Wind resistance control is an essential feature for quadcopters to maintain their position to avoid deviation from target position and prevent collisions with obstacles. Conventionally, cascaded PID controller is used for the control of quadcopters for its simplicity and ease of tuning its parameters. However, it is weak against wind disturbances and the quadcopter can easily deviate from target position. In this work, we propose a residual reinforcement learning based approach to build a wind resistance controller of a quadcopter. By learning only the residual that compensates the disturbance, we can continue using the cascaded PID controller as the base controller of the quadcopter but improve its performance against wind disturbances. To avoid unexpected crashes and destructions of quadcopters, our method does not require real hardware for data collection and training. The controller is trained only on a simulator and directly applied to the target hardware without extra finetuning process. We demonstrate the effectiveness of our approach through various experiments including an experiment in an outdoor scene with wind speed greater than 13 m/s. Despite its simplicity, our controller reduces the position deviation by approximately 50% compared to the quadcopter controlled with the conventional cascaded PID controller. Furthermore, trained controller is robust and preserves its performance even though the quadcopter's mass and propeller's lift coefficient is changed between 50% to 150% from original training time.
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A crucial task for a randomized controlled trial (RCT) is to specify a statistical method that can yield an efficient estimator and powerful test for the treatment effect. A novel and effective strategy to obtain efficient and powerful treatment effect inferences is to incorporate predictions from generative artificial intelligence (AI) algorithms into covariate adjustment for the regression analysis of a RCT. Training a generative AI algorithm on historical control data enables one to construct a digital twin generator (DTG) for RCT participants, which utilizes a participant's baseline covariates to generate a probability distribution for their potential control outcome. Summaries of the probability distribution from the DTG are highly predictive of the trial outcome, and adjusting for these features via regression can thus improve the quality of treatment effect inferences, while satisfying regulatory guidelines on statistical analyses, for a RCT. However, a critical assumption in this strategy is homoskedasticity, or constant variance of the outcome conditional on the covariates. In the case of heteroskedasticity, existing covariate adjustment methods yield inefficient estimators and underpowered tests. We propose to address heteroskedasticity via a weighted prognostic covariate adjustment methodology (Weighted PROCOVA) that adjusts for both the mean and variance of the regression model using information obtained from the DTG. We prove that our method yields unbiased treatment effect estimators, and demonstrate via comprehensive simulation studies and case studies from Alzheimer's disease that it can reduce the variance of the treatment effect estimator, maintain the Type I error rate, and increase the power of the test for the treatment effect from 80% to 85%~90% when the variances from the DTG can explain 5%~10% of the variation in the RCT participants' outcomes.
Principal components computed via PCA (principal component analysis) are traditionally used to reduce dimensionality in genomic data or to correct for population stratification. In this paper, we explore the penalized eigenvalue problem (PEP) which reformulates the computation of the first eigenvector as an optimization problem and adds an L1 penalty constraint. The contribution of our article is threefold. First, we extend PEP by applying Nesterov smoothing to the original LASSO-type L1 penalty. This allows one to compute analytical gradients which enable faster and more efficient minimization of the objective function associated with the optimization problem. Second, we demonstrate how higher order eigenvectors can be calculated with PEP using established results from singular value decomposition (SVD). Third, using data from the 1000 Genome Project dataset, we empirically demonstrate that our proposed smoothed PEP allows one to increase numerical stability and obtain meaningful eigenvectors. We further investigate the utility of the penalized eigenvector approach over traditional PCA.
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE). These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of $\mathcal{O}(\epsilon^2)$, for $\epsilon>0$ given, the associated work is $\mathcal{O}(\epsilon^{-2})$. Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples.
Vectorial dual-bent functions have recently attracted some researchers' interest as they play a significant role in constructing partial difference sets, association schemes, bent partitions and linear codes. In this paper, we further study vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$, where $2\leq m \leq \frac{n}{2}$, $V_{n}^{(p)}$ denotes an $n$-dimensional vector space over the prime field $\mathbb{F}_{p}$. We give new characterizations of certain vectorial dual-bent functions (called vectorial dual-bent functions with Condition A) in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. When $p=2$, we characterize vectorial dual-bent functions with Condition A in terms of bent partitions. Furthermore, we characterize certain bent partitions in terms of amorphic association schemes, linear codes and generalized Hadamard matrices, respectively. For general vectorial dual-bent functions $F: V_{n}^{(p)}\rightarrow V_{m}^{(p)}$ with $F(0)=0, F(x)=F(-x)$ and $2\leq m \leq \frac{n}{2}$, we give a necessary and sufficient condition on constructing association schemes. Based on such a result, more association schemes are constructed from vectorial dual-bent functions.
Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of $\textbf{calf}$ in the Agda theorem prover.
Accurate load forecasting remains a formidable challenge in numerous sectors, given the intricate dynamics of dynamic power systems, which often defy conventional statistical models. As a response, time-series methodologies like ARIMA and sophisticated deep learning techniques such as Artificial Neural Networks (ANN) and Long Short-Term Memory (LSTM) networks have demonstrated their mettle by achieving enhanced predictive performance. In our investigation, we delve into the efficacy of the relatively recent Gated Recurrent Network (GRU) model within the context of load forecasting. GRU models are garnering attention due to their inherent capacity to adeptly capture and model temporal dependencies within data streams. Our methodology entails harnessing the power of Differential Evolution, a versatile optimization technique renowned for its prowess in delivering scalable, robust, and globally optimal solutions, especially in scenarios involving non-differentiable, multi-objective, or constrained optimization challenges. Through rigorous analysis, we undertake a comparative assessment of the proposed Gated Recurrent Network model, collaboratively fused with various metaheuristic algorithms, evaluating their performance by leveraging established numerical benchmarks such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our empirical investigations are conducted using power load data originating from the Ontario province, Canada. Our research findings cast a spotlight on the remarkable potential of metaheuristic-augmented Gated Recurrent Network models in substantially augmenting load forecasting precision, offering tailored, optimal hyperparameter configurations uniquely suited to each model's performance characteristics.
Medical image segmentation with deep learning is an important and widely studied topic because segmentation enables quantifying target structure size and shape that can help in disease diagnosis, prognosis, surgery planning, and understanding. Recent advances in the foundation VLMs and their adaptation to segmentation tasks in natural images with VLSMs have opened up a unique opportunity to build potentially powerful segmentation models for medical images that enable providing helpful information via language prompt as input, leverage the extensive range of other medical imaging datasets by pooled dataset training, adapt to new classes, and be robust against out-of-distribution data with human-in-the-loop prompting during inference. Although transfer learning from natural to medical images for image-only segmentation models has been studied, no studies have analyzed how the joint representation of vision-language transfers to medical images in segmentation problems and understand gaps in leveraging their full potential. We present the first benchmark study on transfer learning of VLSMs to 2D medical images with thoughtfully collected 11 existing 2D medical image datasets of diverse modalities with carefully presented 9 types of language prompts from 14 attributes. Our results indicate that VLSMs trained in natural image-text pairs transfer reasonably to the medical domain in zero-shot settings when prompted appropriately for non-radiology photographic modalities; when finetuned, they obtain comparable performance to conventional architectures, even in X-rays and ultrasound modalities. However, the additional benefit of language prompts during finetuning may be limited, with image features playing a more dominant role; they can better handle training on pooled datasets combining diverse modalities and are potentially more robust to domain shift than the conventional segmentation models.
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given architecture. This can lead to high-complexity controls which are impractical in applications. In this paper, we take the opposite, constructive approach: We impose various structural restrictions on system dynamics and consequently characterize the class of functions that can be realized by such a system. The systems are implemented as a cascade interconnection of a neural stochastic differential equation (Neural SDE), a deterministic dynamical system, and a readout map. Both probabilistic and geometric (Lie-theoretic) methods are used to characterize the classes of functions realized by such systems.
Computer simulations have become essential for analyzing complex systems, but high-fidelity simulations often come with significant computational costs. To tackle this challenge, multi-fidelity computer experiments have emerged as a promising approach that leverages both low-fidelity and high-fidelity simulations, enhancing both the accuracy and efficiency of the analysis. In this paper, we introduce a new and flexible statistical model, the Recursive Non-Additive (RNA) emulator, that integrates the data from multi-fidelity computer experiments. Unlike conventional multi-fidelity emulation approaches that rely on an additive auto-regressive structure, the proposed RNA emulator recursively captures the relationships between multi-fidelity data using Gaussian process priors without making the additive assumption, allowing the model to accommodate more complex data patterns. Importantly, we derive the posterior predictive mean and variance of the emulator, which can be efficiently computed in a closed-form manner, leading to significant improvements in computational efficiency. Additionally, based on this emulator, we introduce three active learning strategies that optimize the balance between accuracy and simulation costs to guide the selection of the fidelity level and input locations for the next simulation run. We demonstrate the effectiveness of the proposed approach in a suite of synthetic examples and a real-world problem. An R package for the proposed methodology is provided in an open repository.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
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