Control variates are variance reduction techniques for Monte Carlo estimators. They can reduce the cost of the estimation of integrals involving computationally expensive scientific models. We propose an extension of control variates, multilevel control functional (MLCF), which uses non-parametric Stein-based control variates and ensembles of multifidelity models with lower cost to gain better performance. MLCF is widely applicable. We show that when the integrand and the density are smooth, and when the dimensionality is not very high, MLCF enjoys a fast convergence rate. We provide both theoretical analysis and empirical assessments on differential equation examples, including a Bayesian inference for ecological model example, to demonstrate the effectiveness of our proposed approach.
相關內容
We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike a fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize conditional independence, our graphical model is based on conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way we avoid the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and variable selection consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.
The central limit theorem (CLT) is one of the most fundamental results in probability; and establishing its rate of convergence has been a key question since the 1940s. For independent random variables, a series of recent works established optimal error bounds under the Wasserstein-p distance (with p>=1). In this paper, we extend those results to locally dependent random variables, which include m-dependent random fields and U-statistics. Under conditions on the moments and the dependency neighborhoods, we derive optimal rates in the CLT for the Wasserstein-p distance. Our proofs rely on approximating the empirical average of dependent observations by the empirical average of i.i.d. random variables. To do so, we expand the Stein equation to arbitrary orders by adapting the Stein's dependency neighborhood method. Finally we illustrate the applicability of our results by obtaining efficient tail bounds.
Statistical measures for group fairness in machine learning reflect the gap in performance of algorithms across different groups. These measures, however, exhibit a high variance between different training instances, which makes them unreliable for empirical evaluation of fairness. What causes this high variance? We investigate the impact on group fairness of different sources of randomness in training neural networks. We show that the variance in group fairness measures is rooted in the high volatility of the learning process on under-represented groups. Further, we recognize the dominant source of randomness as the stochasticity of data order during training. Based on these findings, we show how one can control group-level accuracy (i.e., model fairness), with high efficiency and negligible impact on the model's overall performance, by simply changing the data order for a single epoch.
Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low intrinsic dimensionality. By introducing a low dimensional bias we can fight the curse of dimensionality affecting these quantities of interest, especially for many-query applications. We seek a gradient-based reduction of the parameter space through linear active subspaces or a nonlinear transformation of the input space. Then we build a low-fidelity response surface based on such reduction, thus enabling nonlinear autoregressive multi-fidelity Gaussian process regression without the need of running new simulations with simplified physical models. This has a great potential in the data scarcity regime affecting many engineering applications. In this work we present a new multi-fidelity approach that involves active subspaces and the nonlinear level-set learning method, starting from the preliminary analysis previously conducted in Romor et al. 2020. The proposed framework is tested on two high-dimensional benchmark functions, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces.
Recent years have witnessed the widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models. Despite their tremendous success, a number of vital problems like ML model brittleness, their fairness, and the lack of interpretability warrant the need for the active developments in explainable artificial intelligence (XAI) and formal ML model verification. The two major lines of work in XAI include feature selection methods, e.g. Anchors, and feature attribution techniques, e.g. LIME and SHAP. Despite their promise, most of the existing feature selection and attribution approaches are susceptible to a range of critical issues, including explanation unsoundness and out-of-distribution sampling. A recent formal approach to XAI (FXAI) although serving as an alternative to the above and free of these issues suffers from a few other limitations. For instance and besides the scalability limitation, the formal approach is unable to tackle the feature attribution problem. Additionally, a formal explanation despite being formally sound is typically quite large, which hampers its applicability in practical settings. Motivated by the above, this paper proposes a way to apply the apparatus of formal XAI to the case of feature attribution based on formal explanation enumeration. Formal feature attribution (FFA) is argued to be advantageous over the existing methods, both formal and non-formal. Given the practical complexity of the problem, the paper then proposes an efficient technique for approximating exact FFA. Finally, it offers experimental evidence of the effectiveness of the proposed approximate FFA in comparison to the existing feature attribution algorithms not only in terms of feature importance and but also in terms of their relative order.
Asymmetry is a crucial characteristic of bilateral mammograms (Bi-MG) when abnormalities are developing. It is widely utilized by radiologists for diagnosis. The question of 'what the symmetrical Bi-MG would look like when the asymmetrical abnormalities have been removed ?' has not yet received strong attention in the development of algorithms on mammograms. Addressing this question could provide valuable insights into mammographic anatomy and aid in diagnostic interpretation. Hence, we propose a novel framework, DisAsymNet, which utilizes asymmetrical abnormality transformer guided self-adversarial learning for disentangling abnormalities and symmetric Bi-MG. At the same time, our proposed method is partially guided by randomly synthesized abnormalities. We conduct experiments on three public and one in-house dataset, and demonstrate that our method outperforms existing methods in abnormality classification, segmentation, and localization tasks. Additionally, reconstructed normal mammograms can provide insights toward better interpretable visual cues for clinical diagnosis. The code will be accessible to the public.
Machine Learning (ML) models in Robotic Assembly Sequence Planning (RASP) need to be introspective on the predicted solutions, i.e. whether they are feasible or not, to circumvent potential efficiency degradation. Previous works need both feasible and infeasible examples during training. However, the infeasible ones are hard to collect sufficiently when re-training is required for swift adaptation to new product variants. In this work, we propose a density-based feasibility learning method that requires only feasible examples. Concretely, we formulate the feasibility learning problem as Out-of-Distribution (OOD) detection with Normalizing Flows (NF), which are powerful generative models for estimating complex probability distributions. Empirically, the proposed method is demonstrated on robotic assembly use cases and outperforms other single-class baselines in detecting infeasible assemblies. We further investigate the internal working mechanism of our method and show that a large memory saving can be obtained based on an advanced variant of NF.
This paper presents a novel approach for optical flow control of Micro Air Vehicles (MAVs). The task is challenging due to the nonlinearity of optical flow observables. Our proposed Incremental Nonlinear Dynamic Inversion (INDI) control scheme incorporates an efficient data-driven method to address the nonlinearity. It directly estimates the inverse of the time-varying control effectiveness in real-time, eliminating the need for the constant assumption and avoiding high computation in traditional INDI. This approach effectively handles fast-changing system dynamics commonly encountered in optical flow control, particularly height-dependent changes. We demonstrate the robustness and efficiency of the proposed control scheme in numerical simulations and also real-world flight tests: multiple landings of an MAV on a static and flat surface with various tracking setpoints, hovering and landings on moving and undulating surfaces. Despite being challenged with the presence of noisy optical flow estimates and the lateral and vertical movement of the landing surfaces, the MAV is able to successfully track or land on the surface with an exponential decay of both height and vertical velocity at almost the same time, as desired.
A long-lasting goal of robotics research is to operate robots safely, while achieving high performance which often involves fast motions. Traditional motor-driven systems frequently struggle to balance these competing demands. Addressing this trade-off is crucial for advancing fields such as manufacturing and healthcare, where seamless collaboration between robots and humans is essential. We introduce a four degree-of-freedom (DoF) tendon-driven robot arm, powered by pneumatic artificial muscles (PAMs), to tackle this challenge. Our new design features low friction, passive compliance, and inherent impact resilience, enabling rapid, precise, high-force, and safe interactions during dynamic tasks. In addition to fostering safer human-robot collaboration, the inherent safety properties are particularly beneficial for reinforcement learning, where the robot's ability to explore dynamic motions without causing self-damage is crucial. We validate our robotic arm through various experiments, including long-term dynamic motions, impact resilience tests, and assessments of its ease of control. On a challenging dynamic table tennis task, we further demonstrate our robot's capabilities in rapid and precise movements. By showcasing our new design's potential, we aim to inspire further research on robotic systems that balance high performance and safety in diverse tasks. Our open-source hardware design, software, and a large dataset of diverse robot motions can be found at \link{//webdav.tuebingen.mpg.de/pamy2/}{webdav.tuebingen.mpg.de/pamy2/}.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191