The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at https://github.com/Epanemu/LiCE.

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems.In testing data quality, for example, one may study the distance of a given dataset, viewed as a distribution, to a given ground-truth reference dataset.However, classical metrics, such as the Total Variation and the Wasserstein distances, are known to have high sample complexities and, therefore, may fail to provide a meaningful distinction in many practical scenarios.In this paper, we propose a new notion of distance, the Maximum Subgroup Discrepancy (MSD).In this metric, two distributions are close if, roughly, discrepancies are low for all feature subgroups.While the number of subgroups may be exponential, we show that the sample complexity is linear in the number of features, thus making it feasible for practical applications.Moreover, we provide a practical algorithm for evaluating the distance based on Mixedinteger optimization (MIO).We also note that the proposed distance is easily interpretable, thus providing clearer paths to fixing the biases once they have been identified.Finally, we describe a natural general bias detection framework, termed MSDD distances, and show that MSD aligns well with this framework.We empirically evaluate MSD by comparing it with other metrics and by demonstrating the above properties of MSD on real-world datasets.

We describe an architecture for a decentralised data market for applications in which agents are incentivised to collaborate to crowd-source their data. The architecture is designed to reward data that furthers the market's collective goal, and distributes reward fairly to all those that contribute with their data. We show that the architecture is resilient to Sybil , wormhole , and data poisoning attacks. In order to evaluate the resilience of the architecture, we characterise its breakdown points for various adversarial threat models in an automotive use case.

There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. We show that binarized neural networks admit a tame representation by reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, which we show to have nice properties. This makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in timeseries forecasting problems: subgroup fairness and instantaneous fairness. These notion extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods.

We consider the design of distributed algorithms that govern the manner in which agents contribute to a social sensing platform. Specifically, we are interested in situations, where fairness among the agents contributing to the platform is needed. A notable example is the platforms operated by public bodies, where fairness is a legal requirement. The design of such distributed systems is challenging due to the fact that we wish to simultaneously realize an efficient social sensing platform but also deliver a predefined quality of service to the agents (for example, a fair opportunity to contribute to the platform). In this article, we introduce iterated function systems (IFSs) as a tool for the design and analysis of systems of this kind. We show how the IFS framework can be used to realize systems that deliver a predictable quality of service to agents, can be used to underpin contracts governing the interaction of agents with the social sensing platform, and which are efficient. To illustrate our design via a use case, we consider a large, high-density network of participating parked vehicles. When awoken by an administrative center, this network proceeds to search for moving missing entities of interest using RFID-based techniques. We regulate which vehicles are actively searching for the moving entity of interest at any point in time. In doing so, we seek to equalize vehicular energy consumption across the network. This is illustrated through simulations of a search for a missing Alzheimer’s patient in Melbourne, Australia. The experimental results are presented to illustrate the efficacy of our system and the predictability of access of agents to the platform independent of initial conditions.

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. When the amounts of training data for the subgroups are not controlled carefully, under-representation bias arises. We introduce two natural notions of subgroup fairness and instantaneous fairness to address such under-representation bias in time-series forecasting problems. In particular, we consider the subgroup-fair and instant-fair learning of a linear dynamical system (LDS) from multiple trajectories of varying lengths and the associated forecasting problems. We provide globally convergent methods for the learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate both the beneficial impact of fairness considerations on statistical performance and the encouraging effects of exploiting sparsity on run time.

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed “sparse” noise. In theory, we bound the tracking error. In practice, our use of randomised coordinate descent is scalable and allows for encouraging results on changedetection.net, a benchmark.

The Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult.Based on this insight, we devise an on-line algorithm for improper learning of a linear dynamical system (LDS), which considers only a few most recent observations. We use our decay results to provide the first regret bounds w.r.t. to Kalman filters within learning an LDS. That is, we compare the results of our algorithm to the best, in hindsight, Kalman filter for a given signal. Also, the algorithm is practical: its per-update run-time is linear in the regression depth.

Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts. In this paper, we propose Entropy-Penalized Semi-Definite Programming (EP-SDP), which provides a unified framework for a broad class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit an efficient numerical algorithm, having (almost) linear time complexity of the gradient computation; this makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.

Many real-world monitoring and surveillance applications require non-trivial anomaly detection to be run in the streaming model. We consider an incremental-learning approach, wherein a deep-autoencoding (DAE) model of what is normal is trained and used to detect anomalies at the same time. In the detection of anomalies, we utilise a novel thresholding mechanism, based on value at risk (VaR). We compare the resulting convolutional neural network (CNN) against a number of subspace methods and present results on changedetection.net.

Urban traffic gathers increasing interest as cities become bigger, crowded and “smart”. We present a system for het-erogeneous stream processing and crowdsourcing supporting intelligent urban traffic management. Complex events related to traffic congestion (trends) are detected from heterogeneous sources involving fixed sensors mounted on intersections and mobile sensors mounted on public transport vehicles. To deal with data veracity, a crowdsourcing component handles and resolves sensor disagreement. Furthermore, to deal with data sparsity, a traffic modelling component offers information in areas with low sensor coverage. We demonstrate the system with a real-world use-case from Dublin city, Ireland.

Jakub Mareček; Handbook of Approximation Algorithms and Metaheuristics, The Computer Journal, Volume 53, Issue 8, 1 October 2010, Pages 1338–1339, https://

Jakub Mareček; Yves Pochet and Laurence A. WolseyProduction Planning Using Mixed Integer Programming.Springer (2006). ISBN 978-0-387-29959-4. £38.50/$59.95.477