We study the prediction of short term wind speed and wind power (every 10 minutes up to 4 hours ahead). Accurate forecasts for those quantities are crucial to mitigate the negative effects of wind farms' intermittent production on energy systems and markets. For those time scales, outputs of numerical weather prediction models are usually overlooked even though they should provide valuable information on higher scales dynamics. In this work, we combine those outputs with local observations using machine learning. So as to make the results usable for practitioners, we focus on simple and well known methods which can handle a high volume of data. We study first variable selection through two simple techniques, a linear one and a nonlinear one. Then we exploit those results to forecast wind speed and wind power still with an emphasis on linear models versus nonlinear ones. For the wind power prediction, we also compare the indirect approach (wind speed predictions passed through a power curve) and the indirect one (directly predict wind power).
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Graph Transformers have demonstrated superiority on various graph learning tasks in recent years. However, the complexity of existing Graph Transformers scales quadratically with the number of nodes, making it hard to scale to graphs with thousands of nodes. To this end, we propose a Neighborhood Aggregation Graph Transformer (NAGphormer) that is scalable to large graphs with millions of nodes. Before feeding the node features into the Transformer model, NAGphormer constructs tokens for each node by a neighborhood aggregation module called Hop2Token. For each node, Hop2Token aggregates neighborhood features from each hop into a representation, and thereby produces a sequence of token vectors. Subsequently, the resulting sequence of different hop information serves as input to the Transformer model. By considering each node as a sequence, NAGphormer could be trained in a mini-batch manner and thus could scale to large graphs. NAGphormer further develops an attention-based readout function so as to learn the importance of each hop adaptively. We conduct extensive experiments on various popular benchmarks, including six small datasets and three large datasets. The results demonstrate that NAGphormer consistently outperforms existing Graph Transformers and mainstream Graph Neural Networks.
Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit to the training data. We prove that this is not the case for the linear model fit by ordinary least squares; rather it estimates the average prediction error of models fit on other unseen training sets drawn from the same population. We further show that this phenomenon occurs for most popular estimates of prediction error, including data splitting, bootstrapping, and Mallow's Cp. Next, the standard confidence intervals for prediction error derived from cross-validation may have coverage far below the desired level. Because each data point is used for both training and testing, there are correlations among the measured accuracies for each fold, and so the usual estimate of variance is too small. We introduce a nested cross-validation scheme to estimate this variance more accurately, and we show empirically that this modification leads to intervals with approximately correct coverage in many examples where traditional cross-validation intervals fail.
We build a field level emulator for cosmic structure formation that is accurate in the nonlinear regime. Our emulator consists of two convolutional neural networks trained to output the nonlinear displacements and velocities of N-body simulation particles based on their linear inputs. Cosmology dependence is encoded in the form of style parameters at each layer of the neural network, enabling the emulator to effectively interpolate the outcomes of structure formation between different flat $\Lambda$CDM cosmologies over a wide range of background matter densities. The neural network architecture makes the model differentiable by construction, providing a powerful tool for fast field level inference. We test the accuracy of our method by considering several summary statistics, including the density power spectrum with and without redshift space distortions, the displacement power spectrum, the momentum power spectrum, the density bispectrum, halo abundances, and halo profiles with and without redshift space distortions. We compare these statistics from our emulator with the full N-body results, the COLA method, and a fiducial neural network with no cosmological dependence. We find our emulator gives accurate results down to scales of $k \sim 1\ \mathrm{Mpc}^{-1}\, h$, representing a considerable improvement over both COLA and the fiducial neural network. We also demonstrate that our emulator generalizes well to initial conditions containing primordial non-Gaussianity, without the need for any additional style parameters or retraining.
Addressing the problem of fairness is crucial to safely use machine learning algorithms to support decisions with a critical impact on people's lives such as job hiring, child maltreatment, disease diagnosis, loan granting, etc. Several notions of fairness have been defined and examined in the past decade, such as statistical parity and equalized odds. The most recent fairness notions, however, are causal-based and reflect the now widely accepted idea that using causality is necessary to appropriately address the problem of fairness. This paper examines an exhaustive list of causal-based fairness notions and study their applicability in real-world scenarios. As the majority of causal-based fairness notions are defined in terms of non-observable quantities (e.g., interventions and counterfactuals), their deployment in practice requires to compute or estimate those quantities using observational data. This paper offers a comprehensive report of the different approaches to infer causal quantities from observational data including identifiability (Pearl's SCM framework) and estimation (potential outcome framework). The main contributions of this survey paper are (1) a guideline to help selecting a suitable fairness notion given a specific real-world scenario, and (2) a ranking of the fairness notions according to Pearl's causation ladder indicating how difficult it is to deploy each notion in practice.
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of these problems are encountered, and standard methods either fail or are not feasible. To overcome the current limitations, we present a generalized formulation of a Bayesian multi-fidelity Monte-Carlo (BMFMC) framework that can exploit lower-fidelity model versions in a small data regime. The goal of our analysis is an efficient and accurate estimation of the complete probabilistic response for high-fidelity models. BMFMC circumvents the curse of dimensionality by learning the relationship between the outputs of a reference high-fidelity model and potentially several lower-fidelity models. While the continuous formulation is mathematically exact and independent of the low-fidelity model's accuracy, we address challenges associated with the small data regime (i.e., only a small number of 50 to 300 high-fidelity model runs can be performed). Specifically, we complement the formulation with a set of informative input features at no extra cost. Despite the inaccurate and noisy information that some low-fidelity models provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained for uncertainty quantification problems in high stochastic dimensions, with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty quantification. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and fluid-structure interaction problems.
End-to-End (E2E) network slicing enables wireless networks to provide diverse services on a common infrastructure. Each E2E slice, including resources of radio access network (RAN) and core network, is rented to mobile virtual network operators (MVNOs) to provide a specific service to end-users. RAN slicing, which is realized through wireless network virtualization, involves sharing the frequency spectrum and base station antennas in RAN. Similarly, in core slicing, which is achieved by network function virtualization, data center resources such as commodity servers and physical links are shared between users of different MVNOs. In this paper, we study E2E slicing with the aim of minimizing the total energy consumption. The stated optimization problem is non-convex that is solved by a sub-optimal algorithm proposed here. The simulation results show that our proposed joint power control, server and link allocation (JPSLA) algorithm achieves 30% improvement compared to the disjoint scheme, where RAN and core are sliced separately.
Integration of intermittent renewable energy sources into electric grids in large proportions is challenging. A well-established approach aimed at addressing this difficulty involves the anticipation of the upcoming energy supply variability to adapt the response of the grid. In solar energy, short-term changes in electricity production caused by occluding clouds can be predicted at different time scales from all-sky cameras (up to 30-min ahead) and satellite observations (up to 6h ahead). In this study, we integrate these two complementary points of view on the cloud cover in a single machine learning framework to improve intra-hour (up to 60-min ahead) irradiance forecasting. Both deterministic and probabilistic predictions are evaluated in different weather conditions (clear-sky, cloudy, overcast) and with different input configurations (sky images, satellite observations and/or past irradiance values). Our results show that the hybrid model benefits predictions in clear-sky conditions and improves longer-term forecasting. This study lays the groundwork for future novel approaches of combining sky images and satellite observations in a single learning framework to advance solar nowcasting.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts. We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, such as quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ Self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.
Traditional methods for link prediction can be categorized into three main types: graph structure feature-based, latent feature-based, and explicit feature-based. Graph structure feature methods leverage some handcrafted node proximity scores, e.g., common neighbors, to estimate the likelihood of links. Latent feature methods rely on factorizing networks' matrix representations to learn an embedding for each node. Explicit feature methods train a machine learning model on two nodes' explicit attributes. Each of the three types of methods has its unique merits. In this paper, we propose SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction), a new framework for link prediction which combines the power of all the three types into a single graph neural network (GNN). GNN is a new type of neural network which directly accepts graphs as input and outputs their labels. In SEAL, the input to the GNN is a local subgraph around each target link. We prove theoretically that our local subgraphs also reserve a great deal of high-order graph structure features related to link existence. Another key feature is that our GNN can naturally incorporate latent features and explicit features. It is achieved by concatenating node embeddings (latent features) and node attributes (explicit features) in the node information matrix for each subgraph, thus combining the three types of features to enhance GNN learning. Through extensive experiments, SEAL shows unprecedentedly strong performance against a wide range of baseline methods, including various link prediction heuristics and network embedding methods.
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