Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from sequential simulation using neural network-based conditional density estimators by minimizing a specific loss function. The SNPE method proposed by Lueckmann et al. (2017) used a calibration kernel to boost the sample weights around the observed data, resulting in a concentrated loss function. However, the use of calibration kernels may increase the variances of both the empirical loss and its gradient, making the training inefficient. To improve the stability of SNPE, this paper proposes to use an adaptive calibration kernel and several variance reduction techniques. The proposed method greatly speeds up the process of training, and provides a better approximation of the posterior than the original SNPE method and some existing competitors as confirmed by numerical experiments.
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The rise of AI in human contexts places new demands on automated systems to be transparent and explainable. We examine some anthropomorphic ideas and principles relevant to such accountablity in order to develop a theoretical framework for thinking about digital systems in complex human contexts and the problem of explaining their behaviour. Structurally, systems are made of modular and hierachical components, which we abstract in a new system model using notions of modes and mode transitions. A mode is an independent component of the system with its own objectives, monitoring data, and algorithms. The behaviour of a mode, including its transitions to other modes, is determined by functions that interpret each mode's monitoring data in the light of its objectives and algorithms. We show how these belief functions can help explain system behaviour by visualising their evaluation as trajectories in higher-dimensional geometric spaces. These ideas are formalised mathematically by abstract and concrete simplicial complexes. We offer three techniques: a framework for design heuristics, a general system theory based on modes, and a geometric visualisation, and apply them in three types of human-centred systems.
In real-world material research, machine learning (ML) models are usually expected to predict and discover novel exceptional materials that deviate from the known materials. It is thus a pressing question to provide an objective evaluation of ML model performances in property prediction of out-of-distribution (OOD) materials that are different from the training set distribution. Traditional performance evaluation of materials property prediction models through random splitting of the dataset frequently results in artificially high performance assessments due to the inherent redundancy of typical material datasets. Here we present a comprehensive benchmark study of structure-based graph neural networks (GNNs) for extrapolative OOD materials property prediction. We formulate five different categories of OOD ML problems for three benchmark datasets from the MatBench study. Our extensive experiments show that current state-of-the-art GNN algorithms significantly underperform for the OOD property prediction tasks on average compared to their baselines in the MatBench study, demonstrating a crucial generalization gap in realistic material prediction tasks. We further examine the latent physical spaces of these GNN models and identify the sources of CGCNN, ALIGNN, and DeeperGATGNN's significantly more robust OOD performance than those of the current best models in the MatBench study (coGN and coNGN), and provide insights to improve their performance.
With insurers benefiting from ever-larger amounts of data of increasing complexity, we explore a data-driven method to model dependence within multilevel claims in this paper. More specifically, we start from a non-parametric estimator for Archimedean copula generators introduced by Genest and Rivest (1993), and we extend it to diverse flexible censoring scenarios using techniques derived from survival analysis. We implement a graphical selection procedure for copulas that we validate using goodness-of-fit methods applied to complete, single-censored, and double-censored bivariate data. We illustrate the performance of our model with multiple simulation studies. We then apply our methodology to a recent Canadian automobile insurance dataset where we seek to model the dependence between the activation delays of correlated coverages. We show that our model performs quite well in selecting the best-fitted copula for the data at hand, especially when the dataset is large, and that the results can then be used as part of a larger claims reserving methodology.
The numerical solution of continuum damage mechanics (CDM) problems suffers from convergence-related challenges during the material softening stage, and consequently existing iterative solvers are subject to a trade-off between computational expense and solution accuracy. In this work, we present a novel unified arc-length (UAL) method, and we derive the formulation of the analytical tangent matrix and governing system of equations for both local and non-local gradient damage problems. Unlike existing versions of arc-length solvers that monolithically scale the external force vector, the proposed method treats the latter as an independent variable and determines the position of the system on the equilibrium path based on all the nodal variations of the external force vector. This approach renders the proposed solver substantially more efficient and robust than existing solvers used in CDM problems. We demonstrate the considerable advantages of the proposed algorithm through several benchmark 1D problems with sharp snap-backs and 2D examples under various boundary conditions and loading scenarios. The proposed UAL approach exhibits a superior ability of overcoming critical increments along the equilibrium path. Moreover, in the presented examples, the proposed UAL method is 1-2 orders of magnitude faster than force-controlled arc-length and monolithic Newton-Raphson solvers.
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it is compatible with functional (but non-continuous) dependence. We then proceed to study a stronger notion of knowability based on uniformly continuous dependence. On the technical logical side, we determine the complete logics of languages that combine general functional dependence, continuous dependence, and uniformly continuous dependence.
Navigating dynamic environments requires the robot to generate collision-free trajectories and actively avoid moving obstacles. Most previous works designed path planning algorithms based on one single map representation, such as the geometric, occupancy, or ESDF map. Although they have shown success in static environments, due to the limitation of map representation, those methods cannot reliably handle static and dynamic obstacles simultaneously. To address the problem, this paper proposes a gradient-based B-spline trajectory optimization algorithm utilizing the robot's onboard vision. The depth vision enables the robot to track and represent dynamic objects geometrically based on the voxel map. The proposed optimization first adopts the circle-based guide-point algorithm to approximate the costs and gradients for avoiding static obstacles. Then, with the vision-detected moving objects, our receding-horizon distance field is simultaneously used to prevent dynamic collisions. Finally, the iterative re-guide strategy is applied to generate the collision-free trajectory. The simulation and physical experiments prove that our method can run in real-time to navigate dynamic environments safely. Our software is available on GitHub as an open-source package.
Fixed point lattice actions are designed to have continuum classical properties unaffected by discretization effects and reduced lattice artifacts at the quantum level. They provide a possible way to extract continuum physics with coarser lattices, thereby allowing to circumvent problems with critical slowing down and topological freezing toward the continuum limit. A crucial ingredient for practical applications is to find an accurate and compact parametrization of a fixed point action, since many of its properties are only implicitly defined. Here we use machine learning methods to revisit the question of how to parametrize fixed point actions. In particular, we obtain a fixed point action for four-dimensional SU(3) gauge theory using convolutional neural networks with exact gauge invariance. The large operator space allows us to find superior parametrizations compared to previous studies, a necessary first step for future Monte Carlo simulations.
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges for most conventional artificial neural network, as they are essentially implemented in a deterministic manner. In this paper, we develop an efficient probabilistic computation framework by truncating the probabilistic representation of neural activation up to its mean and covariance and construct a moment neural network that encapsulates the nonlinear coupling between the mean and covariance of the underlying stochastic network. We reveal that when only the mean but not the covariance is supervised during gradient-based learning, the unsupervised covariance spontaneously emerges from its nonlinear coupling with the mean and faithfully captures the uncertainty associated with model predictions. Our findings highlight the inherent simplicity of probabilistic computation by seamlessly incorporating uncertainty into model prediction, paving the way for integrating it into large-scale AI systems.
The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an $\epsilon$-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.
The frontier of quantum computing (QC) simulation on classical hardware is quickly reaching the hard scalability limits for computational feasibility. Nonetheless, there is still a need to simulate large quantum systems classically, as the Noisy Intermediate Scale Quantum (NISQ) devices are yet to be considered fault tolerant and performant enough in terms of operations per second. Each of the two main exact simulation techniques, state vector and tensor network simulators, boasts specific limitations. The exponential memory requirement of state vector simulation, when compared to the qubit register sizes of currently available quantum computers, quickly saturates the capacity of the top HPC machines currently available. Tensor network contraction approaches, which encode quantum circuits into tensor networks and then contract them over an output bit string to obtain its probability amplitude, still fall short of the inherent complexity of finding an optimal contraction path, which maps to a max-cut problem on a dense mesh, a notably NP-hard problem. This article aims at investigating the limits of current state-of-the-art simulation techniques on a test bench made of eight widely used quantum subroutines, each in 31 different configurations, with special emphasis on performance. We then correlate the performance measures of the simulators with the metrics that characterise the benchmark circuits, identifying the main reasons behind the observed performance trend. From our observations, given the structure of a quantum circuit and the number of qubits, we highlight how to select the best simulation strategy, obtaining a speedup of up to an order of magnitude.
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