本文介绍了基于可见性的移动机器人的\传感器\的数学模型。提供类似于针对计算机视觉的针孔摄像机模型的目的，介绍的模型有望提供有用的，理想化的与任务相关信息的特征，可以从其输出或观察值中推断出来。可能的任务包括当在未知环境中部署移动机器人时导航，本地化和映射。这些模型可以在传统的深度传感器之间进行直接比较，并突出显示触摸传感可能与飞行时间或视觉传感器互换的案例，并表征触摸传感提供的独特优势。这些模型包括接触检测，压缩，负载轴承和挠度。该结果可以作为移动机器人传感器融合系统创新触摸传感器设计的基本构建块。

Advances in reinforcement learning have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens. Central to our work is the idea that the transition dynamics induce a low dimensional manifold of reachable states embedded in the high-dimensional nominal state space. We prove that, under certain conditions, the dimensionality of this manifold is at most the dimensionality of the action space plus one. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments. We further demonstrate the applicability of our result by learning a policy in this low dimensional representation. To do so we introduce an algorithm that learns a mapping to a low dimensional representation, as a narrow hidden layer of a deep neural network, in tandem with the policy using DDPG. Our experiments show that a policy learnt this way perform on par or better for four MuJoCo control suite tasks.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

Maximum Inner Product Search (MIPS) is a popular problem in the machine learning literature due to its applicability in a wide array of applications, such as recommender systems. In high-dimensional settings, however, MIPS queries can become computationally expensive as most existing solutions do not scale well with data dimensionality. In this work, we present a state-of-the-art algorithm for the MIPS problem in high dimensions, dubbed BanditMIPS. BanditMIPS is a randomized algorithm that borrows techniques from multi-armed bandits to reduce the MIPS problem to a best-arm identification problem. BanditMIPS reduces the complexity of state-of-the-art algorithms from $O(\sqrt{d})$ to $O(\text{log}d)$, where $d$ is the dimension of the problem data vectors. On high-dimensional real-world datasets, BanditMIPS runs approximately 12 times faster than existing approaches and returns the same solution. BanditMIPS requires no preprocessing of the data and includes a hyperparameter that practitioners may use to trade off accuracy and runtime. We also propose a variant of our algorithm, named BanditMIPS-$\alpha$, which employs non-uniform sampling across the data dimensions to provide further speedups.

Random forests are some of the most widely used machine learning models today, especially in domains that necessitate interpretability. We present an algorithm that accelerates the training of random forests and other popular tree-based learning methods. At the core of our algorithm is a novel node-splitting subroutine, dubbed MABSplit, used to efficiently find split points when constructing decision trees. Our algorithm borrows techniques from the multi-armed bandit literature to judiciously determine how to allocate samples and computational power across candidate split points. We provide theoretical guarantees that MABSplit improves the sample complexity of each node split from linear to logarithmic in the number of data points. In some settings, MABSplit leads to 100x faster training (an 99% reduction in training time) without any decrease in generalization performance. We demonstrate similar speedups when MABSplit is used across a variety of forest-based variants, such as Extremely Random Forests and Random Patches. We also show our algorithm can be used in both classification and regression tasks. Finally, we show that MABSplit outperforms existing methods in generalization performance and feature importance calculations under a fixed computational budget. All of our experimental results are reproducible via a one-line script at https://github.com/ThrunGroup/FastForest.

Concept bottleneck models (CBMs) (Koh et al. 2020) are interpretable neural networks that first predict labels for human-interpretable concepts relevant to the prediction task, and then predict the final label based on the concept label predictions.We extend CBMs to interactive prediction settings where the model can query a human collaborator for the label to some concepts. We develop an interaction policy that, at prediction time, chooses which concepts to request a label for so as to maximally improve the final prediction. We demonstrate thata simple policy combining concept prediction uncertainty and influence of the concept on the final prediction achieves strong performance and outperforms a static approach proposed in Koh et al. (2020) as well as active feature acquisition methods proposed in the literature. We show that the interactiveCBM can achieve accuracy gains of 5-10% with only 5 interactions over competitive baselines on the Caltech-UCSDBirds, CheXpert and OAI datasets.

Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underline{\alpha})$ of a set of spectral-bands $\underline{\alpha}$. Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underline{\alpha} \subset \mathbb{R}^+$ such that the energies $\textbf{E}(\underline{\alpha})$ of these bands can optimally discriminate between the two classes. We introduce EGO-MDA, an unsupervised method to identify optimal spectral-bands $\underline{\alpha}^*$ for given samples of spectra from two classes. EGO-MDA employs a statistical approach that iteratively minimizes an adjusted multinomial log-likelihood (deviance) criterion $\mathcal{D}(\underline{\alpha},\mathcal{M})$. Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underline{\alpha}, \mathcal{M})$ and identify a classifier that optimally discriminates between two classes for a given spectral representation. The Efficient Global Optimization (EGO) finds the spectral-bands $\underline{\alpha}^* = \underset{\underline{\alpha}}{\rm argmin}~\mathcal{D}(\underline{\alpha},\mathcal{M})$ for given GMM parameters $\mathcal{M}$. For pathological cases of low separation between mixtures and model misspecification, we discuss the effect of the sample size and the number of iterations on the estimates of parameters $\mathcal{M}$ and therefore the classifier performance. A case study on a synthetic data set is provided. In an engineering application of optimal spectral-banding for anomaly tracking, EGO-MDA achieved at least 70% improvement in the median deviance relative to other methods tested.

Human activity recognition (HAR) using drone-mounted cameras has attracted considerable interest from the computer vision research community in recent years. A robust and efficient HAR system has a pivotal role in fields like video surveillance, crowd behavior analysis, sports analysis, and human-computer interaction. What makes it challenging are the complex poses, understanding different viewpoints, and the environmental scenarios where the action is taking place. To address such complexities, in this paper, we propose a novel Sparse Weighted Temporal Attention (SWTA) module to utilize sparsely sampled video frames for obtaining global weighted temporal attention. The proposed SWTA is comprised of two parts. First, temporal segment network that sparsely samples a given set of frames. Second, weighted temporal attention, which incorporates a fusion of attention maps derived from optical flow, with raw RGB images. This is followed by a basenet network, which comprises a convolutional neural network (CNN) module along with fully connected layers that provide us with activity recognition. The SWTA network can be used as a plug-in module to the existing deep CNN architectures, for optimizing them to learn temporal information by eliminating the need for a separate temporal stream. It has been evaluated on three publicly available benchmark datasets, namely Okutama, MOD20, and Drone-Action. The proposed model has received an accuracy of 72.76%, 92.56%, and 78.86% on the respective datasets thereby surpassing the previous state-of-the-art performances by a margin of 25.26%, 18.56%, and 2.94%, respectively.

Causal phenomena associated with rare events frequently occur across a wide range of engineering and mathematical problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links between random variables that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel algorithm that performs statistical independence tests on data collected from time-invariant dynamical systems in which rare but consequential events occur. We seek to understand if the state of the dynamical system causally affects the likelihood of the rare event. In particular, we exploit the time-invariance of the underlying data to superimpose the occurrences of rare events, thus creating a new dataset, with rare events are better represented, on which conditional independence tests can be more efficiently performed. We provide non-asymptotic bounds for the consistency of our algorithm, and validate the performance of our algorithm across various simulated scenarios, with applications to traffic accidents.

Drone-camera based human activity recognition (HAR) has received significant attention from the computer vision research community in the past few years. A robust and efficient HAR system has a pivotal role in fields like video surveillance, crowd behavior analysis, sports analysis, and human-computer interaction. What makes it challenging are the complex poses, understanding different viewpoints, and the environmental scenarios where the action is taking place. To address such complexities, in this paper, we propose a novel Sparse Weighted Temporal Fusion (SWTF) module to utilize sparsely sampled video frames for obtaining global weighted temporal fusion outcome. The proposed SWTF is divided into two components. First, a temporal segment network that sparsely samples a given set of frames. Second, weighted temporal fusion, that incorporates a fusion of feature maps derived from optical flow, with raw RGB images. This is followed by base-network, which comprises a convolutional neural network module along with fully connected layers that provide us with activity recognition. The SWTF network can be used as a plug-in module to the existing deep CNN architectures, for optimizing them to learn temporal information by eliminating the need for a separate temporal stream. It has been evaluated on three publicly available benchmark datasets, namely Okutama, MOD20, and Drone-Action. The proposed model has received an accuracy of 72.76%, 92.56%, and 78.86% on the respective datasets thereby surpassing the previous state-of-the-art performances by a significant margin.