Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts consistent across levels of aggregation. In this study, we propose to augment neural forecasting architectures with a coherent multivariate mixture output. We optimize the networks with a composite likelihood objective, allowing us to capture time series' relationships while maintaining high computational efficiency. Our approach demonstrates 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines. We conduct ablation studies of the framework components and provide theoretical foundations for them. To assist related work, the code is available at this https://github.com/Nixtla/neuralforecast.

In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the squared error loss, this article turns the focus towards probabilistic predictions, which aim to comprehensively quantify the uncertainty of an outcome variable given covariates. Within a causality-inspired framework, we investigate the invariance and robustness of probabilistic predictions with respect to proper scoring rules. We show that arbitrary distribution shifts do not, in general, admit invariant and robust probabilistic predictions, in contrast to the setting of point prediction. We illustrate how to choose evaluation metrics and restrict the class of distribution shifts to allow for identifiability and invariance in the prototypical Gaussian heteroscedastic linear model. Motivated by these findings, we propose a method to yield invariant probabilistic predictions, called IPP, and study the consistency of the underlying parameters. Finally, we demonstrate the empirical performance of our proposed procedure on simulated as well as on single-cell data.

Online portfolio selection (PS) has been extensively studied in artificial intelligence and machine learning communities in recent years. An important practical issue of online PS is transaction cost, which is unavoidable and nontrivial in real financial trading markets. Most existing strategies, such as universal portfolio (UP) based strategies, often rebalance their target portfolio vectors at every investment period, and thus the total transaction cost increases rapidly and the final cumulative wealth degrades severely. To overcome the limitation, in this paper we investigate new investment strategies that rebalances its portfolio only at some selected instants. Specifically, we design a novel on-line PS strategy named semi-universal portfolio (SUP) strategy under transaction cost, which attempts to avoid rebalancing when the transaction cost outweighs the benefit of trading. We show that the proposed SUP strategy is universal and has an upper bound on the regret. We present an efficient implementation of the strategy based on non-uniform random walks and online factor graph algorithms. Empirical simulation on real historical markets show that SUP can overcome the drawback of existing UP based transaction cost aware algorithms and achieve significantly better performance. Furthermore, SUP has a polynomial complexity in the number of stocks and thus is efficient and scalable in practice.

In the context of interactive, virtual experiences, the use of personality models to maintain consistent character behaviour is becoming more widespread in both industry and academia. Most current techniques, however, are limited in one of three ways: either they overly restrict user actions, have a high cost for creating varied content, or rely on a representation that prohibits conveying complex content to the user.  Toward addressing these issues, we introduce Socially Consistent Role Passing, a mechanism for ensuring consistent character behaviour that leverages the design of PaSSAGE, an existing system for generating adaptive, interactive stories.  While results from previous human user studies have shown that PaSSAGE improves the enjoyment of players with little gaming experience, we present results from a new study showing that PaSSAGE's adaptive stories, augmented with Socially Consistent Role Passing, improve the enjoyment of all players versus a set of fixed-structure alternatives.