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Probability predictions are essential to inform decision making in medicine, economics, image classification, sports analytics, entertainment, and many other fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, i.e., far from the base rate of the event. Predictions that satisfy these three criteria are informative for decision making. However, there is a fundamental tension between calibration and boldness, since calibration metrics can be high when predictions are overly cautious, i.e., non-bold. The purpose of this work is to develop a hypothesis test and Bayesian model selection approach to assess calibration, and a strategy for boldness-recalibration that enables practitioners to responsibly embolden predictions subject to their required level of calibration. Specifically, we allow the user to pre-specify their desired posterior probability of calibration, then maximally embolden predictions subject to this constraint. We verify the performance of our procedures via simulation, then demonstrate the breadth of applicability by applying these methods to real world case studies in each of the fields mentioned above. We find that very slight relaxation of calibration probability (e.g., from 0.99 to 0.95) can often substantially embolden predictions (e.g., widening Hockey predictions' range from .25-.75 to .10-.90)

Electoral control types are ways of trying to change the outcome of elections by altering aspects of their composition and structure [BTT92]. We say two compatible (i.e., having the same input types) control types that are about the same election system E form a collapsing pair if for every possible input (which typically consists of a candidate set, a vote set, a focus candidate, and sometimes other parameters related to the nature of the attempted alteration), either both or neither of the attempted attacks can be successfully carried out [HHM20]. For each of the seven general (i.e., holding for all election systems) electoral control type collapsing pairs found by Hemaspaandra, Hemaspaandra, and Menton [HHM20] and for each of the additional electoral control type collapsing pairs of Carleton et al. [CCH+ 22] for veto and approval (and many other election systems in light of that paper's Theorems 3.6 and 3.9), both members of the collapsing pair have the same complexity since as sets they are the same set. However, having the same complexity (as sets) is not enough to guarantee that as search problems they have the same complexity. In this paper, we explore the relationships between the search versions of collapsing pairs. For each of the collapsing pairs of Hemaspaandra, Hemaspaandra, and Menton [HHM20] and Carleton et al. [CCH+ 22], we prove that the pair's members' search-version complexities are polynomially related (given access, for cases when the winner problem itself is not in polynomial time, to an oracle for the winner problem). Beyond that, we give efficient reductions that from a solution to one compute a solution to the other. For the concrete systems plurality, veto, and approval, we completely determine which of their (due to our results) polynomially-related collapsing search-problem pairs are polynomial-time computable and which are NP-hard.

Prior works for reconstructing hand-held objects from a single image rely on direct 3D shape supervision which is challenging to gather in real world at scale. Consequently, these approaches do not generalize well when presented with novel objects in in-the-wild settings. While 3D supervision is a major bottleneck, there is an abundance of in-the-wild raw video data showing hand-object interactions. In this paper, we automatically extract 3D supervision (via multiview 2D supervision) from such raw video data to scale up the learning of models for hand-held object reconstruction. This requires tackling two key challenges: unknown camera pose and occlusion. For the former, we use hand pose (predicted from existing techniques, e.g. FrankMocap) as a proxy for object pose. For the latter, we learn data-driven 3D shape priors using synthetic objects from the ObMan dataset. We use these indirect 3D cues to train occupancy networks that predict the 3D shape of objects from a single RGB image. Our experiments on the MOW and HO3D datasets show the effectiveness of these supervisory signals at predicting the 3D shape for real-world hand-held objects without any direct real-world 3D supervision.

NeRF acquisition typically requires careful choice of near planes for the different cameras or suffers from background collapse, creating floating artifacts on the edges of the captured scene. The key insight of this work is that background collapse is caused by a higher density of samples in regions near cameras. As a result of this sampling bias, near-camera volumes receive significantly more gradients, leading to incorrect density buildup. We propose a gradient scaling approach to counter-balance this bias, removing the need for near planes, while preventing background collapse. Our method can be implemented in a few lines, does not induce any significant overhead, and is compatible with most NeRF implementations.

Future collaborative robots must be capable of finding objects. As such a fundamental skill, we expect object search to eventually become an off-the-shelf capability for any robot, similar to e.g., object detection, SLAM, and motion planning. However, existing approaches either make unrealistic compromises (e.g., reduce the problem from 3D to 2D), resort to ad-hoc, greedy search strategies, or attempt to learn end-to-end policies in simulation that are yet to generalize across real robots and environments. This thesis argues that through using Partially Observable Markov Decision Processes (POMDPs) to model object search while exploiting structures in the human world (e.g., octrees, correlations) and in human-robot interaction (e.g., spatial language), a practical and effective system for generalized object search can be achieved. In support of this argument, I develop methods and systems for (multi-)object search in 3D environments under uncertainty due to limited field of view, occlusion, noisy, unreliable detectors, spatial correlations between objects, and possibly ambiguous spatial language (e.g., "The red car is behind Chase Bank"). Besides evaluation in simulators such as PyGame, AirSim, and AI2-THOR, I design and implement a robot-independent, environment-agnostic system for generalized object search in 3D and deploy it on the Boston Dynamics Spot robot, the Kinova MOVO robot, and the Universal Robots UR5e robotic arm, to perform object search in different environments. The system enables, for example, a Spot robot to find a toy cat hidden underneath a couch in a kitchen area in under one minute. This thesis also broadly surveys the object search literature, proposing taxonomies in object search problem settings, methods and systems.

Precise calibration is the basis for the vision-guided robot system to achieve high-precision operations. Systems with multiple eyes (cameras) and multiple hands (robots) are particularly sensitive to calibration errors, such as micro-assembly systems. Most existing methods focus on the calibration of a single unit of the whole system, such as poses between hand and eye, or between two hands. These methods can be used to determine the relative pose between each unit, but the serialized incremental calibration strategy cannot avoid the problem of error accumulation in a large-scale system. Instead of focusing on a single unit, this paper models the multi-eye and multi-hand system calibration problem as a graph and proposes a method based on the minimum spanning tree and graph optimization. This method can automatically plan the serialized optimal calibration strategy in accordance with the system settings to get coarse calibration results initially. Then, with these initial values, the closed-loop constraints are introduced to carry out global optimization. Simulation experiments demonstrate the performance of the proposed algorithm under different noises and various hand-eye configurations. In addition, experiments on real robot systems are presented to further verify the proposed method.

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.