Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.

Excavation plans are crucial in construction projects, dictating the dirt disposal strategy and excavation sequence based on the final geometry and machinery available. While most construction processes rely heavily on coarse sequence planning and local execution planning driven by human expertise and intuition, fully automated planning tools are notably absent from the industry. This paper introduces a fully autonomous excavation planning system. Initially, the site is mapped, followed by user selection of the desired excavation geometry. The system then invokes a global planner to determine the sequence of poses for the excavator, ensuring complete site coverage. For each pose, a local excavation planner decides how to move the soil around the machine, and a digging planner subsequently dictates the sequence of digging trajectories to complete a patch. We showcased our system by autonomously excavating the largest pit documented so far, achieving an average digging cycle time of roughly 30 seconds, comparable to the one of a human operator.

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the same company and stocks linked through supply-demand chains, momentum spillover implies a propagation of momentum risk premium from one asset to another. The similarity of momentum risk premium, exemplified by co-movement patterns, has been spotted across multiple asset classes including commodities, equities, bonds and currencies. However, studying the network effect of momentum spillover across these classes has been challenging due to a lack of readily available common characteristics or economic ties beyond the company level. In this paper, we explore the interconnections of momentum features across a diverse range of 64 continuous future contracts spanning these four classes. We utilise a linear and interpretable graph learning model with minimal assumptions to reveal the intricacies of the momentum spillover network. By leveraging the learned networks, we construct a network momentum strategy that exhibits a Sharpe ratio of 1.5 and an annual return of 22%, after volatility scaling, from 2000 to 2022. This paper pioneers the examination of momentum spillover across multiple asset classes using only pricing data, presents a multi-asset investment strategy based on network momentum, and underscores the effectiveness of this strategy through robust empirical analysis.

Data-driven, deep-learning modeling frameworks have been recently developed for forecasting time series data. Such machine learning models may be useful in multiple domains including the atmospheric and oceanic ones, and in general, the larger fluids community. The present work investigates the possible effectiveness of such deep neural operator models for reproducing and predicting classic fluid flows and simulations of realistic ocean dynamics. We first briefly evaluate the capabilities of such deep neural operator models when trained on a simulated two-dimensional fluid flow past a cylinder. We then investigate their application to forecasting ocean surface circulation in the Middle Atlantic Bight and Massachusetts Bay, learning from high-resolution data-assimilative simulations employed for real sea experiments. We confirm that trained deep neural operator models are capable of predicting idealized periodic eddy shedding. For realistic ocean surface flows and our preliminary study, they can predict several of the features and show some skill, providing potential for future research and applications.

Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict their spatiotemporal complexities. A machine-learning framework is proposed based on the physical modeling of morphogenesis triggered by internal or external forcing. Digital libraries of structural patterns are constructed from the simulation data, which are then used to recognize the abnormalities, predict their development, and assist in risk assessment and prognosis. The capabilities to identify the key bifurcation characteristics and predict the history-dependent development from the global and local features are demonstrated by examples of brain growth and aerospace structural design, which offer guidelines for disease diagnosis/prognosis and instability-tolerant design.

The widespread adoption of DNNs in NLP software has highlighted the need for robustness. Researchers proposed various automatic testing techniques for adversarial test cases. However, existing methods suffer from two limitations: weak error-discovering capabilities, with success rates ranging from 0% to 24.6% for BERT-based NLP software, and time inefficiency, taking 177.8s to 205.28s per test case, making them challenging for time-constrained scenarios. To address these issues, this paper proposes LEAP, an automated test method that uses LEvy flight-based Adaptive Particle swarm optimization integrated with textual features to generate adversarial test cases. Specifically, we adopt Levy flight for population initialization to increase the diversity of generated test cases. We also design an inertial weight adaptive update operator to improve the efficiency of LEAP's global optimization of high-dimensional text examples and a mutation operator based on the greedy strategy to reduce the search time. We conducted a series of experiments to validate LEAP's ability to test NLP software and found that the average success rate of LEAP in generating adversarial test cases is 79.1%, which is 6.1% higher than the next best approach (PSOattack). While ensuring high success rates, LEAP significantly reduces time overhead by up to 147.6s compared to other heuristic-based methods. Additionally, the experimental results demonstrate that LEAP can generate more transferable test cases and significantly enhance the robustness of DNN-based systems.

The interest in using reinforcement learning (RL) controllers in safety-critical applications such as robot navigation around pedestrians motivates the development of additional safety mechanisms. Running RL-enabled systems among uncertain dynamic agents may result in high counts of collisions and failures to reach the goal. The system could be safer if the pre-trained RL policy was uncertainty-informed. For that reason, we propose conformal predictive safety filters that: 1) predict the other agents' trajectories, 2) use statistical techniques to provide uncertainty intervals around these predictions, and 3) learn an additional safety filter that closely follows the RL controller but avoids the uncertainty intervals. We use conformal prediction to learn uncertainty-informed predictive safety filters, which make no assumptions about the agents' distribution. The framework is modular and outperforms the existing controllers in simulation. We demonstrate our approach with multiple experiments in a collision avoidance gym environment and show that our approach minimizes the number of collisions without making overly-conservative predictions.

Climate projections using data driven machine learning models acting as emulators, is one of the prevailing areas of research to enable policy makers make informed decisions. Use of machine learning emulators as surrogates for computationally heavy GCM simulators reduces time and carbon footprints. In this direction, ClimateBench [1] is a recently curated benchmarking dataset for evaluating the performance of machine learning emulators designed for climate data. Recent studies have reported that despite being considered fundamental, regression models offer several advantages pertaining to climate emulations. In particular, by leveraging the kernel trick, regression models can capture complex relationships and improve their predictive capabilities. This study focuses on evaluating non-linear regression models using the aforementioned dataset. Specifically, we compare the emulation capabilities of three non-linear regression models. Among them, Gaussian Process Regressor demonstrates the best-in-class performance against standard evaluation metrics used for climate field emulation studies. However, Gaussian Process Regression suffers from being computational resource hungry in terms of space and time complexity. Alternatively, Support Vector and Kernel Ridge models also deliver competitive results and but there are certain trade-offs to be addressed. Additionally, we are actively investigating the performance of composite kernels and techniques such as variational inference to further enhance the performance of the regression models and effectively model complex non-linear patterns, including phenomena like precipitation.

This paper outlines a natural conversational approach to solving personalized energy-related problems using large language models (LLMs). We focus on customizable optimization problems that necessitate repeated solving with slight variations in modeling and are user-specific, hence posing a challenge to devising a one-size-fits-all model. We put forward a strategy that augments an LLM with an optimization solver, enhancing its proficiency in understanding and responding to user specifications and preferences while providing nonlinear reasoning capabilities. Our approach pioneers the novel concept of human-guided optimization autoformalism, translating a natural language task specification automatically into an optimization instance. This enables LLMs to analyze, explain, and tackle a variety of instance-specific energy-related problems, pushing beyond the limits of current prompt-based techniques. Our research encompasses various commonplace tasks in the energy sector, from electric vehicle charging and Heating, Ventilation, and Air Conditioning (HVAC) control to long-term planning problems such as cost-benefit evaluations for installing rooftop solar photovoltaics (PVs) or heat pumps. This pilot study marks an essential stride towards the context-based formulation of optimization using LLMs, with the potential to democratize optimization processes. As a result, stakeholders are empowered to optimize their energy consumption, promoting sustainable energy practices customized to personal needs and preferences.

We study deregulated power markets with strategic power suppliers. In deregulated markets, each supplier submits its supply function (i.e., the amount of electricity it is willing to produce at various prices) to the independent system operator (ISO), who based on the submitted supply functions, dispatches the suppliers to clear the market with minimal total generation cost. If all suppliers reported their true marginal cost functions as supply functions, the market outcome would be efficient (i.e., the total generation cost is minimized). However, when suppliers are strategic and aim to maximize their own profits, the reported supply functions are not necessarily the true marginal cost functions, and the resulting market outcome may be inefficient. The efficiency loss depends crucially on the topology of the underlying transmission network. This paper provides an analytical upper bound of the efficiency loss due to strategic suppliers, and proves that the bound is tight under a large class of transmission networks (i.e., weakly cyclic networks). Our upper bound sheds light on how the efficiency loss depends on the transmission network topology (e.g., the degrees of nodes, the admittances and flow limits of transmission lines).