Learning multi-agent dynamics is a core AI problem with broad applications in robotics and autonomous driving. While most existing works focus on deterministic prediction, producing probabilistic forecasts to quantify uncertainty and assess risks is critical for downstream decision-making tasks such as motion planning and collision avoidance. Multi-agent dynamics often contains internal symmetry. By leveraging symmetry, specifically rotation equivariance, we can improve not only the prediction accuracy but also uncertainty calibration. We introduce Energy Score, a proper scoring rule, to evaluate probabilistic predictions. We propose a novel deep dynamics model, Probabilistic Equivariant Continuous COnvolution (PECCO) for probabilistic prediction of multi-agent trajectories. PECCO extends equivariant continuous convolution to model the joint velocity distribution of multiple agents. It uses dynamics integration to propagate the uncertainty from velocity to position. On both synthetic and real-world datasets, PECCO shows significant improvements in accuracy and calibration compared to non-equivariant baselines.
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讓 iOS 8 和 OS X Yosemite 無縫切換的一個新特性。
> Apple products have always been designed to work together beautifully. But now they may really surprise you. With iOS 8 and OS X Yosemite, you’ll be able to do more wonderful things than ever before.
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The process of designing costmaps for off-road driving tasks is often a challenging and engineering-intensive task. Recent work in costmap design for off-road driving focuses on training deep neural networks to predict costmaps from sensory observations using corpora of expert driving data. However, such approaches are generally subject to over-confident mispredictions and are rarely evaluated in-the-loop on physical hardware. We present an inverse reinforcement learning-based method of efficiently training deep cost functions that are uncertainty-aware. We do so by leveraging recent advances in highly parallel model-predictive control and robotic risk estimation. In addition to demonstrating improvement at reproducing expert trajectories, we also evaluate the efficacy of these methods in challenging off-road navigation scenarios. We observe that our method significantly outperforms a geometric baseline, resulting in 44% improvement in expert path reconstruction and 57% fewer interventions in practice. We also observe that varying the risk tolerance of the vehicle results in qualitatively different navigation behaviors, especially with respect to higher-risk scenarios such as slopes and tall grass.
In this paper we present a novel method, $\textit{Knowledge Persistence}$ ($\mathcal{KP}$), for faster evaluation of Knowledge Graph (KG) completion approaches. Current ranking-based evaluation is quadratic in the size of the KG, leading to long evaluation times and consequently a high carbon footprint. $\mathcal{KP}$ addresses this by representing the topology of the KG completion methods through the lens of topological data analysis, concretely using persistent homology. The characteristics of persistent homology allow $\mathcal{KP}$ to evaluate the quality of the KG completion looking only at a fraction of the data. Experimental results on standard datasets show that the proposed metric is highly correlated with ranking metrics (Hits@N, MR, MRR). Performance evaluation shows that $\mathcal{KP}$ is computationally efficient: In some cases, the evaluation time (validation+test) of a KG completion method has been reduced from 18 hours (using Hits@10) to 27 seconds (using $\mathcal{KP}$), and on average (across methods & data) reduces the evaluation time (validation+test) by $\approx$ $\textbf{99.96}\%$.
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. Under the assumption that the initial conditions and forcing terms are radially symmetric and compactly supported (which is common in applications), we propose an approximation of the propagating wave as the sum of some special nonlinear space-time functions: each term in this sum identifies a particular ray, modeling the result of a single reflection or diffraction effect. We describe an algorithm for identifying such rays automatically, based on the domain geometry. To showcase our proposed method, we present several numerical examples, such as waves scattering off wedges and waves propagating through a room in presence of obstacles.
The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear as a suitable remedy conveying the predictive ability of ML methods with the probabilistically-oriented practice of econometric research. By adopting a state-of-the-art second-order optimization algorithm, we train a Bayesian bilinear neural network with temporal attention, suitable for the challenging time-series task of predicting mid-price movements in ultra-high-frequency limit-order book markets. We thoroughly compare our Bayesian model with traditional ML alternatives by addressing the use of predictive distributions to analyze errors and uncertainties associated with the estimated parameters and model forecasts. Our results underline the feasibility of the Bayesian deep-learning approach and its predictive and decisional advantages in complex econometric tasks, prompting future research in this direction.
With increasingly more computation being shifted to the edge of the network, monitoring of critical infrastructures, such as intermediate processing nodes in autonomous driving, is further complicated due to the typically resource-constrained environments. In order to reduce the resource overhead on the network link imposed by monitoring, various methods have been discussed that either follow a filtering approach for data-emitting devices or conduct dynamic sampling based on employed prediction models. Still, existing methods are mainly requiring adaptive monitoring on edge devices, which demands device reconfigurations, utilizes additional resources, and limits the sophistication of employed models. In this paper, we propose a sampling-based and cloud-located approach that internally utilizes probabilistic forecasts and hence provides means of quantifying model uncertainties, which can be used for contextualized adaptations of sampling frequencies and consequently relieves constrained network resources. We evaluate our prototype implementation for the monitoring pipeline on a publicly available streaming dataset and demonstrate its positive impact on resource efficiency in a method comparison.
Handling trust is one of the core requirements for facilitating effective interaction between the human and the AI agent. Thus, any decision-making framework designed to work with humans must possess the ability to estimate and leverage human trust. In this paper, we propose a mental model based theory of trust that not only can be used to infer trust, thus providing an alternative to psychological or behavioral trust inference methods, but also can be used as a foundation for any trust-aware decision-making frameworks. First, we introduce what trust means according to our theory and then use the theory to define trust evolution, human reliance and decision making, and a formalization of the appropriate level of trust in the agent. Using human subject studies, we compare our theory against one of the most common trust scales (Muir scale) to evaluate 1) whether the observations from the human studies match our proposed theory and 2) what aspects of trust are more aligned with our proposed theory.
We consider optimal sensor placement for a family of linear Bayesian inverse problems characterized by a deterministic hyper-parameter. The hyper-parameter describes distinct configurations in which measurements can be taken of the observed physical system. To optimally reduce the uncertainty in the system's model with a single set of sensors, the initial sensor placement needs to account for the non-linear state changes of all admissible configurations. We address this requirement through an observability coefficient which links the posteriors' uncertainties directly to the choice of sensors. We propose a greedy sensor selection algorithm to iteratively improve the observability coefficient for all configurations through orthogonal matching pursuit. The algorithm allows explicitly correlated noise models even for large sets of candidate sensors, and remains computationally efficient for high-dimensional forward models through model order reduction. We demonstrate our approach on a large-scale geophysical model of the Perth Basin, and provide numerical studies regarding optimality and scalability with regard to classic optimal experimental design utility functions.
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are tailored to specific problems, with particular forward models and priors. Here, we present a generalized approach to sparse Bayesian learning. It has the advantage that it can be used for various types of data acquisitions and prior information. Some preliminary results on image reconstruction/recovery indicate its potential use for denoising, deblurring, and magnetic resonance imaging.
We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
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