified framework with functional biological plausibility using variational Bayesian inference.

Working together on complex collaborative tasks requires agents to coordinate their actions. Doing this explicitly or completely prior to the actual interaction is not always possible nor sufficient. Agents also need to continuously understand the current actions of others and quickly adapt their own behavior appropriately. Here we investigate how efficient, automatic coordination processes at the level of mental states (intentions, goals), which we call belief resonance, can lead to collaborative situated problem-solving. We present a model of hierarchical active inference for collaborative agents (HAICA). It combines efficient Bayesian Theory of Mind processes with a perception-action system based on predictive processing and active inference. Belief resonance is realized by letting the inferred mental states of one agent influence another agent's predictive beliefs about its own goals and intentions. This way, the inferred mental states influence the agent's own task behavior without explicit collaborative reasoning. We implement and evaluate this model in the Overcooked domain, in which two agents with varying degrees of belief resonance team up to fulfill meal orders. Our results demonstrate that agents based on HAICA achieve a team performance comparable to recent state of the art approaches, while incurring much lower computational costs. We also show that belief resonance is especially beneficial in settings were the agents have asymmetric knowledge about the environment. The results indicate that belief resonance and active inference allow for quick and efficient agent coordination, and thus can serve as a building block for collaborative cognitive agents.

Adversarial robustness is a critical property in a variety of modern machine learning applications. While it has been the subject of several recent theoretical studies, many important questions related to adversarial robustness are still open. In this work, we study a fundamental question regarding Bayes optimality for adversarial robustness. We provide general sufficient conditions under which the existence of a Bayes optimal classifier can be guaranteed for adversarial robustness. Our results can provide a useful tool for a subsequent study of surrogate losses in adversarial robustness and their consistency properties. This manuscript is the extended version of the paper On the Existence of the Adversarial Bayes Classifier published in NeurIPS (Awasthi et al., 2021b). The results of the original paper did not apply to some non-strictly convex norms. Here we extend our results to all possible norms.

Within the last few years, there has been a move towards using statistical models in conjunction with neural networks with the end goal of being able to better answer the question, "what do our models know?". From this trend, classical metrics such as Prediction Interval Coverage Probability (PICP) and new metrics such as calibration error have entered the general repertoire of model evaluation in order to gain better insight into how the uncertainty of our model compares to reality. One important component of uncertainty modeling is model uncertainty (epistemic uncertainty), a measurement of what the model does and does not know. However, current evaluation techniques tends to conflate model uncertainty with aleatoric uncertainty (irreducible error), leading to incorrect conclusions. In this paper, using posterior predictive checks, we show how calibration error and its variants are almost always incorrect to use given model uncertainty, and further show how this mistake can lead to trust in bad models and mistrust in good models. Though posterior predictive checks has often been used for in-sample evaluation of Bayesian models, we show it still has an important place in the modern deep learning world.

Learning the structure of a Bayesian Network (BN) with score-based solutions involves exploring the search space of possible graphs and moving towards the graph that maximises a given objective function. Some algorithms offer exact solutions that guarantee to return the graph with the highest objective score, while others offer approximate solutions in exchange for reduced computational complexity. This paper describes an approximate BN structure learning algorithm, which we call Model Averaging Hill-Climbing (MAHC), that combines two novel strategies with hill-climbing search. The algorithm starts by pruning the search space of graphs, where the pruning strategy can be viewed as an aggressive version of the pruning strategies that are typically applied to combinatorial optimisation structure learning problems. It then performs model averaging in the hill-climbing search process and moves to the neighbouring graph that maximises the objective function, on average, for that neighbouring graph and over all its valid neighbouring graphs. Comparisons with other algorithms spanning different classes of learning suggest that the combination of aggressive pruning with model averaging is both effective and efficient, particularly in the presence of data noise.

Autonomous Land Vehicles (ALV) shall efficiently recognize the ground in unknown environments. A novel $\mathcal{GP}$-based method is proposed for the ground segmentation task in rough driving scenarios. A non-stationary covariance function is utilized as the kernel for the $\mathcal{GP}$. The ground surface behavior is assumed to only demonstrate local-smoothness. Thus, point estimates of the kernel's length-scales are obtained. Thus, two Gaussian processes are introduced to separately model the observation and local characteristics of the data. While, the \textit{observation process} is used to model the ground, the \textit{latent process} is put on length-scale values to estimate point values of length-scales at each input location. Input locations for this latent process are chosen in a physically-motivated procedure to represent an intuition about ground condition. Furthermore, an intuitive guess of length-scale value is represented by assuming the existence of hypothetical surfaces in the environment that every bunch of data points may be assumed to be resulted from measurements from this surfaces. Bayesian inference is implemented using \textit{maximum a Posteriori} criterion. The log-marginal likelihood function is assumed to be a multi-task objective function, to represent a whole-frame unbiased view of the ground at each frame. Simulation results shows the effectiveness of the proposed method even in an uneven, rough scene which outperforms similar Gaussian process based ground segmentation methods. While adjacent segments do not have similar ground structure in an uneven scene, the proposed method gives an efficient ground estimation based on a whole-frame viewpoint instead of just estimating segment-wise probable ground surfaces.

Generative models which use explicit density modeling (e.g., variational autoencoders, flow-based generative models) involve finding a mapping from a known distribution, e.g. Gaussian, to the unknown input distribution. This often requires searching over a class of non-linear functions (e.g., representable by a deep neural network). While effective in practice, the associated runtime/memory costs can increase rapidly, usually as a function of the performance desired in an application. We propose a much cheaper (and simpler) strategy to estimate this mapping based on adapting known results in kernel transfer operators. We show that our formulation enables highly efficient distribution approximation and sampling, and offers surprisingly good empirical performance that compares favorably with powerful baselines, but with significant runtime savings. We show that the algorithm also performs well in small sample size settings (in brain imaging).

Owing to the benefits for customers (lower prices), drivers (higher revenues), aggregation companies (higher revenues) and the environment (fewer vehicles), on-demand ride pooling (e.g., Uber pool, Grab Share) has become quite popular. The significant computational complexity of matching vehicles to combinations of requests has meant that traditional ride pooling approaches are myopic in that they do not consider the impact of current matches on future value for vehicles/drivers. Recently, Neural Approximate Dynamic Programming (NeurADP) has employed value decomposition with Approximate Dynamic Programming (ADP) to outperform leading approaches by considering the impact of an individual agent's (vehicle) chosen actions on the future value of that agent. However, in order to ensure scalability and facilitate city-scale ride pooling, NeurADP completely ignores the impact of other agents actions on individual agent/vehicle value. As demonstrated in our experimental results, ignoring the impact of other agents actions on individual value can have a significant impact on the overall performance when there is increased competition among vehicles for demand. Our key contribution is a novel mechanism based on computing conditional expectations through joint conditional probabilities for capturing dependencies on other agents actions without increasing the complexity of training or decision making. We show that our new approach, Conditional Expectation based Value Decomposition (CEVD) outperforms NeurADP by up to 9.76% in terms of overall requests served, which is a significant improvement on a city wide benchmark taxi dataset.

Power curves capture the relationship between wind speed and output power for a specific wind turbine. Accurate regression models of this function prove useful in monitoring, maintenance, design, and planning. In practice, however, the measurements do not always correspond to the ideal curve: power curtailments will appear as (additional) functional components. Such multivalued relationships cannot be modelled by conventional regression, and the associated data are usually removed during pre-processing. The current work suggests an alternative method to infer multivalued relationships in curtailed power data. Using a population-based approach, an overlapping mixture of probabilistic regression models is applied to signals recorded from turbines within an operational wind farm. The model is shown to provide an accurate representation of practical power data across the population.