Originating in game theory, Shapley values are widely used for explaining a machine learning model’s prediction by quantifying the contribution of each feature’s value to the prediction. This requires a scalar prediction as in binary classification, whereas a multiclass probabilistic prediction is a discrete probability distribution, living on a multidimensional simplex. In such a multiclass setting the Shapley values are typically computed separately on each class in a one-vs-rest manner, ignoring the compositional nature of the output distribution. In this paper, we introduce Shapley compositions as a well-founded way to properly explain a multiclass probabilistic prediction, using the Aitchison geometry from compositional data analysis. We prove that the Shapley composition is the unique quantity satisfying linearity, symmetry and efficiency on the Aitchison simplex, extending the corresponding axiomatic properties of the standard Shapley value. We demonstrate this proper multiclass treatment in a range of scenarios.

Abstract This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its instance-wise predictions. This is essential for critical applications, optimal decision making, cost-sensitive classification, and for some types of context change. Calibration research has a rich history which predates the birth of machine learning as an academic field by decades. However, a recent increase in the interest on calibration has led to new methods and the extension from binary to the multiclass setting. The space of options and issues to consider is large, and navigating it requires the right set of concepts and tools. We provide both introductory material and up-to-date technical details of the main concepts and methods, including proper scoring rules and other evaluation metrics, visualisation approaches, a comprehensive account of post-hoc calibration methods for binary and multiclass classification, and several advanced topics.

Activity of daily living is an important indicator of the health status and functional capabilities of an individual. Activity recognition, which aims at understanding the behavioral patterns of people, has increasingly received attention in recent years. However, there are still a number of challenges confronting the task. First, labelling training data is expensive and time-consuming, leading to limited availability of annotations. Secondly, activities performed by individuals have considerable variability, which renders the generally used supervised learning with a fixed label set unsuitable. To address these issues, we propose a dynamic active learning-based activity recognition method in this work. Different from traditional active learning methods which select samples based on a fixed label set, the proposed method not only selects informative samples from known classes, but also dynamically identifies new activities which are not included in the predefined label set. Starting with a classifier that has access to a limited number of labelled samples, we iteratively extend the training set with informative labels by fully considering the uncertainty, diversity and representativeness of samples, based on which better-informed classifiers can be trained, further reducing the annotation cost. We evaluate the proposed method on two synthetic datasets and two existing benchmark datasets. Experimental results demonstrate that our method not only boosts the activity recognition performance with considerably reduced annotation cost, but also enables adaptive daily activity analysis allowing the presence and detection of novel activities and patterns.

This paper explores the mechanisms to efficiently combine annotations of different quality for multiclass classification datasets, as we argue that it is easier to obtain large collections of weak labels as opposed to true labels. Since labels come from different sources, their annotations may have different degrees of reliability (e.g., noisy labels, supersets of labels, complementary labels or annotations performed by domain experts), and we must make sure that the addition of potentially inaccurate labels does not degrade the performance achieved when using only true labels. For this reason, we consider each group of annotations as being weakly supervised and pose the problem as finding the optimal combination of such collections. We propose an efficient algorithm based on expectation-maximization and show its performance in both synthetic and real-world classification tasks in a variety of weak label scenarios.

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.

The SPHERE project is devoted to advancing eHealth in a smart-home context, and supports full-scale sensing and data analysis to enable a generic healthcare service. We describe, from a data-science perspective, our experience of taking the system out of the laboratory into more than thirty homes in Bristol, UK. We describe the infrastructure and processes that had to be developed along the way, describe how we train and deploy Machine Learning systems in this context, and give a realistic appraisal of the state of the deployed systems.

We introduce a powerful technique to make classifiers more reliable and versatile. Background Check equips classifiers with the ability to assess the difference of unlabelled test data from the training data. In particular, Background Check gives classifiers the capability to (i) perform cautious classification with a reject option, (ii) identify outliers, and (iii) better assess the confidence in their predictions. We derive the method from first principles and consider four particular relationships between background and foreground distributions. One of these assumes an affine relationship with two parameters, and we show how this bivariate parameter space naturally interpolates between the above capabilities. We demonstrate the versatility of the approach by comparing it experimentally with published special-purpose solutions for outlier detection and confident classification on 41 benchmark datasets. Results show that Background Check can match and in many cases surpass the performances of specialised approaches.