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Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are computationally expensive, requiring many neural function evaluations (NFEs). In this work, we propose an anytime diffusion-based method that can generate viable images when stopped at arbitrary times before completion. Using existing pretrained diffusion models, we show that the generation scheme can be recomposed as two nested diffusion processes, enabling fast iterative refinement of a generated image. In experiments on ImageNet and Stable Diffusion-based text-to-image generation, we show, both qualitatively and quantitatively, that our method's intermediate generation quality greatly exceeds that of the original diffusion model, while the final generation result remains comparable. We illustrate the applicability of Nested Diffusion in several settings, including for solving inverse problems, and for rapid text-based content creation by allowing user intervention throughout the sampling process.

U-Net style networks are commonly utilized in unsupervised image registration to predict dense displacement fields, which for high-resolution volumetric image data is a resource-intensive and time-consuming task. To tackle this challenge, we first propose Fourier-Net, which replaces the costly U-Net style expansive path with a parameter-free model-driven decoder. Instead of directly predicting a full-resolution displacement field, our Fourier-Net learns a low-dimensional representation of the displacement field in the band-limited Fourier domain which our model-driven decoder converts to a full-resolution displacement field in the spatial domain. Expanding upon Fourier-Net, we then introduce Fourier-Net+, which additionally takes the band-limited spatial representation of the images as input and further reduces the number of convolutional layers in the U-Net style network's contracting path. Finally, to enhance the registration performance, we propose a cascaded version of Fourier-Net+. We evaluate our proposed methods on three datasets, on which our proposed Fourier-Net and its variants achieve comparable results with current state-of-the art methods, while exhibiting faster inference speeds, lower memory footprint, and fewer multiply-add operations. With such small computational cost, our Fourier-Net+ enables the efficient training of large-scale 3D registration on low-VRAM GPUs. Our code is publicly available at \url{//github.com/xi-jia/Fourier-Net}.

In communication between humans, gestures are often preferred or complementary to verbal expression since the former offers better spatial referral. Finger pointing gesture conveys vital information regarding some point of interest in the environment. In human-robot interaction, a user can easily direct a robot to a target location, for example, in search and rescue or factory assistance. State-of-the-art approaches for visual pointing estimation often rely on depth cameras, are limited to indoor environments and provide discrete predictions between limited targets. In this paper, we explore the learning of models for robots to understand pointing directives in various indoor and outdoor environments solely based on a single RGB camera. A novel framework is proposed which includes a designated model termed PointingNet. PointingNet recognizes the occurrence of pointing followed by approximating the position and direction of the index finger. The model relies on a novel segmentation model for masking any lifted arm. While state-of-the-art human pose estimation models provide poor pointing angle estimation accuracy of 28deg, PointingNet exhibits mean accuracy of less than 2deg. With the pointing information, the target is computed followed by planning and motion of the robot. The framework is evaluated on two robotic systems yielding accurate target reaching.

Many stochastic processes in the physical and biological sciences can be modelled using Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the diffusion term is configuration-dependent. One remedy is to construct a transform to a constant-diffusion process and sample the transformed process instead. In this work, we explain how coordinate-based and time-rescaling-based transforms can be used either individually or in combination to map a general class of variable-diffusion Brownian motion processes into constant-diffusion ones. The transforms are invertible, thus allowing recovery of the original dynamics. We motivate our methodology using examples in one dimension before then considering multivariate diffusion processes. We illustrate the benefits of the transforms through numerical simulations, demonstrating how the right combination of integrator and transform can improve computational efficiency and the order of convergence to the invariant distribution. Notably, the transforms that we derive are applicable to a class of multibody, anisotropic Stokes-Einstein diffusion that has applications in biophysical modelling.

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.

Robots are notoriously difficult to design because of complex interdependencies between their physical structure, sensory and motor layouts, and behavior. Despite this, almost every detail of every robot built to date has been manually determined by a human designer after several months or years of iterative ideation, prototyping, and testing. Inspired by evolutionary design in nature, the automated design of robots using evolutionary algorithms has been attempted for two decades, but it too remains inefficient: days of supercomputing are required to design robots in simulation that, when manufactured, exhibit desired behavior. Here we show for the first time de-novo optimization of a robot's structure to exhibit a desired behavior, within seconds on a single consumer-grade computer, and the manufactured robot's retention of that behavior. Unlike other gradient-based robot design methods, this algorithm does not presuppose any particular anatomical form; starting instead from a randomly-generated apodous body plan, it consistently discovers legged locomotion, the most efficient known form of terrestrial movement. If combined with automated fabrication and scaled up to more challenging tasks, this advance promises near instantaneous design, manufacture, and deployment of unique and useful machines for medical, environmental, vehicular, and space-based tasks.

Observational studies are frequently used to estimate the effect of an exposure or treatment on an outcome. To obtain an unbiased estimate of the treatment effect, it is crucial to measure the exposure accurately. A common type of exposure misclassification is recall bias, which occurs in retrospective cohort studies when study subjects may inaccurately recall their past exposure. Specifically, differential recall bias can be problematic when examining the effect of a self-reported binary exposure since the magnitude of recall bias can differ between groups. In this paper, we provide the following contributions: 1) we derive bounds for the average treatment effect (ATE) in the presence of recall bias; 2) we develop several estimation approaches under different identification strategies; 3) we conduct simulation studies to evaluate their performance under several scenarios of model misspecification; 4) we propose a sensitivity analysis method that can examine the robustness of our results with respect to different assumptions; and 5) we apply the proposed framework to an observational study, estimating the effect of childhood physical abuse on adulthood mental health.

The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of the marginal splines must be used, which leads to an unmanageable number of basis functions when the order of interaction is high and results in low estimation efficiency. In this paper, we improve the performance of MARS by using linear combinations of the covariates which achieve sufficient dimension reduction. The special basis functions of MARS facilitate calculation of gradients of the regression function, and estimation of the linear combinations is obtained via eigen-analysis of the outer-product of the gradients. Under some technical conditions, the asymptotic theory is established for the proposed estimation method. Numerical studies including both simulation and empirical applications show its effectiveness in dimension reduction and improvement over MARS and other commonly-used nonparametric methods in regression estimation and prediction.

In this paper, we consider estimation of average treatment effect on the treated (ATT), an interpretable and relevant causal estimand to policy makers when treatment assignment is endogenous. By considering shadow variables that are unrelated to the treatment assignment but related to interested outcomes, we establish identification of the ATT. Then we focus on efficient estimation of the ATT by characterizing the geometric structure of the likelihood, deriving the semiparametric efficiency bound for ATT estimation and proposing an estimator that can achieve this bound. We rigorously establish the theoretical results of the proposed estimator. The finite sample performance of the proposed estimator is studied through comprehensive simulation studies as well as an application to our motivating study.

This paper addresses the exploration-exploitation dilemma inherent in decision-making, focusing on multi-armed bandit problems. The problems involve an agent deciding whether to exploit current knowledge for immediate gains or explore new avenues for potential long-term rewards. We here introduce a novel algorithm, approximate information maximization (AIM), which employs an analytical approximation of the entropy gradient to choose which arm to pull at each point in time. AIM matches the performance of Infomax and Thompson sampling while also offering enhanced computational speed, determinism, and tractability. Empirical evaluation of AIM indicates its compliance with the Lai-Robbins asymptotic bound and demonstrates its robustness for a range of priors. Its expression is tunable, which allows for specific optimization in various settings.