Predicting the results of matches in sport is a challenging and interesting task. In this paper, we review a selection of studies from 1996 to 2019 that used machine learning for predicting match results in team sport. Considering both invasion sports and striking/fielding sports, we discuss commonly applied machine learning algorithms, as well as common approaches related to data and evaluation. Our study considers accuracies that have been achieved across different sports, and explores whether evidence exists to support the notion that outcomes of some sports may be inherently more difficult to predict. We also uncover common themes of future research directions and propose recommendations for future researchers. Although there remains a lack of benchmark datasets (apart from in soccer), and the differences between sports, datasets and features makes between-study comparisons difficult, as we discuss, it is possible to evaluate accuracy performance in other ways. Artificial Neural Networks were commonly applied in early studies, however, our findings suggest that a range of models should instead be compared. Selecting and engineering an appropriate feature set appears to be more important than having a large number of instances. For feature selection, we see potential for greater inter-disciplinary collaboration between sport performance analysis, a sub-discipline of sport science, and machine learning.

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Machine learning (ML) has become ubiquitous in scientific disciplines. In some applications, accurate data-driven predictions are all that is required; however, in many others, interpretability and explainability of the model is equally important. Interpretability and explainability can provide justification for decisions, promote scientific discovery and ultimately lead to better control/improvement of models [1, 2]. In a complementary fashion, ML models can provide further insight by conveying their level of uncertainty in predictions [3]. Especially in cases of low risk tolerance this type of insight is crucial for building trust in ML models [4]. Rather than focus on black-box ML methods (e.g., neural networks or Gaussian process regression) combined with post hoc explainability tools, the current work focuses on inherently interpretable methods. Interpretable ML methods can be competitive with black-box ML in terms of accuracy and do not require a separate explainability toolkit [4, 5]. Symbolic regression is one such inherently interpretable form of ML wherein an analytic equation is produced that best models input data.

In the road so far, we have talked about MLP, CNN, and RNN architectures. These are discriminative models, that is models that can make predictions. Discriminative models essentially learn to estimate a conditional probability distribution p( x); that is, given a value, they try to predict the outcome based on what they learned about the probability distribution of x. Generative models are architectures of neural networks that learn the probability distribution of the data and learn how to generate data that seems to come from that probability distribution. Creating synthetic data is one use of generative models, but is not the only one.

Linear projections are widely used in the analysis of high-dimensional data. In unsupervised settings where the data harbour latent classes/clusters, the question of whether class discriminatory signals are retained under projection is crucial. In the case of mean differences between classes, this question has been well studied. However, in many contemporary applications, notably in biomedicine, group differences at the level of covariance or graphical model structure are important. Motivated by such applications, in this paper we ask whether linear projections can preserve differences in second order structure between latent groups. We focus on unsupervised projections, which can be computed without knowledge of class labels. We discuss a simple theoretical framework to study the behaviour of such projections which we use to inform an analysis via quasi-exhaustive enumeration. This allows us to consider the performance, over more than a hundred thousand sets of data-generating population parameters, of two popular projections, namely random projections (RP) and Principal Component Analysis (PCA). Across this broad range of regimes, PCA turns out to be more effective at retaining second order signals than RP and is often even competitive with supervised projection. We complement these results with fully empirical experiments showing 0-1 loss using simulated and real data. We study also the effect of projection dimension, drawing attention to a bias-variance trade-off in this respect. Our results show that PCA can indeed be a suitable first-step for unsupervised analysis, including in cases where differential covariance or graphical model structure are of interest.

A challenging problem in task-free continual learning is the online selection of a representative replay memory from data streams. In this work, we investigate the online memory selection problem from an information-theoretic perspective. To gather the most information, we propose the surprise and the learnability criteria to pick informative points and to avoid outliers. We present a Bayesian model to compute the criteria efficiently by exploiting rank-one matrix structures. We demonstrate that these criteria encourage selecting informative points in a greedy algorithm for online memory selection. Furthermore, by identifying the importance of the timing to update the memory, we introduce a stochastic informationtheoretic reservoir sampler (InfoRS), which conducts sampling among selective points with high information. Compared to reservoir sampling, InfoRS demonstrates improved robustness against data imbalance. Continual learning (Robins, 1995; Goodfellow et al., 2013; Kirkpatrick et al., 2017) aims at training models through a non-stationary data stream without catastrophic forgetting of past experiences. Specifically, replay-based methods (Lopez-Paz & Ranzato, 2017; Rebuffi et al., 2017; Rolnick et al., 2019) tackle the continual learning problem by keeping a replay memory for rehearsals over the past data. Given the limited memory budget, selecting a representative memory becomes critical. The majority of existing approaches focus on task-based continual learning and update the memory based on the given task boundaries. Since the requirement for task boundaries is usually not realistic, general continual learning (GCL) (Aljundi et al., 2019a; Delange et al., 2021; Buzzega et al., 2020) has received increasing attention, which assumes that the agent observes the streaming data in an online fashion without knowing task boundaries. GCL makes the online memory selection more challenging since one needs to update the memory in each iteration based only on instant observations. So, successful memory management for GCL needs to be both efficient and effective.

Maximum Likelihood Estimation (MLE) is a probabilistic based approach to determine values for the parameters of the model. Parameters could be defined as blueprints for the model because based on that the algorithm works. MLE is a widely used technique in machine learning, time series, panel data and discrete data. The motive of MLE is to maximize the likelihood of values for the parameter to get the desired outcomes. Following are the topics to be covered.

Despite recent improvements in computer vision, artificial visual systems' design is still daunting since an explanation of visual computing algorithms remains elusive. Salient object detection is one problem that is still open due to the difficulty of understanding the brain's inner workings. Progress on this research area follows the traditional path of hand-made designs using neuroscience knowledge. In recent years two different approaches based on genetic programming appear to enhance their technique. One follows the idea of combining previous hand-made methods through genetic programming and fuzzy logic. The other approach consists of improving the inner computational structures of basic hand-made models through artificial evolution. This research work proposes expanding the artificial dorsal stream using a recent proposal to solve salient object detection problems. This approach uses the benefits of the two main aspects of this research area: fixation prediction and detection of salient objects. We decided to apply the fusion of visual saliency and image segmentation algorithms as a template. The proposed methodology discovers several critical structures in the template through artificial evolution. We present results on a benchmark designed by experts with outstanding results in comparison with the state-of-the-art.

Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more ambiguously determined from the data. As such, existing inference methods tend to yield very noisy and underestimated OEF maps, while overestimating DBV. This work describes a novel probabilistic machine learning approach that can infer plausible distributions of OEF and DBV. Initially, we create a model that produces informative voxelwise prior distribution based on synthetic training data. Contrary to prior work, we model the joint distribution of OEF and DBV through a scaled multivariate logit-Normal distribution, which enables the values to be constrained within a plausible range. The prior distribution model is used to train an efficient amortized variational Bayesian inference model. This model learns to infer OEF and DBV by predicting real image data, with few training data required, using the signal equations as a forward model. We demonstrate that our approach enables the inference of smooth OEF and DBV maps, with a physiologically plausible distribution that can be adapted through specification of an informative prior distribution. Other benefits include model comparison (via the evidence lower bound) and uncertainty quantification for identifying image artefacts. Results are demonstrated on a small study comparing subjects undergoing hyperventilation and at rest. We illustrate that the proposed approach allows measurement of gray matter differences in OEF and DBV and enables voxelwise comparison between conditions, where we observe significant increases in OEF and $R_2^\prime$ during hyperventilation.

We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation is based on the idea of statistical model criticism, popular in Bayesian data analysis, whereby a statistical model is evaluated in terms of its ability to reproduce statistics of an unknown data generating process from which we can obtain samples. A VAE learns not one, but two joint distributions over a shared sample space, each exploiting a choice of factorisation that makes sampling tractable in one of two directions (latent-to-data, data-to-latent). We evaluate samples from these distributions, assessing their (marginal) fit to the observed data and our choice of prior, and we also evaluate samples through a pipeline that connects the two distributions starting from a data sample, assessing whether together they exploit and reveal latent factors of variation that are useful to a practitioner. We show that this methodology offers possibilities for model selection qualitatively beyond intrinsic evaluation metrics and at a finer granularity than commonly used statistics can offer.