This short note reviews so-called Natural Gradient Descent (NGD) for multivariate Gaussians. The Fisher Information Matrix (FIM) is derived for several different parameterizations of Gaussians. Careful attention is paid to the symmetric nature of the covariance matrix when calculating derivatives. We show that there are some advantages to choosing a parameterization comprising the mean and inverse covariance matrix and provide a simple NGD update that accounts for the symmetric (and sparse) nature of the inverse covariance matrix.

The article considers smooth optimization of functions on Lie groups. By generalizing NAG variational principle in vector space (Wibisono et al., 2016) to Lie groups, continuous Lie-NAG dynamics which are guaranteed to converge to local optimum are obtained. They correspond to momentum versions of gradient flow on Lie groups. A particular case of $\mathsf{SO}(n)$ is then studied in details, with objective functions corresponding to leading Generalized EigenValue problems: the Lie-NAG dynamics are first made explicit in coordinates, and then discretized in structure preserving fashions, resulting in optimization algorithms with faithful energy behavior (due to conformal symplecticity) and exactly remaining on the Lie group. Stochastic gradient versions are also investigated. Numerical experiments on both synthetic data and practical problem (LDA for MNIST) demonstrate the effectiveness of the proposed methods as optimization algorithms ($not$ as a classification method).

Standard supervised machine learning assumes that the distribution of the source samples used to train an algorithm is the same as the one of the target samples on which it is supposed to make predictions. However, as any data scientist will confirm, this is hardly ever the case in practice. The set of statistical and numerical methods that deal with such situations is known as domain adaptation, a field with a long and rich history. The myriad of methods available and the unfortunate lack of a clear and universally accepted terminology can however make the topic rather daunting for the newcomer. Therefore, rather than aiming at completeness, which leads to exhibiting a tedious catalog of methods, this pedagogical review aims at a coherent presentation of four important special cases: (1) \emph{prior shift}, a situation in which training samples were selected according to their labels without any knowledge of their actual distribution in the target, (2) \emph{covariate shift} which deals with a situation where training examples were picked according to their features but with some selection bias, (3) \emph{concept shift} where the dependence of the labels on the features defers between the source and the target, and last but not least (4) \emph{subspace mapping} which deals with a situation where features in the target have been subjected to an unknown distortion with respect to the source features. In each case we first build an intuition, next we provide the appropriate mathematical framework and eventually we describe a practical application.

Reinforcement Learning (RL) has demonstrated a great potential for automatically solving decision making problems in complex uncertain environments. Basically, RL proposes a computational approach that allows learning through interaction in an environment of stochastic behavior, with agents taking actions to maximize some cumulative short-term and long-term rewards. Some of the most impressive results have been shown in Game Theory where agents exhibited super-human performance in games like Go or Starcraft 2, which led to its adoption in many other domains including Cloud Computing. Particularly, workflow autoscaling exploits the Cloud elasticity to optimize the execution of workflows according to a given optimization criteria. This is a decision-making problem in which it is necessary to establish when and how to scale-up/down computational resources; and how to assign them to the upcoming processing workload. Such actions have to be taken considering some optimization criteria in the Cloud, a dynamic and uncertain environment. Motivated by this, many works apply RL to the autoscaling problem in Cloud. In this work we survey exhaustively those proposals from major venues, and uniformly compare them based on a set of proposed taxonomies. We also discuss open problems and provide a prospective of future research in the area.

Weather is an important factor affecting transportation and road safety. In this paper, we leverage state-of-the-art convolutional neural networks in labelling images taken by street and highway cameras located across across North America. Road camera snapshots were used in experiments with multiple deep learning frameworks to classify images by road condition. The training data for these experiments used images labelled as dry, wet, snow/ice, poor, and offline. The experiments tested different configurations of six convolutional neural networks (VGG-16, ResNet50, Xception, InceptionResNetV2, EfficientNet-B0 and EfficientNet-B4) to assess their suitability to this problem. The precision, accuracy, and recall were measured for each framework configuration. In addition, the training sets were varied both in overall size and by size of individual classes. The final training set included 47,000 images labelled using the five aforementioned classes. The EfficientNet-B4 framework was found to be most suitable to this problem, achieving validation accuracy of 90.6%, although EfficientNet-B0 achieved an accuracy of 90.3% with half the execution time. It was observed that VGG-16 with transfer learning proved to be very useful for data acquisition and pseudo-labelling with limited hardware resources, throughout this project. The EfficientNet-B4 framework was then placed into a real-time production environment, where images could be classified in real-time on an ongoing basis. The classified images were then used to construct a map showing real-time road conditions at various camera locations across North America. The choice of these frameworks and our analysis take into account unique requirements of real-time map building functions. A detailed analysis of the process of semi-automated dataset labelling using these frameworks is also presented in this paper.

Experimental corn hybrids are created in plant breeding programs by crossing two parents, so-called inbred and tester, together. Identification of best parent combinations for crossing is challenging since the total number of possible cross combinations of parents is large and it is impractical to test all possible cross combinations due to limited resources of time and budget. In the 2020 Syngenta Crop Challenge, Syngenta released several large datasets that recorded the historical yield performances of around 4% of total cross combinations of 593 inbreds with 496 testers which were planted in 280 locations between 2016 and 2018 and asked participants to predict the yield performance of cross combinations of inbreds and testers that have not been planted based on the historical yield data collected from crossing other inbreds and testers. In this paper, we present a collaborative filtering method which is an ensemble of matrix factorization method and neural networks to solve this problem. Our computational results suggested that the proposed model significantly outperformed other models such as LASSO, random forest (RF), and neural networks. Presented method and results were produced within the 2020 Syngenta Crop Challenge.

There is fast-growing literature on estimating heterogeneous treatment effects via random forests in observational studies. However, there are few approaches available for right-censored survival data. In clinical trials, right-censored survival data are frequently encountered. Quantifying the causal relationship between a treatment and the survival outcome is of great interest. Random forests provide a robust, nonparametric approach to statistical estimation. In addition, recent developments allow forest-based methods to quantify the uncertainty of the estimated heterogeneous treatment effects. We propose causal survival forests that directly target on estimating the treatment effect from an observational study. We establish consistency and asymptotic normality of the proposed estimators and provide an estimator of the asymptotic variance that enables valid confidence intervals of the estimated treatment effect. The performance of our approach is demonstrated via extensive simulations and data from an HIV study.

In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use Gaussian process (GP) priors to impose our knowledge about the characteristics of the underlying stationary segments, and use a nonparametric distribution to partition the sequences into such segments, formulated in terms of a prior distribution on segment length. Given the segmentation, the model can be viewed as a variant of a Gaussian mixture model where the mixture components are described using the covariance function of a GP. We demonstrate the effectiveness of our model on synthetic data as well as on real time-series data of heartbeats where the task is to segment the indicative types of beats and to classify the heartbeat recordings into classes that correspond to healthy and abnormal heart sounds.

In few-shot classification, the aim is to learn models able to discriminate classes with only a small number of labelled examples. Most of the literature considers the problem of labelling a single unknown input at a time. Instead, it can be beneficial to consider a setting where a batch of unlabelled inputs are treated conjointly and non-independently. In this paper, we propose a method able to exploit three levels of information: a) feature extractors pretrained on generic datasets, b) few labelled examples of classes to discriminate and c) other available unlabelled inputs. If for a), we use state-of-the-art approaches, we introduce the use of simplified graph convolutions to perform b) and c) together. Our proposed model reaches state-of-the-art accuracy with a $6-11\%$ increase compared to available alternatives on standard few-shot vision classification datasets.

Since DeepMind's AlphaZero, Zero learning quickly became the state-of-the-art method for many board games. It can be improved using a fully convolutional structure (no fully connected layer). Using such an architecture plus global pooling, we can create bots independent of the board size. The training can be made more robust by keeping track of the best checkpoints during the training and by training against them. Using these features, we release Polygames, our framework for Zero learning, with its library of games and its checkpoints. We won against strong humans at the game of Hex in 19x19, which was often said to be untractable for zero learning; and in Havannah. We also won several first places at the TAAI competitions.