This is the supplementary information pertaining to the main manuscript. In this supplementary material, we provide the comparative performance of Neurochaos Learning with Deep Neural Network, 1DConvolutional Neural Network (1D CNN), and Long Short term Memory (LSTM) for evaluation of cause-effect classification of timeseries data generated from coupled chaotic master-slave system and autoregressive (AR) processes. We also check whether each of these architectures are able to preserve cause-effect relationship between the corresponding features extracted from the original cause and effect time series. To evaluate the efficacy of Neurochaos Learning (NL: ChaosNet) and deep learning algorithms for the classification of cause-effect, we used simulated datasets from (a) coupled autoregressive (AR) processes, and (b) coupled 1D chaotic skew tent-maps in master-slave configuration. The governing equations for the coupled AR processes are the following: M(t)=a1M(t 1)+γr(t), (1) S(t)=a2S(t 1)+ηM(t 1)+γr(t), (2) where M(t) and S(t) are the independent and the dependent (or the cause and effect) time series respectively; a1 = 0.8, a2 = 0.9, the noise intensity γ = 0.03 and r(t) is independent and identically distributed additive Gaussian noise drawn from a standard normal distribution.

Discovering cause and effect variables from observational data is an important but challenging problem in science and engineering. In this work, a recently proposed brain inspired learning algorithm namely-Neurochaos Learning (NL) is used for the classification of cause and effect time series generated using coupled autoregressive processes, coupled 1D chaotic skew tent maps, coupled 1D chaotic logistic maps and a real-world prey-predator system. In the case of coupled skew tent maps, the proposed method consistently outperforms a five layer Deep Neural Network (DNN) and Long Short Term Memory (LSTM) architecture for unidirectional coupling coefficient values ranging from 0.1 to 0.7. Further, we investigate the preservation of causality in the feature extracted space of NL using Granger Causality for coupled autoregressive processes and Compression-Complexity Causality for coupled chaotic systems and real-world prey-predator dataset. Unlike DNN, LSTM and 1DConvolutional Neural Network, it is found that NL preserves the inherent causal structures present in the input timeseries data. These findings are promising for the theory and applications of causal machine learning and open up the possibility to explore the potential of NL for more sophisticated causal learning tasks.

Monocular 3D object detection (Mono3D) in mobile settings (e.g., on a vehicle, a drone, or a robot) is an important yet challenging task. Due to the near-far disparity phenomenon of monocular vision and the ever-changing camera pose, it is hard to acquire high detection accuracy, especially for far objects. Inspired by the insight that the depth of an object can be well determined according to the depth of the ground where it stands, in this paper, we propose a novel Mono3D framework, called MoGDE, which constantly estimates the corresponding ground depth of an image and then utilizes the estimated ground depth information to guide Mono3D. To this end, we utilize a pose detection network to estimate the pose of the camera and then construct a feature map portraying pixel-level ground depth according to the 3D-to-2D perspective geometry. Moreover, to improve Mono3D with the estimated ground depth, we design an RGB-D feature fusion network based on the transformer structure, where the long-range self-attention mechanism is utilized to effectively identify ground-contacting points and pin the corresponding ground depth to the image feature map.

Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been sparse. The theoretical investigation of the generalization performance is beneficial for understanding fundamental issues (such as fairness) of GNN models and designing better learning methods. In this paper, we present a novel PAC-Bayesian analysis for GNNs under a non-IID semi-supervised learning setup. Moreover, we analyze the generalization performances on different subgroups of unlabeled nodes, which allows us to further study an accuracy-(dis)parity-style (un)fairness of GNNs from a theoretical perspective. Under reasonable assumptions, we demonstrate that the distance between a test subgroup and the training set can be a key factor affecting the GNN performance on that subgroup, which calls special attention to the training node selection for fair learning. Experiments across multiple GNN models and datasets support our theoretical results4.

Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision making and search under uncertainty. In modern applications however, one is often faced with a tremendously large number of options and even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similarity relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms is captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one that has sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms GRUB (GRaph based UcB) and ζ-GRUB for these problems and provide theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement that shows a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information.