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Blind source separation (BSS) aims to recover an unobserved signal $S$ from its mixture $X=f(S)$ under the condition that the effecting transformation $f$ is invertible but unknown. As this is a basic problem with many practical applications, a fundamental issue is to understand how the solutions to this problem behave when their supporting statistical prior assumptions are violated. In the classical context of linear mixtures, we present a general framework for analysing such violations and quantifying their impact on the blind recovery of $S$ from $X$. Modelling $S$ as a multidimensional stochastic process, we introduce an informative topology on the space of possible causes underlying a mixture $X$, and show that the behaviour of a generic BSS-solution in response to general deviations from its defining structural assumptions can be profitably analysed in the form of explicit continuity guarantees with respect to this topology. This allows for a flexible and convenient quantification of general model uncertainty scenarios and amounts to the first comprehensive robustness framework for BSS. Our approach is entirely constructive, and we demonstrate its utility with novel theoretical guarantees for a number of statistical applications.

A novel stochastic geometry framework is proposed in this paper to study the downlink coverage performance in a millimeter wave (mmWave) cellular network by jointly considering the polar coordinates of the Base Stations (BSs) with respect to the typical user located at the origin. Specifically, both the Euclidean and the angular distances of the BSs in a maximum power-based association policy for the UE are considered to account for realistic beam management considerations, which have been largely ignored in the literature, especially in the cell association phase. For completeness, two other association schemes are considered and exact-form expressions for the coverage probability are derived. Subsequently, the key role of angular distances is highlighted by defining the dominant interferer using angular distance-based criteria instead of Euclidean distance-based, and conducting a dominant interferer-based coverage probability analysis. Among others, the numerical results revealed that considering angular distance-based criteria for determining both the serving and the dominant interfering BS, can approximate the coverage performance more accurately as compared to utilizing Euclidean distance-based criteria. To the best of the authors$'$ knowledge, this is the first work that rigorously explores the role of angular distances in the association policy and analysis of cellular networks.

New emerging technologies powered by Artificial Intelligence (AI) have the potential to disruptively transform our societies for the better. In particular, data-driven learning approaches (i.e., Machine Learning (ML)) have been a true revolution in the advancement of multiple technologies in various application domains. But at the same time there is growing concern about certain intrinsic characteristics of these methodologies that carry potential risks to both safety and fundamental rights. Although there are mechanisms in the adoption process to minimize these risks (e.g., safety regulations), these do not exclude the possibility of harm occurring, and if this happens, victims should be able to seek compensation. Liability regimes will therefore play a key role in ensuring basic protection for victims using or interacting with these systems. However, the same characteristics that make AI systems inherently risky, such as lack of causality, opacity, unpredictability or their self and continuous learning capabilities, may lead to considerable difficulties when it comes to proving causation. This paper presents three case studies, as well as the methodology to reach them, that illustrate these difficulties. Specifically, we address the cases of cleaning robots, delivery drones and robots in education. The outcome of the proposed analysis suggests the need to revise liability regimes to alleviate the burden of proof on victims in cases involving AI technologies.

Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields contain per-pixel information about the camera view, parameterized as an up vector and a latitude value. This representation has a number of advantages as it makes minimal assumptions about the camera model and is invariant or equivariant to common image editing operations like cropping, warping, and rotation. It is also more interpretable and aligned with human perception. We train a neural network to predict Perspective Fields and the predicted Perspective Fields can be converted to calibration parameters easily. We demonstrate the robustness of our approach under various scenarios compared with camera calibration-based methods and show example applications in image compositing.

This paper studies an $N$--agent cost-coupled game where the agents are connected via an unreliable capacity constrained network. Each agent receives state information over that network which loses packets with probability $p$. A Base station (BS) actively schedules agent communications over the network by minimizing a weighted Age of Information (WAoI) based cost function under a capacity limit $\mathcal{C} < N$ on the number of transmission attempts at each instant. Under a standard information structure, we show that the problem can be decoupled into a scheduling problem for the BS and a game problem for the $N$ agents. Since the scheduling problem is an NP hard combinatorics problem, we propose an approximately optimal solution which approaches the optimal solution as $N \rightarrow \infty$. In the process, we also provide some insights on the case without channel erasure. Next, to solve the large population game problem, we use the mean-field game framework to compute an approximate decentralized Nash equilibrium. Finally, we validate the theoretical results using a numerical example.

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov chain, where one specifies a certain structure (regression) for the one-step conditional Fr\'echet mean with respect to a natural probability metric. We construct and explore different models based on iterated random function systems of optimal transport maps. While the properties and interpretation of these models depend on how they relate to the iterated transport system, they can all be analyzed theoretically in a unified way. We present such a theoretical analysis, including convergence rates, and illustrate our methodology using real and simulated data. Our approach generalises or extends certain existing models of transportation-based regression and autoregression, and in doing so also provides some additional insights on existing models.

Efficient multi-robot task allocation (MRTA) is fundamental to various time-sensitive applications such as disaster response, warehouse operations, and construction. This paper tackles a particular class of these problems that we call MRTA-collective transport or MRTA-CT -- here tasks present varying workloads and deadlines, and robots are subject to flight range, communication range, and payload constraints. For large instances of these problems involving 100s-1000's of tasks and 10s-100s of robots, traditional non-learning solvers are often time-inefficient, and emerging learning-based policies do not scale well to larger-sized problems without costly retraining. To address this gap, we use a recently proposed encoder-decoder graph neural network involving Capsule networks and multi-head attention mechanism, and innovatively add topological descriptors (TD) as new features to improve transferability to unseen problems of similar and larger size. Persistent homology is used to derive the TD, and proximal policy optimization is used to train our TD-augmented graph neural network. The resulting policy model compares favorably to state-of-the-art non-learning baselines while being much faster. The benefit of using TD is readily evident when scaling to test problems of size larger than those used in training.

Musicians and audio engineers sculpt and transform their sounds by connecting multiple processors, forming an audio processing graph. However, most deep-learning methods overlook this real-world practice and assume fixed graph settings. To bridge this gap, we develop a system that reconstructs the entire graph from a given reference audio. We first generate a realistic graph-reference pair dataset and train a simple blind estimation system composed of a convolutional reference encoder and a transformer-based graph decoder. We apply our model to singing voice effects and drum mixing estimation tasks. Evaluation results show that our method can reconstruct complex signal routings, including multi-band processing and sidechaining.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.