Mathematics for Machine Learning:Mathematics is essential to understanding the notations of machine learning. It also provides the basics to solve machine learning-related problems. This is a specialization on Coursera to develop mathematical intuition by Imperial College London named Mathematics for Machine Learning. This specialization contains three courses containing Linear Algebra, Calculus, and Principal Component Analysis. Python for everybody: The specialization Python for everybody contains five courses to learn python.

Active Position Estimation (APE) is the task of localizing one or more targets using one or more sensing platforms. APE is a key task for search and rescue missions, wildlife monitoring, source term estimation, and collaborative mobile robotics. Success in APE depends on the level of cooperation of the sensing platforms, their number, their degrees of freedom and the quality of the information gathered. APE control laws enable active sensing by satisfying either pure-exploitative or pure-explorative criteria. The former minimizes the uncertainty on position estimation; whereas the latter drives the platform closer to its task completion. In this paper, we define the main elements of APE to systematically classify and critically discuss the state of the art in this domain. We also propose a reference framework as a formalism to classify APE-related solutions. Overall, this survey explores the principal challenges and envisages the main research directions in the field of autonomous perception systems for localization tasks. It is also beneficial to promote the development of robust active sensing methods for search and tracking applications.

Reliable traffic flow prediction is crucial to creating intelligent transportation systems. Many big-data-based prediction approaches have been developed but they do not reflect complicated dynamic interactions between roads considering time and location. In this study, we propose a dynamically localised long short-term memory (LSTM) model that involves both spatial and temporal dependence between roads. To do so, we use a localised dynamic spatial weight matrix along with its dynamic variation. Moreover, the LSTM model can deal with sequential data with long dependency as well as complex non-linear features. Empirical results indicated superior prediction performances of the proposed model compared to two different baseline methods.

For example, electronic health records store the history of a patient's diagnoses, medications, laboratory values, and treatment plans [1-3]. Wearables collect granular sensor measurements of various neurophysiological body functions over time [4-6]. Intensive care units (ICUs) monitor disease progression via continuous physiological measurements (eg, electrocardiograms) [7-10]. As a result, patient data in digital medicine are regularly of longitudinal form (ie, consisting of health events from multiple time points) and thus form patient trajectories. Analyzing patient trajectories provides opportunities for more effective care in digital medicine [2,7,11]. Patient trajectories encode rich information on the history of health states that are also predictive of the future course of a disease (eg, individualized differences in disease progression or responsiveness to medications) [9,10,12]. As such, it is possible to construct patient trajectories that capture the entire disease course and characterize the many possible disease progression patterns, such as recurrent, stable, or rapidly deteriorating disease states (Figure 1). Hence, modeling the patient trajectories allows one to build robust models of diseases that capture disease dynamics seen in patient trajectories. Here, we replace disease models with data from only a single or a small number of time points by disease models that account for the longitudinal nature of patient trajectories, thus offering vast potential for digital medicine. Several studies have previously introduced artificial intelligence (AI) in medicine for practitioners [13,14].

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Accurately predicting possible behaviors of traffic participants is an essential capability for autonomous vehicles. Since autonomous vehicles need to navigate in dynamically changing environments, they are expected to make accurate predictions regardless of where they are and what driving circumstances they encountered. Therefore, generalization capability to unseen domains is crucial for prediction models when autonomous vehicles are deployed in the real world. In this paper, we aim to address the domain generalization problem for vehicle intention prediction tasks and a causal-based time series domain generalization (CTSDG) model is proposed. We construct a structural causal model for vehicle intention prediction tasks to learn an invariant representation of input driving data for domain generalization. We further integrate a recurrent latent variable model into our structural causal model to better capture temporal latent dependencies from time-series input data. The effectiveness of our approach is evaluated via real-world driving data. We demonstrate that our proposed method has consistent improvement on prediction accuracy compared to other state-of-the-art domain generalization and behavior prediction methods.

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.

This paper studies an instance of the multi-armed bandit (MAB) problem, specifically where several causal MABs operate chronologically in the same dynamical system. Practically the reward distribution of each bandit is governed by the same non-trivial dependence structure, which is a dynamic causal model. Dynamic because we allow for each causal MAB to depend on the preceding MAB and in doing so are able to transfer information between agents. Our contribution, the Chronological Causal Bandit (CCB), is useful in discrete decision-making settings where the causal effects are changing across time and can be informed by earlier interventions in the same system. In this paper, we present some early findings of the CCB as demonstrated on a toy problem.

The advent of automated and autonomous vehicles (AVs) creates opportunities to achieve system-level goals using multiple AVs, such as traffic congestion reduction. Past research has shown that multiagent congestion-reducing driving policies can be learned in a variety of simulated scenarios. While initial proofs of concept were in small, closed traffic networks with a centralized controller, recently successful results have been demonstrated in more realistic settings with distributed control policies operating in open road networks where vehicles enter and leave. However, these driving policies were mostly tested under the same conditions they were trained on, and have not been thoroughly tested for robustness to different traffic conditions, which is a critical requirement in real-world scenarios. This paper presents a learned multiagent driving policy that is robust to a variety of open-network traffic conditions, including vehicle flows, the fraction of AVs in traffic, AV placement, and different merging road geometries. A thorough empirical analysis investigates the sensitivity of such a policy to the amount of AVs in both a simple merge network and a more complex road with two merging ramps. It shows that the learned policy achieves significant improvement over simulated human-driven policies even with AV penetration as low as 2%. The same policy is also shown to be capable of reducing traffic congestion in more complex roads with two merging ramps.

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.