Many current approaches to shrinkage within the time-varying parameter framework assume that each state is equipped with only one innovation variance for all time points. Sparsity is then induced by shrinking this variance towards zero. We argue that this is not sufficient if the states display large jumps or structural changes, something which is often the case in time series analysis. To remedy this, we propose the dynamic triple gamma prior, a stochastic process that has a well-known triple gamma marginal form, while still allowing for autocorrelation. Crucially, the triple gamma has many interesting limiting and special cases (including the horseshoe shrinkage prior) which can also be chosen as the marginal distribution. Not only is the marginal form well understood, we further derive many interesting properties of the dynamic triple gamma, which showcase its dynamic shrinkage characteristics. We develop an efficient Markov chain Monte Carlo algorithm to sample from the posterior and demonstrate the performance through sparse covariance modeling and forecasting of the returns of the components of the EURO STOXX 50 index.
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A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing
The partially observable generalized linear model (POGLM) is a powerful tool for understanding neural connectivity under the assumption of existing hidden neurons. With spike trains only recorded from visible neurons, existing works use variational inference to learn POGLM meanwhile presenting the difficulty of learning this latent variable model. There are two main issues: (1) the sampled Poisson hidden spike count hinders the use of the pathwise gradient estimator in VI; and (2) the existing design of the variational model is neither expressive nor time-efficient, which further affects the performance. For (1), we propose a new differentiable POGLM, which enables the pathwise gradient estimator, better than the score function gradient estimator used in existing works. For (2), we propose the forward-backward message-passing sampling scheme for the variational model. Comprehensive experiments show that our differentiable POGLMs with our forward-backward message passing produce a better performance on one synthetic and two real-world datasets. Furthermore, our new method yields more interpretable parameters, underscoring its significance in neuroscience.
Current validation methods often rely on recorded data and basic functional checks, which may not be sufficient to encompass the scenarios an autonomous vehicle might encounter. In addition, there is a growing need for complex scenarios with changing vehicle interactions for comprehensive validation. This work introduces a novel synchronous multi-agent simulation framework for autonomous vehicles in interactive scenarios. Our approach creates an interactive scenario and incorporates publicly available edge-case scenarios wherein simulated vehicles are replaced by agents navigating to predefined destinations. We provide a platform that enables the integration of different autonomous driving planning methodologies and includes a set of evaluation metrics to assess autonomous driving behavior. Our study explores different planning setups and adjusts simulation complexity to test the framework's adaptability and performance. Results highlight the critical role of simulating vehicle interactions to enhance autonomous driving systems. Our setup offers unique insights for developing advanced algorithms for complex driving tasks to accelerate future investigations and developments in this field. The multi-agent simulation framework is available as open-source software: //github.com/TUM-AVS/Frenetix-Motion-Planner
Multi-antenna relays and intelligent reflecting surfaces (IRSs) have been utilized to construct favorable channels to improve the performance of wireless systems. A common feature between relay systems and IRS-aided systems is the two-hop multiple-input multiple-output (MIMO) channel. As a result, the mutual information (MI) of two-hop MIMO channels has been widely investigated with very engaging results. However, a rigorous investigation on the fundamental limits of two-hop MIMO channels, i.e., the first and second-order analysis, is not yet available in the literature, due to the difficulties caused by the two-hop (product) channel and the noise introduced by the relay (active IRS). In this paper, we employ large-scale random matrix theory (RMT), specifically Gaussian tools, to derive the closed-form deterministic approximation for the mean and variance of the MI. Additionally, we determine the convergence rate for the mean, variance and the characteristic function of the MI, and prove the asymptotic Gaussianity. Furthermore, we also investigate the analytical properties of the fundamental equations that describe the closed-form approximation and prove the existence and uniqueness of the solution. An iterative algorithm is then proposed to obtain the solution for the fundamental equations. Numerical results validate the accuracy of the theoretical analysis.
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble modification of the test space and connect the method with the general upwinding approach used in finite difference discretization. We write the finite difference and the finite element systems such that the two corresponding linear systems have the same stiffness matrices, and compare the right hand side load vectors for the two methods. This new approach allows for improving well known upwinding finite difference methods and for obtaining new error estimates. We prove that the exponential bubble Petrov-Galerkin discretization can recover the interpolant of the exact solution. As a consequence, we estimate the closeness of the related finite difference solutions to the interpolant. The ideas we present in this work, can lead to building efficient new discretization methods for multidimensional convection dominated problems.
Extremely large aperture arrays can enable unprecedented spatial multiplexing in beyond 5G systems due to their extremely narrow beamfocusing capabilities. However, acquiring the spatial correlation matrix to enable efficient channel estimation is a complex task due to the vast number of antenna dimensions. Recently, a new estimation method called the "reduced-subspace least squares (RS-LS) estimator" has been proposed for densely packed arrays. This method relies solely on the geometry of the array to limit the estimation resources. In this paper, we address a gap in the existing literature by deriving the average spectral efficiency for a certain distribution of user equipments (UEs) and a lower bound on it when using the RS-LS estimator. This bound is determined by the channel gain and the statistics of the normalized spatial correlation matrices of potential UEs but, importantly, does not require knowledge of a specific UE's spatial correlation matrix. We establish that there exists a pilot length that maximizes this expression. Additionally, we derive an approximate expression for the optimal pilot length under low signal-to-noise ratio (SNR) conditions. Simulation results validate the tightness of the derived lower bound and the effectiveness of using the optimized pilot length.
Machine unlearning has emerged as a new paradigm to deliberately forget data samples from a given model in order to adhere to stringent regulations. However, existing machine unlearning methods have been primarily focused on classification models, leaving the landscape of unlearning for generative models relatively unexplored. This paper serves as a bridge, addressing the gap by providing a unifying framework of machine unlearning for image-to-image generative models. Within this framework, we propose a computationally-efficient algorithm, underpinned by rigorous theoretical analysis, that demonstrates negligible performance degradation on the retain samples, while effectively removing the information from the forget samples. Empirical studies on two large-scale datasets, ImageNet-1K and Places-365, further show that our algorithm does not rely on the availability of the retain samples, which further complies with data retention policy. To our best knowledge, this work is the first that represents systemic, theoretical, empirical explorations of machine unlearning specifically tailored for image-to-image generative models. Our code is available at //github.com/jpmorganchase/l2l-generator-unlearning.
Multi-modal 3D scene understanding has gained considerable attention due to its wide applications in many areas, such as autonomous driving and human-computer interaction. Compared to conventional single-modal 3D understanding, introducing an additional modality not only elevates the richness and precision of scene interpretation but also ensures a more robust and resilient understanding. This becomes especially crucial in varied and challenging environments where solely relying on 3D data might be inadequate. While there has been a surge in the development of multi-modal 3D methods over past three years, especially those integrating multi-camera images (3D+2D) and textual descriptions (3D+language), a comprehensive and in-depth review is notably absent. In this article, we present a systematic survey of recent progress to bridge this gap. We begin by briefly introducing a background that formally defines various 3D multi-modal tasks and summarizes their inherent challenges. After that, we present a novel taxonomy that delivers a thorough categorization of existing methods according to modalities and tasks, exploring their respective strengths and limitations. Furthermore, comparative results of recent approaches on several benchmark datasets, together with insightful analysis, are offered. Finally, we discuss the unresolved issues and provide several potential avenues for future research.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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