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The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes the value function avoiding the construction of a space grid and the need for interpolation techniques using a discrete set of controls. However, the computation of the control is strictly linked to control set chosen in the computation of the tree. Here, we extend and complete the method selecting a finer control set in the computation of the feedback. This requires to use an interpolation method for scattered data which allows us to reconstruct the value function for nodes not belonging to the tree. The effectiveness of the method is shown via a numerical example.

Many problems in computational science and engineering can be described in terms of approximating a smooth function of $d$ variables, defined over an unknown domain of interest $\Omega\subset \mathbb{R}^d$, from sample data. Here both the curse of dimensionality ($d\gg 1$) and the lack of domain knowledge with $\Omega$ potentially irregular and/or disconnected are confounding factors for sampling-based methods. Na\"{i}ve approaches often lead to wasted samples and inefficient approximation schemes. For example, uniform sampling can result in upwards of 20\% wasted samples in some problems. In surrogate model construction in computational uncertainty quantification (UQ), the high cost of computing samples needs a more efficient sampling procedure. In the last years, methods for computing such approximations from sample data have been studied in the case of irregular domains. The advantages of computing sampling measures depending on an approximation space $P$ of $\dim(P)=N$ have been shown. In particular, such methods confer advantages such as stability and well-conditioning, with $\mathcal{O}(N\log(N))$ as sample complexity. The recently-proposed adaptive sampling for general domains (ASGD) strategy is one method to construct these sampling measures. The main contribution of this paper is to improve ASGD by adaptively updating the sampling measures over unknown domains. We achieve this by first introducing a general domain adaptivity strategy (GDAS), which approximates the function and domain of interest from sample points. Second, we propose adaptive sampling for unknown domains (ASUD), which generates sampling measures over a domain that may not be known in advance. Our results show that the ASUD approach consistently achieves the same or smaller errors as uniform sampling, but using fewer, and often significantly fewer evaluations.

Anomaly detection in time-series has a wide range of practical applications. While numerous anomaly detection methods have been proposed in the literature, a recent survey concluded that no single method is the most accurate across various datasets. To make matters worse, anomaly labels are scarce and rarely available in practice. The practical problem of selecting the most accurate model for a given dataset without labels has received little attention in the literature. This paper answers this question i.e. Given an unlabeled dataset and a set of candidate anomaly detectors, how can we select the most accurate model? To this end, we identify three classes of surrogate (unsupervised) metrics, namely, prediction error, model centrality, and performance on injected synthetic anomalies, and show that some metrics are highly correlated with standard supervised anomaly detection performance metrics such as the $F_1$ score, but to varying degrees. We formulate metric combination with multiple imperfect surrogate metrics as a robust rank aggregation problem. We then provide theoretical justification behind the proposed approach. Large-scale experiments on multiple real-world datasets demonstrate that our proposed unsupervised approach is as effective as selecting the most accurate model based on partially labeled data.

Multi-view implicit scene reconstruction methods have become increasingly popular due to their ability to represent complex scene details. Recent efforts have been devoted to improving the representation of input information and to reducing the number of views required to obtain high quality reconstructions. Yet, perhaps surprisingly, the study of which views to select to maximally improve scene understanding remains largely unexplored. We propose an uncertainty-driven active vision approach for implicit scene reconstruction, which leverages occupancy uncertainty accumulated across the scene using volume rendering to select the next view to acquire. To this end, we develop an occupancy-based reconstruction method which accurately represents scenes using either 2D or 3D supervision. We evaluate our proposed approach on the ABC dataset and the in the wild CO3D dataset, and show that: (1) we are able to obtain high quality state-of-the-art occupancy reconstructions; (2) our perspective conditioned uncertainty definition is effective to drive improvements in next best view selection and outperforms strong baseline approaches; and (3) we can further improve shape understanding by performing a gradient-based search on the view selection candidates. Overall, our results highlight the importance of view selection for implicit scene reconstruction, making it a promising avenue to explore further.

Today, many industrial processes are undergoing digital transformation, which often requires the integration of well-understood domain models and state-of-the-art machine learning technology in business processes. However, requirements elicitation and design decision making about when, where and how to embed various domain models and end-to-end machine learning techniques properly into a given business workflow requires further exploration. This paper aims to provide an overview of the requirements engineering process for machine learning applications in terms of cross domain collaborations. We first review the literature on requirements engineering for machine learning, and then go through the collaborative requirements analysis process step-by-step. An example case of industrial data-driven intelligence applications is also discussed in relation to the aforementioned steps.

In predictive modeling with simulation or machine learning, it is critical to assess the quality of estimated values through output analysis accurately. In recent decades output analysis has become enriched with methods that quantify the impact of input data uncertainty in the model outputs to increase robustness. However, most developments apply when the input data can be parametrically parameterized. We propose a unified output analysis framework for simulation and machine learning outputs through the lens of Monte Carlo sampling. This framework provides nonparametric quantification of the variance and bias induced in the outputs with higher-order accuracy. Our new bias-corrected estimation from the model outputs leverages the extension of fast iterative bootstrap sampling and higher-order influence functions. For the scalability of the proposed estimation methods, we devise budget-optimal rules and leverage control variates for variance reduction. Our numerical results demonstrate a clear advantage in building better and more robust confidence intervals for both simulation and machine learning frameworks.

High-fidelity 3D scene reconstruction from monocular videos continues to be challenging, especially for complete and fine-grained geometry reconstruction. The previous 3D reconstruction approaches with neural implicit representations have shown a promising ability for complete scene reconstruction, while their results are often over-smooth and lack enough geometric details. This paper introduces a novel neural implicit scene representation with volume rendering for high-fidelity online 3D scene reconstruction from monocular videos. For fine-grained reconstruction, our key insight is to incorporate geometric priors into both the neural implicit scene representation and neural volume rendering, thus leading to an effective geometry learning mechanism based on volume rendering optimization. Benefiting from this, we present MonoNeuralFusion to perform the online neural 3D reconstruction from monocular videos, by which the 3D scene geometry is efficiently generated and optimized during the on-the-fly 3D monocular scanning. The extensive comparisons with state-of-the-art approaches show that our MonoNeuralFusion consistently generates much better complete and fine-grained reconstruction results, both quantitatively and qualitatively.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.