Interacting particle or agent systems that display a rich variety of swarming behaviours are ubiquitous in science and engineering. A fundamental and challenging goal is to understand the link between individual interaction rules and swarming. In this paper, we study the data-driven discovery of a second-order particle swarming model that describes the evolution of $N$ particles in $\mathbb{R}^d$ under radial interactions. We propose a learning approach that models the latent radial interaction function as Gaussian processes, which can simultaneously fulfill two inference goals: one is the nonparametric inference of {the} interaction function with pointwise uncertainty quantification, and the other one is the inference of unknown scalar parameters in the non-collective friction forces of the system. We formulate the learning problem as a statistical inverse problem and provide a detailed analysis of recoverability conditions, establishing that a coercivity condition is sufficient for recoverability. Given data collected from $M$ i.i.d trajectories with independent Gaussian observational noise, we provide a finite-sample analysis, showing that our posterior mean estimator converges in a Reproducing kernel Hilbert space norm, at an optimal rate in $M$ equal to the one in the classical 1-dimensional Kernel Ridge regression. As a byproduct, we show we can obtain a parametric learning rate in $M$ for the posterior marginal variance using $L^{\infty}$ norm, and the rate could also involve $N$ and $L$ (the number of observation time instances for each trajectory), depending on the condition number of the inverse problem. Numerical results on systems that exhibit different swarming behaviors demonstrate efficient learning of our approach from scarce noisy trajectory data.
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IFIP TC13 Conference on Human-Computer Interaction是人機交互領域的研究者和實踐者展示其工作的重要平臺。多年來，這些會議吸引了來自幾個國家和文化的研究人員。官網鏈接： ·
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In recent years, stochastic parametrizations have been ubiquitous in modelling uncertainty in fluid dynamics models. One source of model uncertainty comes from the coarse graining of the fine-scale data and is in common usage in computational simulations at coarser scales. In this paper, we look at two such stochastic parametrizations: the Stochastic Advection by Lie Transport (SALT) parametrization introduced by Holm and the Location Uncertainty (LU) parametrization introduced by M\'emin. Whilst both parametrizations are available for full-scale models, we study their reduced order versions obtained by projecting them on a complex vector Fourier mode triad of eigenfunctions of the curl. Remarkably, these two parametrizations lead to the same reduced order model, which we term the helicity-preserving stochastic triad (HST). This reduced order model is then compared with an alternative model which preserves the energy of the system, and which is termed the energy preserving stochastic triad (EST). These low-dimensional models are ideal benchmark models for testing new Data Assimilation algorithms: they are easy to implement, exhibit diverse behaviours depending on the choice of the coefficients and come with natural physical properties such as the conservation of energy and helicity.
Many decision-making problems feature multiple objectives. In such problems, it is not always possible to know the preferences of a decision-maker for different objectives. However, it is often possible to observe the behavior of decision-makers. In multi-objective decision-making, preference inference is the process of inferring the preferences of a decision-maker for different objectives. This research proposes a Dynamic Weight-based Preference Inference (DWPI) algorithm that can infer the preferences of agents acting in multi-objective decision-making problems, based on observed behavior trajectories in the environment. The proposed method is evaluated on three multi-objective Markov decision processes: Deep Sea Treasure, Traffic, and Item Gathering. The performance of the proposed DWPI approach is compared to two existing preference inference methods from the literature, and empirical results demonstrate significant improvements compared to the baseline algorithms, in terms of both time requirements and accuracy of the inferred preferences. The Dynamic Weight-based Preference Inference algorithm also maintains its performance when inferring preferences for sub-optimal behavior demonstrations. In addition to its impressive performance, the Dynamic Weight-based Preference Inference algorithm does not require any interactions during training with the agent whose preferences are inferred, all that is required is a trajectory of observed behavior.
Estimating state of health is a critical function of a battery management system but remains challenging due to the variability of operating conditions and usage requirements of real applications. As a result, techniques based on fitting equivalent circuit models may exhibit inaccuracy at extremes of performance and over long-term ageing, or instability of parameter estimates. Pure data-driven techniques, on the other hand, suffer from lack of generality beyond their training dataset. In this paper, we propose a hybrid approach combining data- and model-driven techniques for battery health estimation. Specifically, we demonstrate a Bayesian data-driven method, Gaussian process regression, to estimate model parameters as functions of states, operating conditions, and lifetime. Computational efficiency is ensured through a recursive approach yielding a unified joint state-parameter estimator that learns parameter dynamics from data and is robust to gaps and varying operating conditions. Results show the efficacy of the method, on both simulated and measured data, including accurate estimates and forecasts of battery capacity and internal resistance. This opens up new opportunities to understand battery ageing in real applications.
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees and this representation is compared with that offered by persistence diagrams. We show that these two structures, although not equivalent, are both invariant under homeomorphic re-parametrizations of the functions they represent, thus allowing for a statistical analysis which is indifferent to functional misalignment. We employ a novel metric for merge trees and we prove some theoretical results related to its specific implementation when merge trees represent functions. To showcase the good properties of our topological approach to functional data analysis, we test it on the Aneurisk65 dataset replicating, from our different perspective, the supervised classification analysis which contributed to make this dataset a benchmark for methods dealing with misaligned functional data.
High stakes classification refers to classification problems where erroneously predicting the wrong class is very bad, but assigning "unknown" is acceptable. We make the argument that these problems require us to give multiple unknown classes, to get the most information out of our analysis. With imperfect data we refer to covariates with a large number of missing values, large noise variance, and some errors in the data. The combination of high stakes classification and imperfect data is very common in practice, but it is very difficult to work on using current methods. We present a one-class classifier (OCC) to solve this problem, and we call it NBP. The classifier is based on Naive Bayes, simple to implement, and interpretable. We show that NBP gives both good predictive performance, and works for high stakes classification based on imperfect data. The model we present is quite simple; it is just an OCC based on density estimation. However, we have always felt a big gap between the applied classification problems we have worked on and the theory and models we use for classification, and this model closes that gap. Our main contribution is the motivation for why this model is a good approach, and we hope that this paper will inspire further development down this path.
Multi-task learning (MTL) is a methodology that aims to improve the general performance of estimation and prediction by sharing common information among related tasks. In the MTL, there are several assumptions for the relationships and methods to incorporate them. One of the natural assumptions in the practical situation is that tasks are classified into some clusters with their characteristics. For this assumption, the group fused regularization approach performs clustering of the tasks by shrinking the difference among tasks. This enables us to transfer common information within the same cluster. However, this approach also transfers the information between different clusters, which worsens the estimation and prediction. To overcome this problem, we propose an MTL method with a centroid parameter representing a cluster center of the task. Because this model separates parameters into the parameters for regression and the parameters for clustering, we can improve estimation and prediction accuracy for regression coefficient vectors. We show the effectiveness of the proposed method through Monte Carlo simulations and applications to real data.
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.
Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. We abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate optimal control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated log-predictive likelihood of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.
This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.
We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss function, we specify the generalized posterior distribution. The problem of frequentist posterior consistency is concerned with whether as more and more samples are observed, the posterior distribution on parameters will asymptotically concentrate on the "right" parameters. We show that posterior consistency can be derived using a combination of classical large deviation techniques, such as Varadhan's lemma, conditional/quenched large deviations, annealed large deviations, and exponential approximations. We show that the posterior distribution will asymptotically concentrate on parameters that minimize the expected loss and a divergence term, and we identify the divergence term as the Donsker-Varadhan relative entropy rate from process-level large deviations. As an application, we prove new quenched and annealed large deviation asymptotics and new Bayesian posterior consistency results for a class of mixing stochastic processes. In the case of Markov processes, one can obtain explicit conditions for posterior consistency, whenever estimates for log-Sobolev constants are available, which makes our framework essentially a black box. We also recover state-of-the-art posterior consistency on classical dynamical systems with a simple proof. Our approach has the potential of proving posterior consistency for a wide range of Bayesian procedures in a unified way.
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