In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction. Despite comprehensive efforts on learning monotonic classifiers, dedicated approaches for explaining monotonic classifiers are scarce and classifier-specific. This paper describes novel algorithms for the computation of one formal explanation of a (black-box) monotonic classifier. These novel algorithms are polynomial in the run time complexity of the classifier and the number of features. Furthermore, the paper presents a practically efficient model-agnostic algorithm for enumerating formal explanations.

Decision-making policies for agents are often synthesized with the constraint that a formal specification of behaviour is satisfied. Here we focus on infinite-horizon properties. On the one hand, Linear Temporal Logic (LTL) is a popular example of a formalism for qualitative specifications. On the other hand, Steady-State Policy Synthesis (SSPS) has recently received considerable attention as it provides a more quantitative and more behavioural perspective on specifications, in terms of the frequency with which states are visited. Finally, rewards provide a classic framework for quantitative properties. In this paper, we study Markov decision processes (MDP) with the specification combining all these three types. The derived policy maximizes the reward among all policies ensuring the LTL specification with the given probability and adhering to the steady-state constraints. To this end, we provide a unified solution reducing the multi-type specification to a multi-dimensional long-run average reward. This is enabled by Limit-Deterministic B\"uchi Automata (LDBA), recently studied in the context of LTL model checking on MDP, and allows for an elegant solution through a simple linear programme. The algorithm also extends to the general $\omega$-regular properties and runs in time polynomial in the sizes of the MDP as well as the LDBA.

In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech recognition, and computer vision. Typical SOPPs have an extremely large label set, which grows exponentially as a function of the size of the output. Existing generalization analysis implies generalization bounds with at least a square-root dependency on the cardinality $d$ of the label set, which can be vacuous in practice. In this paper, we significantly improve the state of the art by developing novel high-probability bounds with a logarithmic dependency on $d$. Moreover, we leverage the lens of algorithmic stability to develop generalization bounds in expectation without any dependency on $d$. Our results therefore build a solid theoretical foundation for learning in large-scale SOPPs. Furthermore, we extend our results to learning with weakly dependent data.

Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC). However, when MCMC is used for evolutionary parameter learning, convergence requires long runs with inefficient exploration of the state space. We introduce Variational Combinatorial Sequential Monte Carlo (VCSMC), a powerful framework that establishes variational sequential search to learn distributions over intricate combinatorial structures. We then develop nested CSMC, an efficient proposal distribution for CSMC and prove that nested CSMC is an exact approximation to the (intractable) locally optimal proposal. We use nested CSMC to define a second objective, VNCSMC which yields tighter lower bounds than VCSMC. We show that VCSMC and VNCSMC are computationally efficient and explore higher probability spaces than existing methods on a range of tasks.

Recently, the Centers for Disease Control and Prevention (CDC) has worked with other federal agencies to identify counties with increasing coronavirus disease 2019 (COVID-19) incidence (hotspots) and offers support to local health departments to limit the spread of the disease. Understanding the spatio-temporal dynamics of hotspot events is of great importance to support policy decisions and prevent large-scale outbreaks. This paper presents a spatio-temporal Bayesian framework for early detection of COVID-19 hotspots (at the county level) in the United States. We assume both the observed number of cases and hotspots depend on a class of latent random variables, which encode the underlying spatio-temporal dynamics of the transmission of COVID-19. Such latent variables follow a zero-mean Gaussian process, whose covariance is specified by a non-stationary kernel function. The most salient feature of our kernel function is that deep neural networks are introduced to enhance the model's representative power while still enjoying the interpretability of the kernel. We derive a sparse model and fit the model using a variational learning strategy to circumvent the computational intractability for large data sets. Our model demonstrates better interpretability and superior hotspot-detection performance compared to other baseline methods.

The increased digitalisation and monitoring of the energy system opens up numerous opportunities % and solutions which can help to decarbonise the energy system. Applications on low voltage (LV), localised networks, such as community energy markets and smart storage will facilitate decarbonisation, but they will require advanced control and management. Reliable forecasting will be a necessary component of many of these systems to anticipate key features and uncertainties. Despite this urgent need, there has not yet been an extensive investigation into the current state-of-the-art of low voltage level forecasts, other than at the smart meter level. This paper aims to provide a comprehensive overview of the landscape, current approaches, core applications, challenges and recommendations. Another aim of this paper is to facilitate the continued improvement and advancement in this area. To this end, the paper also surveys some of the most relevant and promising trends. It establishes an open, community-driven list of the known LV level open datasets to encourage further research and development.

The graphical structure of Probabilistic Graphical The implication problem is the task of determining whether Models (PGMs) encodes the conditional independence a set of CIs termed antecedents logically entail another (CI) relations that hold in the modeled distribution. CI, called the consequent, and it has received considerable Graph algorithms, such as d-separation, attention from both the AI and Database communities use this structure to infer additional conditional [10, 12, 15, 16, 22, 23]. Known algorithms for deriving independencies, and to query whether a specific CIs from the topological structure of the graphical model CI holds in the distribution. The premise of all are, in fact, an instance of implication. Notably, the DAG current systems-of-inference for deriving CIs in structure of Bayesian Networks is generated based on a set PGMs, is that the set of CIs used for the construction of CIs termed the recursive basis [11], and the d-separation of the PGM hold exactly. In practice, algorithms algorithm is used to derive additional CIs, implied by this for extracting the structure of PGMs from set. The d-separation algorithm is a sound and complete data, discover approximate CIs that do not hold exactly method for deriving CIs in probability distributions represented in the distribution. In this paper, we ask how by DAGs [10, 11], and hence completely characterizes the error in this set propagates to the inferred CIs the CIs that hold in the distribution.

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage several times higher than their deterministic counterparts. To address this, we augment the weight matrix of each layer with a small number of inducing weights, thereby projecting the uncertainty quantification into such low dimensional spaces. We further extend Matheron's conditional Gaussian sampling rule to enable fast weight sampling, which enables our inference method to maintain reasonable run-time as compared with ensembles. Importantly, our approach achieves competitive performance to the state-of-the-art in prediction and uncertainty estimation tasks with fully connected neural networks and ResNets, while reducing the parameter size to $\leq 24.3\%$ of that of a $single$ neural network.

This paper introduces a new acquisition function under the Bayesian active learning framework, namely BABA. It is motivated by previously well-established works BALD, and BatchBALD which capture the mutual information between the model parameters and the predictive outputs of the data. Our proposed measure, BABA, endeavors to quantify the normalized mutual information by approximating the stochasticity of predictive probabilities using Beta distributions. BABA outperforms the well-known family of acquisition functions, including BALD and BatchBALD. We demonstrate this by showing extensive experimental results obtained from MNIST and EMNIST datasets.

Measuring public opinion is a key focus during democratic elections, enabling candidates to gauge their popularity and alter their campaign strategies accordingly. Traditional survey polling remains the most popular estimation technique, despite its cost and time intensity, measurement errors, lack of real-time capabilities and lagged representation of public opinion. In recent years, Twitter opinion mining has attempted to combat these issues. Despite achieving promising results, it experiences its own set of shortcomings such as an unrepresentative sample population and a lack of long term stability. This paper aims to merge data from both these techniques using Bayesian data assimilation to arrive at a more accurate estimate of true public opinion for the Brexit referendum. This paper demonstrates the effectiveness of the proposed approach using Twitter opinion data and survey data from trusted pollsters. Firstly, the possible existence of a time gap of 16 days between the two data sets is identified. This gap is subsequently incorporated into a proposed assimilation architecture. This method was found to adequately incorporate information from both sources and measure a strong upward trend in Leave support leading up to the Brexit referendum. The proposed technique provides useful estimates of true opinion, which is essential to future opinion measurement and forecasting research.