Real-world relational data are seldom stationary, yet traditional collaborative filtering algorithms generally rely on this assumption. Motivated by our sales prediction problem, we propose a factor-based algorithm that is able to take time into account. By introducing additional factors for time, we formalize this problem as a tensor factorization with a special constraint on the time dimension. Further, we provide a fully Bayesian treatment to avoid tuning parameters and achieve automatic model complexity control. To learn the model we develop an efficient sampling procedure that is capable of analyzing large-scale data sets. This new algorithm, called Bayesian Probabilistic Tensor Factorization (BPTF), is evaluated on several real-world problems including sales prediction and movie recommendation. Empirical results demonstrate the superiority of our temporal model.

Autonomous driving presents one of the largest problems that the robotics and artificial intelligence communities are facing at the moment, both in terms of difficulty and potential societal impact. Self-driving vehicles (SDVs) are expected to prevent road accidents and save millions of lives while improving the livelihood and life quality of many more. However, despite large interest and a number of industry players working in the autonomous domain, there still remains more to be done in order to develop a system capable of operating at a level comparable to best human drivers. One reason for this is high uncertainty of traffic behavior and large number of situations that an SDV may encounter on the roads, making it very difficult to create a fully generalizable system. To ensure safe and efficient operations, an autonomous vehicle is required to account for this uncertainty and to anticipate a multitude of possible behaviors of traffic actors in its surrounding. We address this critical problem and present a method to predict multiple possible trajectories of actors while also estimating their probabilities. The method encodes each actor's surrounding context into a raster image, used as input by deep convolutional networks to automatically derive relevant features for the task. Following extensive offline evaluation and comparison to state-of-the-art baselines, the method was successfully tested on SDVs in closed-course tests.

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This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models. The proposed method is shown to be statistically consistent in determining of the number of components. A modified EM algorithm is developed to simultaneously select the number of components and to estimate the mixing weights, i.e. the mixing probabilities, and unknown parameters of Gaussian distributions. Simulations and a real data analysis are presented to illustrate the performance of the proposed method.

Patients with congenital pulmonic stenosis who present in late adolescence or adult life can be treated with percutaneous balloon valvuloplasty with excellent short-term and long-term results that are similar to those in young children.