The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by the rules of European club football competitions: in order to maintain their international character, the organiser usually imposes an association constraint both in the group stage and the first round of the subsequent knockout phase, that is, teams from the same country cannot be drawn against each other. The effects of similar restrictions are explored in both theoretical and simulation models. Using an association constraint in the first round(s) is verified to increase the likelihood of a same nation matchup to approximately the same extent in each subsequent round. Furthermore, if the favourite teams are concentrated in some associations, they have a higher probability to win the tournament in the presence of association constraints. Our results essentially justify a recent decision of the Union of European Football Associations (UEFA).
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new theory about inference with missing data. It proves that as the sample size increases and the extent of missingness decreases, the mean-loglikelihood function generated by partial data and that ignores the missingness mechanism will almost surely converge uniformly to that which would have been generated by complete data; and if the data are Missing at Random (or "partially missing at random"), this convergence depends only on sample size. Thus, inferences from partial data, such as posterior modes, uncertainty estimates, confidence intervals, likelihood ratios, and indeed, all quantities or features derived from the partial-data loglikelihood function, will be consistently estimated. They will approximate their complete-data analogues. This adds to previous research which has only proved the consistency of the posterior mode. Practical implications of this result are discussed, and the theory is verified using a previous study of International Human Rights Law.
Many modern organisations employ methods which involve monitoring of employees' actions in order to encourage teamwork in the workplace. While monitoring promotes a transparent working environment, the effects of making monitoring itself transparent may be ambiguous and have received surprisingly little attention in the literature. Using a novel laboratory experiment, we create a working environment in which first movers can (or cannot) observe second mover's monitoring at the end of a round. Our framework consists of a standard repeated sequential Prisoner's Dilemma, where the second mover can observe the choices made by first movers either exogenously or endogenously. We show that mutual cooperation occurs significantly more frequently when monitoring is made transparent. Additionally, our results highlight the key role of conditional cooperators (who are more likely to monitor) in promoting teamwork. Overall, the observed cooperation enhancing effects are due to monitoring actions that carry information about first movers who use it to better screen the type of their co-player and thereby reduce the risk of being exploited.
Machine learning driven medical image segmentation has become standard in medical image analysis. However, deep learning models are prone to overconfident predictions. This has led to a renewed focus on calibrated predictions in the medical imaging and broader machine learning communities. Calibrated predictions are estimates of the probability of a label that correspond to the true expected value of the label conditioned on the confidence. Such calibrated predictions have utility in a range of medical imaging applications, including surgical planning under uncertainty and active learning systems. At the same time it is often an accurate volume measurement that is of real importance for many medical applications. This work investigates the relationship between model calibration and volume estimation. We demonstrate both mathematically and empirically that if the predictor is calibrated per image, we can obtain the correct volume by taking an expectation of the probability scores per pixel/voxel of the image. Furthermore, we show that convex combinations of calibrated classifiers preserve volume estimation, but do not preserve calibration. Therefore, we conclude that having a calibrated predictor is a sufficient, but not necessary condition for obtaining an unbiased estimate of the volume. We validate our theoretical findings empirically on a collection of 18 different (calibrated) training strategies on the tasks of glioma volume estimation on BraTS 2018, and ischemic stroke lesion volume estimation on ISLES 2018 datasets.
Machine learning solutions for pattern classification problems are nowadays widely deployed in society and industry. However, the lack of transparency and accountability of most accurate models often hinders their safe use. Thus, there is a clear need for developing explainable artificial intelligence mechanisms. There exist model-agnostic methods that summarize feature contributions, but their interpretability is limited to predictions made by black-box models. An open challenge is to develop models that have intrinsic interpretability and produce their own explanations, even for classes of models that are traditionally considered black boxes like (recurrent) neural networks. In this paper, we propose a Long-Term Cognitive Network for interpretable pattern classification of structured data. Our method brings its own mechanism for providing explanations by quantifying the relevance of each feature in the decision process. For supporting the interpretability without affecting the performance, the model incorporates more flexibility through a quasi-nonlinear reasoning rule that allows controlling nonlinearity. Besides, we propose a recurrence-aware decision model that evades the issues posed by the unique fixed point while introducing a deterministic learning algorithm to compute the tunable parameters. The simulations show that our interpretable model obtains competitive results when compared to state-of-the-art white and black-box models.
Signaling design for secure transmission in two-user multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) networks is investigated in this paper. The base station broadcasts multicast data to all users and also integrates additional services, unicast data targeted to certain users, and confidential data protected against eavesdroppers. We categorize the above MIMO-NOMA with different security requirements into several communication scenarios. The associated problem in each scenario is nonconvex. We propose a unified approach, called the power splitting scheme, for optimizing the rate equations corresponding to the scenarios. The proposed method decomposes the optimization of the secure MIMO-NOMA channel into a set of simpler problems, including multicast, point-to-point, and wiretap MIMO problems, corresponding to the three basic messages: multicast, private/unicast, and confidential messages. We then leverage existing solutions to design signaling for the above problems such that the messages are transmitted with high security and reliability. Numerical results illustrate the efficacy of the proposed covariance matrix design in secure MIMO-NOMA transmission. The proposed method also outperforms existing solutions, when applicable. In the case of no multicast messages, we also reformulate the nonconvex problem into weighted sum rate (WSR) maximization problems by applying the block successive maximization method and generalizing the zero duality gap. The two methods have their advantages and limitations. Power splitting is a general tool that can be applied to the MIMO-NOMA with any combination of the three messages (multicast, private, and confidential) whereas WSR maximization shows greater potential for secure MIMO-NOMA communication without multicasting. In such cases, WSR maximization provides a slightly better rate than the power splitting method.
The key challenge in learning dense correspondences lies in the lack of ground-truth matches for real image pairs. While photometric consistency losses provide unsupervised alternatives, they struggle with large appearance changes, which are ubiquitous in geometric and semantic matching tasks. Moreover, methods relying on synthetic training pairs often suffer from poor generalisation to real data. We propose Warp Consistency, an unsupervised learning objective for dense correspondence regression. Our objective is effective even in settings with large appearance and view-point changes. Given a pair of real images, we first construct an image triplet by applying a randomly sampled warp to one of the original images. We derive and analyze all flow-consistency constraints arising between the triplet. From our observations and empirical results, we design a general unsupervised objective employing two of the derived constraints. We validate our warp consistency loss by training three recent dense correspondence networks for the geometric and semantic matching tasks. Our approach sets a new state-of-the-art on several challenging benchmarks, including MegaDepth, RobotCar and TSS. Code and models will be released at //github.com/PruneTruong/DenseMatching.
When we humans look at a video of human-object interaction, we can not only infer what is happening but we can even extract actionable information and imitate those interactions. On the other hand, current recognition or geometric approaches lack the physicality of action representation. In this paper, we take a step towards a more physical understanding of actions. We address the problem of inferring contact points and the physical forces from videos of humans interacting with objects. One of the main challenges in tackling this problem is obtaining ground-truth labels for forces. We sidestep this problem by instead using a physics simulator for supervision. Specifically, we use a simulator to predict effects and enforce that estimated forces must lead to the same effect as depicted in the video. Our quantitative and qualitative results show that (a) we can predict meaningful forces from videos whose effects lead to accurate imitation of the motions observed, (b) by jointly optimizing for contact point and force prediction, we can improve the performance on both tasks in comparison to independent training, and (c) we can learn a representation from this model that generalizes to novel objects using few shot examples.
To solve complex real-world problems with reinforcement learning, we cannot rely on manually specified reward functions. Instead, we can have humans communicate an objective to the agent directly. In this work, we combine two approaches to learning from human feedback: expert demonstrations and trajectory preferences. We train a deep neural network to model the reward function and use its predicted reward to train an DQN-based deep reinforcement learning agent on 9 Atari games. Our approach beats the imitation learning baseline in 7 games and achieves strictly superhuman performance on 2 games without using game rewards. Additionally, we investigate the goodness of fit of the reward model, present some reward hacking problems, and study the effects of noise in the human labels.
Active learning has long been a topic of study in machine learning. However, as increasingly complex and opaque models have become standard practice, the process of active learning, too, has become more opaque. There has been little investigation into interpreting what specific trends and patterns an active learning strategy may be exploring. This work expands on the Local Interpretable Model-agnostic Explanations framework (LIME) to provide explanations for active learning recommendations. We demonstrate how LIME can be used to generate locally faithful explanations for an active learning strategy, and how these explanations can be used to understand how different models and datasets explore a problem space over time. In order to quantify the per-subgroup differences in how an active learning strategy queries spatial regions, we introduce a notion of uncertainty bias (based on disparate impact) to measure the discrepancy in the confidence for a model's predictions between one subgroup and another. Using the uncertainty bias measure, we show that our query explanations accurately reflect the subgroup focus of the active learning queries, allowing for an interpretable explanation of what is being learned as points with similar sources of uncertainty have their uncertainty bias resolved. We demonstrate that this technique can be applied to track uncertainty bias over user-defined clusters or automatically generated clusters based on the source of uncertainty.
In this work, we compare three different modeling approaches for the scores of soccer matches with regard to their predictive performances based on all matches from the four previous FIFA World Cups 2002 - 2014: Poisson regression models, random forests and ranking methods. While the former two are based on the teams' covariate information, the latter method estimates adequate ability parameters that reflect the current strength of the teams best. Within this comparison the best-performing prediction methods on the training data turn out to be the ranking methods and the random forests. However, we show that by combining the random forest with the team ability parameters from the ranking methods as an additional covariate we can improve the predictive power substantially. Finally, this combination of methods is chosen as the final model and based on its estimates, the FIFA World Cup 2018 is simulated repeatedly and winning probabilities are obtained for all teams. The model slightly favors Spain before the defending champion Germany. Additionally, we provide survival probabilities for all teams and at all tournament stages as well as the most probable tournament outcome.