We propose to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. A key idea of the new procedure is to project a generalized eigenequation defined in terms of rank-reduced matrices to a lower-dimensional one with full-ranked matrices, to avoid the intricacy of the former of which the number of eigenvalues can be zero, finite and infinity. The asymptotic theory has been established under a general setting without the stationarity. It shows, for example, that all the component coefficient vectors in the CP-decomposition are estimated consistently with the different error rates, depending on the relative sizes between the dimensions of time series and the sample size. The proposed model and the estimation method are further illustrated with both simulated and real data; showing effective dimension-reduction in modelling and forecasting matrix time series.

As the world reopened cautiously in 2021, our correspondents seized the chance to venture out in search of stories that would astonish, delight, provoke and enlighten. We went from the heights of a Himalayan ski slope to the ocean depths off the Philippines where amiable giants dive, and from a rugged island where a whistling language is still used to an Italian atelier where robots carve the sculptures. If the pandemic often kept our reporters confined to urban settings in 2020, this year afforded them the chance to explore deep into the countryside. We observed a (bogus) diamond rush in rural South Africa and accompanied Indigenous hunters in Taiwan. We trekked to Canada's beaver dams, swam in a contested stream in northern Israel and returned home to a Tuscan village sliding back in time.

This is just one of a series of posts giving our valued community a review of our 2021 achievements… and a small peek at what comes next! This Roadmap End-of-Year Review Series will be followed up next year with an in-depth series on the Roadmap plans for 2022 in January/February. Don't miss the rest of this series! Mindplex is developing a media platform and AI accessories to decentralize and democratize media. The Mindplex Content Factory will match content creators and content consumers based on an AI-driven reputation system, combined with tokenomics, to help the platform to be more decentralized, community-led, and merit-based.

This year at Future Tense Fiction we've spent a lot of time thinking about how, in many ways, 2021 has felt a lot like 2020. But at the same time, so much has changed--how we work and think, how we commute, how we interact with animals, technology, and our fellow humans. This year we published 11 stories (we took December off!) that touch upon relationships, transportation, right to repair and supply chain shortages, communication, information overload and scarcity, and much, much more. We broadly explored themes like learning futures, with Simon Brown's "Speaker" (where humans learn to communicate with other species and struggle to overcome the assumption of human excellence), Leigh Alexander's "The Void" (about the struggle with information scarcity in an information-overloaded world) and Shiv Ramdas' "The Trolley Solution" (about a university attempting to automate how it teaches its students), as well as ideas of mobility--a theme we're continuing into 2022, so stay tuned--with Linda Nagata's "Ride" (about a neighborhood that's embraced an algorithm to run all of its traffic and transit patterns). We began publishing fiction back in 2016 and made it monthly as of January 2018.

Deep learning is pervasive in our daily life, including self-driving cars, virtual assistants, social network services, healthcare services, face recognition, etc. However, deep neural networks demand substantial compute resources during training and inference. The machine learning community has mainly focused on model-level optimizations such as architectural compression of deep learning models, while the system community has focused on implementation-level optimization. In between, various arithmetic-level optimization techniques have been proposed in the arithmetic community. This article provides a survey on resource-efficient deep learning techniques in terms of model-, arithmetic-, and implementation-level techniques and identifies the research gaps for resource-efficient deep learning techniques across the three different level techniques. Our survey clarifies the influence from higher to lower-level techniques based on our resource-efficiency metric definition and discusses the future trend for resource-efficient deep learning research.

Autoregressive (AR) and Non-autoregressive (NAR) models have their own superiority on the performance and latency, combining them into one model may take advantage of both. Current combination frameworks focus more on the integration of multiple decoding paradigms with a unified generative model, e.g. Masked Language Model. However, the generalization can be harmful to the performance due to the gap between training objective and inference. In this paper, we aim to close the gap by preserving the original objective of AR and NAR under a unified framework. Specifically, we propose the Directional Transformer (Diformer) by jointly modelling AR and NAR into three generation directions (left-to-right, right-to-left and straight) with a newly introduced direction variable, which works by controlling the prediction of each token to have specific dependencies under that direction. The unification achieved by direction successfully preserves the original dependency assumption used in AR and NAR, retaining both generalization and performance. Experiments on 4 WMT benchmarks demonstrate that Diformer outperforms current united-modelling works with more than 1.5 BLEU points for both AR and NAR decoding, and is also competitive to the state-of-the-art independent AR and NAR models.

Both the industrialized and developing worlds are facing unprecedented demographic changes. Birth rates have reached a minimum in some of the world's largest countries, while literally billions of workers prepare to enter retirement. Researchers and policymakers have, over the last two decades, started to actively seek ways of dealing with the rising healthcare costs of aging populations. Across the board, AI has come to be considered the most advantageous solution. Not only does artificial intelligence automate basic tasks, removing the need for expensive human intervention in many cases, but it can be used to give a greater sense of privacy and discretion to patients.

Electrical utilities depend on short-term demand forecasting to proactively adjust production and distribution in anticipation of major variations. This systematic review analyzes 240 works published in scholarly journals between 2000 and 2019 that focus on applying Artificial Intelligence (AI), statistical, and hybrid models to short-term load forecasting (STLF). This work represents the most comprehensive review of works on this subject to date. A complete analysis of the literature is conducted to identify the most popular and accurate techniques as well as existing gaps. The findings show that although Artificial Neural Networks (ANN) continue to be the most commonly used standalone technique, researchers have been exceedingly opting for hybrid combinations of different techniques to leverage the combined advantages of individual methods. The review demonstrates that it is commonly possible with these hybrid combinations to achieve prediction accuracy exceeding 99%. The most successful duration for short-term forecasting has been identified as prediction for a duration of one day at an hourly interval. The review has identified a deficiency in access to datasets needed for training of the models. A significant gap has been identified in researching regions other than Asia, Europe, North America, and Australia.

We study a multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in $d$ dimensions. KTF is a natural extension of univariate trend filtering (Steidl et al., 2006; Kim et al., 2009; Tibshirani, 2014), and is defined by minimizing a penalized least squares problem whose penalty term sums the absolute (higher-order) differences of the parameter to be estimated along each of the coordinate directions. The corresponding penalty operator can be written in terms of Kronecker products of univariate trend filtering penalty operators, hence the name Kronecker trend filtering. Equivalently, one can view KTF in terms of an $\ell_1$-penalized basis regression problem where the basis functions are tensor products of falling factorial functions, a piecewise polynomial (discrete spline) basis that underlies univariate trend filtering. This paper is a unification and extension of the results in Sadhanala et al. (2016, 2017). We develop a complete set of theoretical results that describe the behavior of $k^{\mathrm{th}}$ order Kronecker trend filtering in $d$ dimensions, for every $k \geq 0$ and $d \geq 1$. This reveals a number of interesting phenomena, including the dominance of KTF over linear smoothers in estimating heterogeneously smooth functions, and a phase transition at $d=2(k+1)$, a boundary past which (on the high dimension-to-smoothness side) linear smoothers fail to be consistent entirely. We also leverage recent results on discrete splines from Tibshirani (2020), in particular, discrete spline interpolation results that enable us to extend the KTF estimate to any off-lattice location in constant-time (independent of the size of the lattice $n$).

Nowadays Machine Learning (ML) techniques are extensively adopted in many socially sensitive systems, thus requiring to carefully study the fairness of the decisions taken by such systems. Many approaches have been proposed to address and to make sure there is no bias against individuals or specific groups which might originally come from biased training datasets or algorithm design. In this regard, we propose a fairness enforcing approach called EiFFFeL:Enforcing Fairness in Forests by Flipping Leaves which exploits tree-based or leaf-based post-processing strategies to relabel leaves of selected decision trees of a given forest. Experimental results show that our approach achieves a user defined group fairness degree without losing a significant amount of accuracy.