Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new weighted Pearson-Matthews Correlation Coefficient (MCC) for binary classification as well as weighted versions of related multiclass measures. The weighted MCC varies between $-1$ and $1$. But crucially, the weighted MCC values are higher for classifiers that perform better on highly weighted observations, and hence is able to distinguish them from classifiers that have a similar overall performance and ones that perform better on the lowly weighted observations. Furthermore, we prove that the weighted measures are robust with respect to the choice of weights in a precise manner: if the weights are changed by at most $ε$, the value of the weighted measure changes at most by a factor of $ε$ in the binary case and by a factor of $ε^2$ in the multiclass case. Our computations demonstrate that the weighted measures clearly identify classifiers that perform better on higher weighted observations, while the unweighted measures remain completely indifferent to the choices of weights.

The impact of meteorological observations on weather forecasting varies with sensor type, location, time, and other environmental factors. Thus, quantitative analysis of observation impacts is crucial for effective and efficient development of weather forecasting systems. However, the existing impact analysis methods are difficult to be widely applied due to their high dependencies on specific forecasting systems. Also, they cannot provide observation impacts at multiple spatio-temporal scales, only global impacts of observation types. To address these issues, we present a novel system called ``CloudNine,'' which allows analysis of individual observations' impacts on specific predictions based on explainable graph neural networks (XGNNs). Combining an XGNN-based atmospheric state estimation model with a numerical weather prediction model, we provide a web application to search for observations in the 3D space of the Earth system and to visualize the impact of individual observations on predictions in specific spatial regions and time periods.

When learning a task as a team, some agents in Multi-Agent Reinforcement Learning (MARL) may fail to understand their true impact in the performance of the team. Such agents end up learning sub-optimal policies, demonstrating undesired lazy behaviours. To investigate this problem, we start by formalising the use of temporal causality applied to MARL problems. We then show how causality can be used to penalise such lazy agents and improve their behaviours. By understanding how their local observations are causally related to the team reward, each agent in the team can adjust their individual credit based on whether they helped to cause the reward or not. We show empirically that using causality estimations in MARL improves not only the holistic performance of the team, but also the individual capabilities of each agent. We observe that the improvements are consistent in a set of different environments.

Commonsense (background) knowledge, at least the kind of knowledge that we fetch and relay upon in the process of language understanding: (i) cannot be learned by processing vast amounts of text because that knowledge is never explicitly stated in the text -- and you cannot find what's not there; and (ii) that background knowledge cannot be learned perceptually from observation since the vast amount of the crucial background knowledge is universal, is not probablistic nor approximate, and so it cannot be susceptible to individual observations. The shared background knowledge needed in the process of language understanding is the kind of knowledge that obeys and respects the laws of nature and as such it has to be codified. In fact, that knowledge must be codified in a symbolic system that quantifies over variables of specific ontological types. There's a consensus among researchers investigating the neurological, psychological and evolutionary aspects of human linguistic communication that languages have evolved according to the information-theoretic principle of least effort. Specifically, it has been established that interacting communicative agents tend to produce utterances that minimize the complexity of coding a thought as well as minimize the process of decoding linguistic utterances back to the intended thought [1] -- thus finding an optimal point where the effort of both speaker and listener is minimal.

Kalman Filtering is a computational tool with widespread applications in robotics, financial and weather forecasting, environmental engineering and defense. Given observation and state transition models, the Kalman Filter (KF) recursively estimates the state variables of a dynamic system. However, the KF requires a cubic time matrix inversion operation at every timestep which prevents its application in domains with large numbers of state variables. We propose Relational Gaussian Models to represent and model dynamic systems with large numbers of variables efficiently. Furthermore, we devise an exact lifted Kalman Filtering algorithm which takes only linear time in the number of random variables at every timestep. We prove that our algorithm takes linear time in the number of state variables even when individual observations apply to each variable. To our knowledge, this is the first lifted (linear time) algorithm for filtering with continuous dynamic relational models.