Intermittent demand forecasting is a ubiquitous and challenging problem in operations and supply chain management. There has been a growing focus on developing forecasting approaches for intermittent demand from academic and practical perspectives in recent years. However, limited attention has been given to forecast combination methods, which have been proved to achieve competitive performance in forecasting fast-moving time series. The current study aims to examine the empirical outcomes of some existing forecast combination methods, and propose a generalized feature-based framework for intermittent demand forecasting. We conduct a simulation study to perform a large-scale comparison of a series of combination methods based on an intermittent demand classification scheme. Further, a real data set is used to investigate the forecasting performance and offer insights with regards the inventory performance of the proposed framework by considering some complementary error measures. The proposed framework leads to a significant improvement in forecast accuracy and offers the potential of flexibility and interpretability in inventory control.
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Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture and quantify different sources of uncertainty, particularly those associated with model errors. In this work we perform toy-model and state-of-the-art model experiments to analyze to what extent artificial neural networks (ANNs) are able to model the different sources of uncertainty present in a forecast. In particular those associated with the accuracy of the initial conditions and those introduced by the model error. We also compare different training strategies: one based on a direct training using the mean and spread of an ensemble forecast as target, the other ones rely on an indirect training strategy using an analyzed state as target in which the uncertainty is implicitly learned from the data. Experiments using the Lorenz'96 model show that the ANNs are able to emulate some of the properties of ensemble forecasts like the filtering of the most unpredictable modes and a state-dependent quantification of the forecast uncertainty. Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the presence of model error. Preliminary experiments conducted with a state-of-the-art forecasting system also confirm the ability of ANNs to produce a reliable quantification of the forecast uncertainty.
We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according to criterion functions based on proper scoring rules, which are chosen to reward the form of forecast accuracy that matters for the problem at hand, and forecast performance is measured using the out-of-sample expectation of said scoring rule. Our results provide novel insights into the behavior of estimated forecast combinations. Firstly, we show that, asymptotically, the sampling variability in the performance of standard forecast combinations is determined solely by estimation of the constituent models, with estimation of the combination weights contributing no sampling variability whatsoever, at first order. Secondly, we show that, if computationally feasible, forecast combinations produced in a single step -- in which the constituent model and combination function parameters are estimated jointly -- have superior predictive accuracy and lower sampling variability than standard forecast combinations -- where constituent model and combination function parameters are estimated in two steps. These theoretical insights are demonstrated numerically, both in simulation settings and in an extensive empirical illustration using a time series of S&P500 returns.
The ability to accurately predict human behavior is central to the safety and efficiency of robot autonomy in interactive settings. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as people's goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as stochastic hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning, mainly due to the fundamental coupling between robot trajectory optimization and human intent inference. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods. The resulting policy is shown to preserve the dual control effect for a broad class of predictive human models with both continuous and categorical uncertainty. The efficacy of our approach is demonstrated with simulated driving examples.
Vanilla Feature Distillation for Improving the Accuracy-Robustness Trade-Off in Adversarial Training
Adversarial training has been widely explored for mitigating attacks against deep models. However, most existing works are still trapped in the dilemma between higher accuracy and stronger robustness since they tend to fit a model towards robust features (not easily tampered with by adversaries) while ignoring those non-robust but highly predictive features. To achieve a better robustness-accuracy trade-off, we propose the Vanilla Feature Distillation Adversarial Training (VFD-Adv), which conducts knowledge distillation from a pre-trained model (optimized towards high accuracy) to guide adversarial training towards higher accuracy, i.e., preserving those non-robust but predictive features. More specifically, both adversarial examples and their clean counterparts are forced to be aligned in the feature space by distilling predictive representations from the pre-trained/clean model, while previous works barely utilize predictive features from clean models. Therefore, the adversarial training model is updated towards maximally preserving the accuracy as gaining robustness. A key advantage of our method is that it can be universally adapted to and boost existing works. Exhaustive experiments on various datasets, classification models, and adversarial training algorithms demonstrate the effectiveness of our proposed method.
Solving combinatorial optimization (CO) on graphs is among the fundamental tasks for upper-stream applications in data mining, machine learning and operations research. Despite the inherent NP-hard challenge for CO, heuristics, branch-and-bound, learning-based solvers are developed to tackle CO problems as accurately as possible given limited time budgets. However, a practical metric for the sensitivity of CO solvers remains largely unexplored. Existing theoretical metrics require the optimal solution which is infeasible, and the gradient-based adversarial attack metric from deep learning is not compatible with non-learning solvers that are usually non-differentiable. In this paper, we develop the first practically feasible robustness metric for general combinatorial optimization solvers. We develop a no worse optimal cost guarantee thus do not require optimal solutions, and we tackle the non-differentiable challenge by resorting to black-box adversarial attack methods. Extensive experiments are conducted on 14 unique combinations of solvers and CO problems, and we demonstrate that the performance of state-of-the-art solvers like Gurobi can degenerate by over 20% under the given time limit bound on the hard instances discovered by our robustness metric, raising concerns about the robustness of combinatorial optimization solvers.
The synthetic control method has become a widely popular tool to estimate causal effects with observational data. Despite this, inference for synthetic control methods remains challenging. Often, inferential results rely on linear factor model data generating processes. In this paper, we characterize the conditions on the factor model primitives (the factor loadings) for which the statistical risk minimizers are synthetic controls (in the simplex). Then, we propose a Bayesian alternative to the synthetic control method that preserves the main features of the standard method and provides a new way of doing valid inference. We explore a Bernstein-von Mises style result to link our Bayesian inference to the frequentist inference. For linear factor model frameworks we show that a maximum likelihood estimator (MLE) of the synthetic control weights can consistently estimate the predictive function of the potential outcomes for the treated unit and that our Bayes estimator is asymptotically close to the MLE in the total variation sense. Through simulations, we show that there is convergence between the Bayes and frequentist approach even in sparse settings. Finally, we apply the method to re-visit the study of the economic costs of the German re-unification. The Bayesian synthetic control method is available in the bsynth R-package.
A multitude of explainability methods and associated fidelity performance metrics have been proposed to help better understand how modern AI systems make decisions. However, much of the current work has remained theoretical -- without much consideration for the human end-user. In particular, it is not yet known (1) how useful current explainability methods are in practice for more real-world scenarios and (2) how well associated performance metrics accurately predict how much knowledge individual explanations contribute to a human end-user trying to understand the inner-workings of the system. To fill this gap, we conducted psychophysics experiments at scale to evaluate the ability of human participants to leverage representative attribution methods for understanding the behavior of different image classifiers representing three real-world scenarios: identifying bias in an AI system, characterizing the visual strategy it uses for tasks that are too difficult for an untrained non-expert human observer as well as understanding its failure cases. Our results demonstrate that the degree to which individual attribution methods help human participants better understand an AI system varied widely across these scenarios. This suggests a critical need for the field to move past quantitative improvements of current attribution methods towards the development of complementary approaches that provide qualitatively different sources of information to human end-users.
We propose a theoretical framework that generalizes simple and fast algorithms for hierarchical agglomerative clustering to weighted graphs with both attractive and repulsive interactions between the nodes. This framework defines GASP, a Generalized Algorithm for Signed graph Partitioning, and allows us to explore many combinations of different linkage criteria and cannot-link constraints. We prove the equivalence of existing clustering methods to some of those combinations and introduce new algorithms for combinations that have not been studied before. We study both theoretical and empirical properties of these combinations and prove that some of these define an ultrametric on the graph. We conduct a systematic comparison of various instantiations of GASP on a large variety of both synthetic and existing signed clustering problems, in terms of accuracy but also efficiency and robustness to noise. Lastly, we show that some of the algorithms included in our framework, when combined with the predictions from a CNN model, result in a simple bottom-up instance segmentation pipeline. Going all the way from pixels to final segments with a simple procedure, we achieve state-of-the-art accuracy on the CREMI 2016 EM segmentation benchmark without requiring domain-specific superpixels.
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.
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