Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many real-world processes that cannot be characterized by a single linear behavior. Alternatively, it is possible to consider a piecewise-linear model which, combined with a switching mechanism, is well suited when several modes of behavior are needed. Nevertheless, switching dynamical systems are intractable because of their computational complexity increases exponentially with time. In this paper, we propose a variational approximation of piecewise linear dynamical systems. We provide full details of the derivation of two variational expectation-maximization algorithms, a filter and a smoother. We show that the model parameters can be split into two sets, static and dynamic parameters, and that the former parameters can be estimated off-line together with the number of linear modes, or the number of states of the switching variable. We apply the proposed method to a visual tracking problem, namely head-pose tracking, and we thoroughly compare our algorithm with several state of the art trackers.

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore provide a new stochastic gradient descent algorithm to efficiently solve this DRO formulation. Our approach applies gradient descent to the outer minimization formulation and estimates the gradient of the inner maximization based on a sample average approximation. The latter uses a subset of the data in each iteration, progressively increasing the subset size to ensure convergence. Theoretical results include establishing the optimal manner for growing the support size to balance a fundamental tradeoff between stochastic error and computational effort. Empirical results demonstrate the significant benefits of our approach over previous work, and also illustrate how learning with DRO can improve generalization.

Subspace clustering methods have been widely studied recently. When the inputs are 2-dimensional (2D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships from original data. In this paper, we propose a novel subspace clustering method for 2D data. It directly uses 2D data as inputs such that the learning of representations benefits from inherent structures and relationships of the data. It simultaneously seeks image projection and representation coefficients such that they mutually enhance each other and lead to powerful data representations. An efficient algorithm is developed to solve the proposed objective function with provable decreasing and convergence property. Extensive experimental results verify the effectiveness of the new method.

Proper training and analytics in eSports require accurately collected and annotated data. Most eSports research focuses exclusively on in-game data analysis, and there is a lack of prior work involving eSports athletes' psychophysiological data. In this paper, we present a dataset collected from professional and amateur teams in 22 matches in League of Legends video game. Recorded data include the players' physiological activity, e.g. movements, pulse, saccades, obtained from various sensors, self-reported after-match survey, and in-game data. An important feature of the dataset is simultaneous data collection from five players, which facilitates the analysis of sensor data on a team level. Upon the collection of dataset we carried out its validation. In particular, we demonstrate that stress and concentration levels for professional players are less correlated, meaning more independent playstyle. Also, we show that the absence of team communication does not affect the professional players as much as amateur ones. To investigate other possible use cases of the dataset, we have trained classical machine learning algorithms for skill prediction and player re-identification using 3-minute sessions of sensor data. Best models achieved 0.856 and 0.521 (0.10 for a chance level) accuracy scores on a validation set for skill prediction and player re-id problems, respectively. The dataset is available at https://github.com/asmerdov/eSports_Sensors_Dataset.

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM, Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques. We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for "from the scratch" implementations and libraries like TensorFlow, Pytorch and SciKit Learn.

We're living in an era of digital switch-over with only one constant – evolve. And that digital transformation is being introduced by high-tech solutions. Hence, it comes as no surprise that mundane business tasks are being completely taken over by tech advancements. Machines, artificial intelligence (AI), and unsupervised learning are reshaping the way businesses vie for a place under the sun. With that being said, let's have a closer look at how unsupervised machine learning is omnipresent in all industries.

R is statistical software that is used for data analysis. There are two main types of learning from data: unsupervised learning, where the structure of data is extracted automatically; and supervised learning, where a labeled part of the data is used to learn the relationship or scores in a target attribute. As important information is often hidden in a lot of data, R helps to extract that information with its many standard and cutting-edge statistical functions. This book is packed with easy-to-follow guidelines that explain the workings of the many key data mining tools of R, which are used to discover knowledge from your data. You will learn how to perform key predictive analytics tasks using R, such as train and test predictive models for classification and regression tasks, score new data sets and so on.

These terms will come up, and it's good to get familiar with them if you aren't already: Goodness of fit is typically a term used to describe how well a dataset aligns with a certain statistical distribution. Here, we're going to think of it as a way of describing how well our model is fitted to our data. If we can think about our regression model in terms of the imaginary "best-fit" line it produces, then it makes sense that we would want to know how well this line matches our data. This goodness of fit can be quantified in a variety of ways, but the R² and the adjusted R² score are two of the most common methods for describing how well our model is capturing the variance in our target data. R² -- also called the coefficient of determination -- is a statistical measure representing the amount of variance for a dependent variable that is captured by your model's predictions.

The log-likelihood of a generative model often involves both positive and negative terms. For a temporal multivariate point process, the negative term sums over all the possible event types at each time and also integrates over all the possible times. As a result, maximum likelihood estimation is expensive. We show how to instead apply a version of noise-contrastive estimation---a general parameter estimation method with a less expensive stochastic objective. Our specific instantiation of this general idea works out in an interestingly non-trivial way and has provable guarantees for its optimality, consistency and efficiency. On several synthetic and real-world datasets, our method shows benefits: for the model to achieve the same level of log-likelihood on held-out data, our method needs considerably fewer function evaluations and less wall-clock time.

With recent advancements in deep learning and the availability of huge amount of data, data-driven prediction in time series has attracted more and more attention. Specifically, traffic forecasting is the key component of a transportation system powered by artificial intelligence[2] [5]. Traditionally, time series forecasting includes methods such as K-nearest Neighbor (KNN), Support Vector Regression (SVR), etc [6]. This paper proposes the stacked LSTM model to capture the complex temporal patterns. The main contributions include: - Analyzing real traffic volume data in Toronto downtown area - Proposing the stacked LSTM model with substantial gain comparing to the baseline model - Improving the model performance with a comprehensive set of training methodologies Deep learning has been widely adopted in time series forecasting[5]. One category is time series classification which assigns predefined class labels to time series output.