13,044 research outputs found

    Propagation of chaos for mean field Schr\"odinger problems

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    In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field Schr\"odinger problem arises as the limit of ``standard'' Schr\"odinger problems over interacting particles. Due to the stochastic maximum principle and a suitable penalization procedure, the result follows as a consequence of novel (quantitative) propagation of chaos results for forward-backwards particle systems. The approach described in the paper seems flexible enough to address other questions in the theory. For instance, our stochastic control technique further allows us to solve the mean field Schr\"odinger problem and characterize its solution, the mean field Schr\"odinger bridge, by a forward-backward planning equation

    Building Reliable Budget-Based Binary-State Networks

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    Everyday life is driven by various network, such as supply chains for distributing raw materials, semi-finished product goods, and final products; Internet of Things (IoT) for connecting and exchanging data; utility networks for transmitting fuel, power, water, electricity, and 4G/5G; and social networks for sharing information and connections. The binary-state network is a basic network, where the state of each component is either success or failure, i.e., the binary-state. Network reliability plays an important role in evaluating the performance of network planning, design, and management. Because more networks are being set up in the real world currently, there is a need for their reliability. It is necessary to build a reliable network within a limited budget. However, existing studies are focused on the budget limit for each minimal path (MP) in networks without considering the total budget of the entire network. We propose a novel concept to consider how to build a more reliable binary-state network under the budget limit. In addition, we propose an algorithm based on the binary-addition-tree algorithm (BAT) and stepwise vectors to solve the problem efficiently

    Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective

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    This paper introduces a comprehensive, multi-stage machine learning methodology that effectively integrates information systems and artificial intelligence to enhance decision-making processes within the domain of operations research. The proposed framework adeptly addresses common limitations of existing solutions, such as the neglect of data-driven estimation for vital production parameters, exclusive generation of point forecasts without considering model uncertainty, and lacking explanations regarding the sources of such uncertainty. Our approach employs Quantile Regression Forests for generating interval predictions, alongside both local and global variants of SHapley Additive Explanations for the examined predictive process monitoring problem. The practical applicability of the proposed methodology is substantiated through a real-world production planning case study, emphasizing the potential of prescriptive analytics in refining decision-making procedures. This paper accentuates the imperative of addressing these challenges to fully harness the extensive and rich data resources accessible for well-informed decision-making

    Offline and Online Models for Learning Pairwise Relations in Data

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    Pairwise relations between data points are essential for numerous machine learning algorithms. Many representation learning methods consider pairwise relations to identify the latent features and patterns in the data. This thesis, investigates learning of pairwise relations from two different perspectives: offline learning and online learning.The first part of the thesis focuses on offline learning by starting with an investigation of the performance modeling of a synchronization method in concurrent programming using a Markov chain whose state transition matrix models pairwise relations between involved cores in a computer process.Then the thesis focuses on a particular pairwise distance measure, the minimax distance, and explores memory-efficient approaches to computing this distance by proposing a hierarchical representation of the data with a linear memory requirement with respect to the number of data points, from which the exact pairwise minimax distances can be derived in a memory-efficient manner. Then, a memory-efficient sampling method is proposed that follows the aforementioned hierarchical representation of the data and samples the data points in a way that the minimax distances between all data points are maximally preserved. Finally, the thesis proposes a practical non-parametric clustering of vehicle motion trajectories to annotate traffic scenarios based on transitive relations between trajectories in an embedded space.The second part of the thesis takes an online learning perspective, and starts by presenting an online learning method for identifying bottlenecks in a road network by extracting the minimax path, where bottlenecks are considered as road segments with the highest cost, e.g., in the sense of travel time. Inspired by real-world road networks, the thesis assumes a stochastic traffic environment in which the road-specific probability distribution of travel time is unknown. Therefore, it needs to learn the parameters of the probability distribution through observations by modeling the bottleneck identification task as a combinatorial semi-bandit problem. The proposed approach takes into account the prior knowledge and follows a Bayesian approach to update the parameters. Moreover, it develops a combinatorial variant of Thompson Sampling and derives an upper bound for the corresponding Bayesian regret. Furthermore, the thesis proposes an approximate algorithm to address the respective computational intractability issue.Finally, the thesis considers contextual information of road network segments by extending the proposed model to a contextual combinatorial semi-bandit framework and investigates and develops various algorithms for this contextual combinatorial setting

    Reinforcement Learning-based User-centric Handover Decision-making in 5G Vehicular Networks

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    The advancement of 5G technologies and Vehicular Networks open a new paradigm for Intelligent Transportation Systems (ITS) in safety and infotainment services in urban and highway scenarios. Connected vehicles are vital for enabling massive data sharing and supporting such services. Consequently, a stable connection is compulsory to transmit data across the network successfully. The new 5G technology introduces more bandwidth, stability, and reliability, but it faces a low communication range, suffering from more frequent handovers and connection drops. The shift from the base station-centric view to the user-centric view helps to cope with the smaller communication range and ultra-density of 5G networks. In this thesis, we propose a series of strategies to improve connection stability through efficient handover decision-making. First, a modified probabilistic approach, M-FiVH, aimed at reducing 5G handovers and enhancing network stability. Later, an adaptive learning approach employed Connectivity-oriented SARSA Reinforcement Learning (CO-SRL) for user-centric Virtual Cell (VC) management to enable efficient handover (HO) decisions. Following that, a user-centric Factor-distinct SARSA Reinforcement Learning (FD-SRL) approach combines time series data-oriented LSTM and adaptive SRL for VC and HO management by considering both historical and real-time data. The random direction of vehicular movement, high mobility, network load, uncertain road traffic situation, and signal strength from cellular transmission towers vary from time to time and cannot always be predicted. Our proposed approaches maintain stable connections by reducing the number of HOs by selecting the appropriate size of VCs and HO management. A series of improvements demonstrated through realistic simulations showed that M-FiVH, CO-SRL, and FD-SRL were successful in reducing the number of HOs and the average cumulative HO time. We provide an analysis and comparison of several approaches and demonstrate our proposed approaches perform better in terms of network connectivity

    Structured Dynamic Pricing: Optimal Regret in a Global Shrinkage Model

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    We consider dynamic pricing strategies in a streamed longitudinal data set-up where the objective is to maximize, over time, the cumulative profit across a large number of customer segments. We consider a dynamic probit model with the consumers' preferences as well as price sensitivity varying over time. Building on the well-known finding that consumers sharing similar characteristics act in similar ways, we consider a global shrinkage structure, which assumes that the consumers' preferences across the different segments can be well approximated by a spatial autoregressive (SAR) model. In such a streamed longitudinal set-up, we measure the performance of a dynamic pricing policy via regret, which is the expected revenue loss compared to a clairvoyant that knows the sequence of model parameters in advance. We propose a pricing policy based on penalized stochastic gradient descent (PSGD) and explicitly characterize its regret as functions of time, the temporal variability in the model parameters as well as the strength of the auto-correlation network structure spanning the varied customer segments. Our regret analysis results not only demonstrate asymptotic optimality of the proposed policy but also show that for policy planning it is essential to incorporate available structural information as policies based on unshrunken models are highly sub-optimal in the aforementioned set-up.Comment: 34 pages, 5 figure

    Inferring networks from time series: a neural approach

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    Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of their emergent dynamics. In this work we present a powerful and fast computational method to infer large network adjacency matrices from time series data using a neural network. Using a neural network provides uncertainty quantification on the prediction in a manner that reflects both the non-convexity of the inference problem as well as the noise on the data. This is useful since network inference problems are typically underdetermined, and a feature that has hitherto been lacking from network inference methods. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from observations of its response to a power cut. Since the problem is underdetermined, many classical statistical tools (e.g. regression) will not be straightforwardly applicable. Our method, in contrast, provides probability densities on each edge, allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the power cut. We also demonstrate our method's ability to learn an entire cost matrix for a non-linear model from a dataset of economic activity in Greater London. Our method outperforms OLS regression on noisy data in terms of both speed and prediction accuracy, and scales as N2N^2 where OLS is cubic. Since our technique is not specifically engineered for network inference, it represents a general parameter estimation scheme that is applicable to any parameter dimension

    Diffusion Schr\"odinger Bridge Matching

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    Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g. Denoising Diffusion Models (DDMs) and Flow Matching Models (FMMs) implement such a transport through a Stochastic Differential Equation (SDE) or an Ordinary Differential Equation (ODE). However, while it is desirable in many applications to approximate the deterministic dynamic Optimal Transport (OT) map which admits attractive properties, DDMs and FMMs are not guaranteed to provide transports close to the OT map. In contrast, Schr\"odinger bridges (SBs) compute stochastic dynamic mappings which recover entropy-regularized versions of OT. Unfortunately, existing numerical methods approximating SBs either scale poorly with dimension or accumulate errors across iterations. In this work, we introduce Iterative Markovian Fitting, a new methodology for solving SB problems, and Diffusion Schr\"odinger Bridge Matching (DSBM), a novel numerical algorithm for computing IMF iterates. DSBM significantly improves over previous SB numerics and recovers as special/limiting cases various recent transport methods. We demonstrate the performance of DSBM on a variety of problems

    A Hierarchical Hybrid Learning Framework for Multi-agent Trajectory Prediction

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    Accurate and robust trajectory prediction of neighboring agents is critical for autonomous vehicles traversing in complex scenes. Most methods proposed in recent years are deep learning-based due to their strength in encoding complex interactions. However, unplausible predictions are often generated since they rely heavily on past observations and cannot effectively capture the transient and contingency interactions from sparse samples. In this paper, we propose a hierarchical hybrid framework of deep learning (DL) and reinforcement learning (RL) for multi-agent trajectory prediction, to cope with the challenge of predicting motions shaped by multi-scale interactions. In the DL stage, the traffic scene is divided into multiple intermediate-scale heterogenous graphs based on which Transformer-style GNNs are adopted to encode heterogenous interactions at intermediate and global levels. In the RL stage, we divide the traffic scene into local sub-scenes utilizing the key future points predicted in the DL stage. To emulate the motion planning procedure so as to produce trajectory predictions, a Transformer-based Proximal Policy Optimization (PPO) incorporated with a vehicle kinematics model is devised to plan motions under the dominant influence of microscopic interactions. A multi-objective reward is designed to balance between agent-centric accuracy and scene-wise compatibility. Experimental results show that our proposal matches the state-of-the-arts on the Argoverse forecasting benchmark. It's also revealed by the visualized results that the hierarchical learning framework captures the multi-scale interactions and improves the feasibility and compliance of the predicted trajectories
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