Credal 贝叶斯深度学习

用于分类中不确定性估计的模型平均的信度包装方法

Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification

本文提出信度包装方法，将BNN和深度集成的模型平均表示为信度集，通过类别概率上下界和交集概率变换改进分类不确定性估计，并在多个OOD检测基准上验证其优于基线且校准误差更低。

Credal Model Averaging for classification: representing prior ignorance and expert opinions

Bayesian model averaging (BMA) is the state of the art approach for overcoming model uncertainty. Yet, especially on small data sets, the results yielded by BMA might be sensitive to the prior over the models. Credal Model Averaging (CMA) addresses this problem by substituting the single prior over the models by a set of priors (credal set). Such approach solves the problem of how to choose the prior over the models and automates sensitivity analysis. We discuss various CMA algorithms for building an ensemble of logistic regressors characterized by different sets of covariates. We show how CMA…

用于不确定性量化的Credal集成蒸馏

Credal Ensemble Distillation for Uncertainty Quantification

针对深度集成推理成本高的问题，提出Credal集成蒸馏（CED）框架，将深度集成压缩为单模型CREDIT，通过预测类概率区间定义Credal集实现不确定性量化，在分布外检测基准上表现优异且推理开销更低。

可信度与区间深度证据分类

Credal and Interval Deep Evidential Classifications

本文提出CDEC和IDEC方法，通过可信度集和证据区间解决分类任务中的不确定性量化问题，实现鲁棒的不确定性评估和预测。

MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation

MMD-Balls as Credal Sets: A PAC-Bayesian Framework for Epistemic Uncertainty in Test-Time Adaptation

本文提出了一种基于PAC-Bayesian框架的测试时间适应方法，通过将MMD球体解释为 credal sets，提供了对epistemic不确定性量化的自然方法，并建立了与MMD相关的泛化界限、有限样本版本、统一最坏情况风险界限以及几何保持界限。

Credal Classification based on AODE and compression coefficients

Bayesian model averaging (BMA) is an approach to average over alternative models; yet, it usually gets excessively concentrated around the single most probable model, therefore achieving only sub-optimal classification performance. The compression-based approach (Boulle, 2007) overcomes this problem, averaging over the different models by applying a logarithmic smoothing over the models' posterior probabilities. This approach has shown excellent performances when applied to ensembles of naive Bayes classifiers. AODE is another ensemble of models with high performance (Webb, 2005), based on a c…

可信图神经网络

Credal Graph Neural Networks

本文提出可信图神经网络（CGNNs），通过集值预测形式扩展可信学习到图领域，在分布外条件下实现更可靠的不确定性估计和异质图上的高性能表现。

Priors in Bayesian Deep Learning: A Review

While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more c…

深度学习中的贝叶斯计算

Bayesian Computation in Deep Learning

本章综述SG-MCMC与VI两类近似贝叶斯计算方法，介绍其在贝叶斯神经网络和深度生成模型中的后验推理挑战及解决方案。

Measuring Uncertainty through Bayesian Learning of Deep Neural Network Structure

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. Instead of building structure from scratch inefficiently, we draw inspirations from neural architecture search to represent the network structure. We then develop an efficient stochastic variational inference approach which unifie…

Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling

Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider a…

Deep Neural Architecture Search with Deep Graph Bayesian Optimization

Bayesian optimization (BO) is an effective method of finding the global optima of black-box functions. Recently BO has been applied to neural architecture search and shows better performance than pure evolutionary strategies. All these methods adopt Gaussian processes (GPs) as surrogate function, with the handcraft similarity metrics as input. In this work, we propose a Bayesian graph neural network as a new surrogate, which can automatically extract features from deep neural architectures, and use such learned features to fit and characterize black-box objectives and their uncertainty. Based …

Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users

Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often challenging to quantify. Bayesian statistics offer a formalism to understand and quantify the uncertainty associated with deep neural network predictions. This tutorial provides an overview of the relevant literature and a complete toolset to design, implement, train, use and evaluate Bayesian Neural Networks, i.e. Stochastic Artificial Neural Networks trained using B…

何时信念集稳定？关于信念集更新的不动点定理

When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updates

本文探讨了在不精确性下信念集更新过程的稳定性问题，通过分析不动点的存在条件和实现方法，揭示了不精确性对学习过程动态的影响。

Explicitly Bayesian Regularizations in Deep Learning

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian regularizations in a specific category of DNNs, i.e., Convolutional Neural Networks (CNNs). First, we introduce a novel probabilistic representation for the hidden layers of CNNs and demonstrate that CNNs correspond to Bayesian networks with the serial connection. Furthermore, we show that the hidden layers close to the input formulate prior distributions, thus CN…

Deep Bayesian Nonparametric Factor Analysis

We propose a deep generative factor analysis model with beta process prior that can approximate complex non-factorial distributions over the latent codes. We outline a stochastic EM algorithm for scalable inference in a specific instantiation of this model and present some preliminary results.

The Case for Bayesian Deep Learning

The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian…

Using Deep Neural Network Approximate Bayesian Network

We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint probability distri- bution of Bayesian Network by learning from a few observation and posterior probability distribution pairs with high accuracy. Compared with traditional approximate method likelihood weighting sampling algorithm, our method is much faster and gains higher accuracy in medium sized Bayesian Network. Another advantage of our method is that our meth…

污染贝叶斯随机特征中的鲁棒预测不确定性与双重下降

Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Features

提出一种鲁棒贝叶斯随机特征回归方法，通过Huber污染集处理先验和似然误设，推导出后验预测密度的上下界，并引入不精确最高密度区域进行鲁棒不确定性量化，证明预测不确定性保持计算可行性并继承经典双重下降相位结构。

Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks

We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. Our analysis inherently overcomes the fact that binary activation function is non-differentiable. The performance…

Adversarial Phenomenon in the Eyes of Bayesian Deep Learning

Deep Learning models are vulnerable to adversarial examples, i.e.\ images obtained via deliberate imperceptible perturbations, such that the model misclassifies them with high confidence. However, class confidence by itself is an incomplete picture of uncertainty. We therefore use principled Bayesian methods to capture model uncertainty in prediction for observing adversarial misclassification. We provide an extensive study with different Bayesian neural networks attacked in both white-box and black-box setups. The behaviour of the networks for noise, attacks and clean test data is compared. W…

Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learning

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support-they assign zero probability to almost all of the weight-space. Unlike these discrete support methods, Radial BNNs' full support makes them suitable for use as a prior for sequential inference. In addition, they solve the conceptual challenges with the a priori implausibility of weight distribut…

Practical Deep Learning with Bayesian Principles

Bayesian methods promise to fix many shortcomings of deep learning, but they are impractical and rarely match the performance of standard methods, let alone improve them. In this paper, we demonstrate practical training of deep networks with natural-gradient variational inference. By applying techniques such as batch normalisation, data augmentation, and distributed training, we achieve similar performance in about the same number of epochs as the Adam optimiser, even on large datasets such as ImageNet. Importantly, the benefits of Bayesian principles are preserved: predictive probabilities ar…

Bayesian Deep Learning and a Probabilistic Perspective of Generalization

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We…

Bayesian Deep Ensembles via the Neural Tangent Kernel

We explore the link between deep ensembles and Gaussian processes (GPs) through the lens of the Neural Tangent Kernel (NTK): a recent development in understanding the training dynamics of wide neural networks (NNs). Previous work has shown that even in the infinite width limit, when NNs become GPs, there is no GP posterior interpretation to a deep ensemble trained with squared error loss. We introduce a simple modification to standard deep ensembles training, through addition of a computationally-tractable, randomised and untrainable function to each ensemble member, that enables a posterior i…

A Bayesian Approach to Invariant Deep Neural Networks

We propose a novel Bayesian neural network architecture that can learn invariances from data alone by inferring a posterior distribution over different weight-sharing schemes. We show that our model outperforms other non-invariant architectures, when trained on datasets that contain specific invariances. The same holds true when no data augmentation is performed.

Uncertainty-Aware (UNA) Bases for Deep Bayesian Regression Using Multi-Headed Auxiliary Networks

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on methodically evaluating the predictive uncertainties of these models. In this work, we demonstrate that traditional training procedures for NLMs drastically underestimate uncertainty on out-of-distribution inputs, and that they therefore cannot be naively deployed in risk-sensitive applications. We identify the underlying reasons for this behavior and p…

Understanding Uncertainty in Bayesian Deep Learning

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on formally evaluating the predictive uncertainties of these models. Furthermore, existing works point out the difficulties of encoding domain knowledge in models like NLMs, making them unsuitable for applications where interpretability is required. In this work, we show that traditional training procedures for NLMs can drastically underestimate uncertainty …

深度自适应贝叶斯筛选

Deep Adaptive Bayesian Screening

研究在高维离散设计空间的自适应因子筛选问题，提出深度自适应贝叶斯筛选方法DABS，通过学习策略网络选择实验，集成吉布斯后验推断，相比经典和贝叶斯基线，在实验预算紧张时准确性和可扩展性更优。

贝叶斯非参数：深度学习的一种替代方案

Bayesian Nonparametrics: An Alternative to Deep Learning

本综述系统阐述了贝叶斯非参数模型的理论基础与应用价值，重点展示其在多目标跟踪等复杂问题中作为深度学习替代方案的灵活性和有效性。

On the generalization of bayesian deep nets for multi-class classification

Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz loss function. To avoid these assumptions, in this paper, we propose a new generalization bound for Bayesian deep nets by exploiting the contractivity of the Log-Sobolev inequalities. Using these inequalities adds an additional loss-gradient norm term to the generalization bound, which is intuitively a surrogate of the model complexity. Empirically, we analyze…

URSABench: Comprehensive Benchmarking of Approximate Bayesian Inference Methods for Deep Neural Networks

While deep learning methods continue to improve in predictive accuracy on a wide range of application domains, significant issues remain with other aspects of their performance including their ability to quantify uncertainty and their robustness. Recent advances in approximate Bayesian inference hold significant promise for addressing these concerns, but the computational scalability of these methods can be problematic when applied to large-scale models. In this paper, we describe initial work on the development ofURSABench(the Uncertainty, Robustness, Scalability, and Accu-racy Benchmark), an…

Enhanced Input Modeling for Construction Simulation using Bayesian Deep Neural Networks

This paper aims to propose a novel deep learning-integrated framework for deriving reliable simulation input models through incorporating multi-source information. The framework sources and extracts multisource data generated from construction operations, which provides rich information for input modeling. The framework implements Bayesian deep neural networks to facilitate the purpose of incorporating richer information in input modeling. A case study on road paving operation is performed to test the feasibility and applicability of the proposed framework. Overall, this research enhances inpu…

Deep Bayesian Gaussian Processes for Uncertainty Estimation in Electronic Health Records

One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the main two scalable uncertainty estimation methods. However, deep Bayesian neural network suffers from lack of expressiveness, and more expressive models such as deep kernel learning, which is an extension of sparse Gaussian process, captures only the uncertainty from the higher level latent space. Therefore, the deep learning model under it lacks interpretabili…

Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations

We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive …

NeuralSurv: 基于贝叶斯不确定性量化的深度生存分析

NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification

NeuralSurv通过贝叶斯不确定性量化提升深度生存分析的校准性能，结合新颖的数据增强方案和高效变分算法，在合成和真实数据中均表现出优越的模型性能。

Subspace Inference for Bayesian Deep Learning

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we construct low-dimensional subspaces of parameter space, such as the first principal components of the stochastic gradient descent (SGD) trajectory, which contain diverse sets of high performing models. In these subspaces, we are able to apply elliptical slice sampling and variati…

Variable Selection with Rigorous Uncertainty Quantification using Deep Bayesian Neural Networks: Posterior Concentration and Bernstein-von Mises Phenomenon

This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable importance effectively in high dimensions, and its learning rate can sometimes "break" the curse of dimensionality. (2) BNN's uncertainty quantification for variable importance is rigorous, in the sense that its 95% credible intervals for variable importance indeed covers the truth…

Performance Measurement for Deep Bayesian Neural Network

Deep Bayesian neural network has aroused a great attention in recent years since it combines the benefits of deep neural network and probability theory. Because of this, the network can make predictions and quantify the uncertainty of the predictions at the same time, which is important in many life-threatening areas. However, most of the recent researches are mainly focusing on making the Bayesian neural network easier to train, and proposing methods to estimate the uncertainty. I notice there are very few works that properly discuss the ways to measure the performance of the Bayesian neural …

关于结合拆分共形预测与贝叶斯深度学习的分布外覆盖性研究

On the Out-of-Distribution Coverage of Combining Split Conformal Prediction and Bayesian Deep Learning

本研究探讨贝叶斯深度学习与拆分共形预测结合对多类别图像分类分布外覆盖性的影响，指出模型校准集置信度高低会带来不同效果，实验发现该结合在部分场景下会产生降低分布外覆盖性的意外后果。

Bayesian Image Classification with Deep Convolutional Gaussian Processes

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty estimates and a marginal likelihood objective, but their weak inductive biases lead to inferior accuracy. This has limited their applicability in certain tasks (e.g. image classification). We propose a translation-insensitive convolutional kernel, which relaxes the translation invariance constraint imposed by previous convolutional GPs. We show how we can use t…

过参数化情形下深度 ReLU 神经网络的 Bayesian 自由能

Bayesian Free Energy of Deep ReLU Neural Network in Overparametrized Cases

本文研究过参数化深度 ReLU 神经网络，证明其 Bayesian 自由能有界，并由此说明充分过参数化不会增加 Bayesian 泛化误差。

Deep Bayesian Quadrature Policy Optimization

We study the problem of obtaining accurate policy gradient estimates using a finite number of samples. Monte-Carlo methods have been the default choice for policy gradient estimation, despite suffering from high variance in the gradient estimates. On the other hand, more sample efficient alternatives like Bayesian quadrature methods have received little attention due to their high computational complexity. In this work, we propose deep Bayesian quadrature policy gradient (DBQPG), a computationally efficient high-dimensional generalization of Bayesian quadrature, for policy gradient estimation.…

Liberty or Depth: Deep Bayesian Neural Nets Do Not Need Complex Weight Posterior Approximations

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distributions in function-space to those induced by shallower networks with complex weight posteriors. We validate our theoretical contributions empirically, both through examination of the weight posterior using Hamiltonian Monte Carlo in small models and by comparing diagonal- to structure…

Generalized Bayesian Posterior Expectation Distillation for Deep Neural Networks

In this paper, we present a general framework for distilling expectations with respect to the Bayesian posterior distribution of a deep neural network classifier, extending prior work on the Bayesian Dark Knowledge framework. The proposed framework takes as input "teacher" and student model architectures and a general posterior expectation of interest. The distillation method performs an online compression of the selected posterior expectation using iteratively generated Monte Carlo samples. We focus on the posterior predictive distribution and expected entropy as distillation targets. We inve…

Calibration of Deep Probabilistic Models with Decoupled Bayesian Neural Networks

Deep Neural Networks (DNNs) have achieved state-of-the-art accuracy performance in many tasks. However, recent works have pointed out that the outputs provided by these models are not well-calibrated, seriously limiting their use in critical decision scenarios. In this work, we propose to use a decoupled Bayesian stage, implemented with a Bayesian Neural Network (BNN), to map the uncalibrated probabilities provided by a DNN to calibrated ones, consistently improving calibration. Our results evidence that incorporating uncertainty provides more reliable probabilistic models, a critical conditio…

ODE$^2$VAE: Deep generative second order ODEs with Bayesian neural networks

We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques.…

Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs -- extracting…

Bayesian Beta-Bernoulli Process Sparse Coding with Deep Neural Networks

Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been unexplored in the context of deep models. We propose a non-parametric iterative algorithm for learning discrete latent representations in such deep models. Additionally, to learn scale invariant discrete features, we propose local data scaling variables. Lastly, to encourage sparsity in our representations, we propose a Beta-Bernoulli process prior on the latent fa…

Global inducing point variational posteriors for Bayesian neural networks and deep Gaussian processes

We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated approximate posterior over the weights at all layers in a Bayesian neural network. We extend this approach to deep Gaussian processes, unifying inference in the two model classes. Our approximate posterior uses learned "global" inducing points, which are defined only at the input layer and propagated through the network to obtain inducing inputs at subsequent l…

BayesDLL：贝叶斯深度学习库

BayesDLL: Bayesian Deep Learning Library

BayesDLL 是一个面向 PyTorch 的大规模贝叶斯神经网络库，支持 ViTs 等大型模型，无需修改骨干网络代码，并支持预训练权重作为先验均值，便于对基础模型进行贝叶斯推断。

BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning

We develop BatchBALD, a tractable approximation to the mutual information between a batch of points and model parameters, which we use as an acquisition function to select multiple informative points jointly for the task of deep Bayesian active learning. BatchBALD is a greedy linear-time $1 - \frac{1}{e}$-approximate algorithm amenable to dynamic programming and efficient caching. We compare BatchBALD to the commonly used approach for batch data acquisition and find that the current approach acquires similar and redundant points, sometimes performing worse than randomly acquiring data. We fini…

Stabilising priors for robust Bayesian deep learning

Bayesian neural networks (BNNs) have developed into useful tools for probabilistic modelling due to recent advances in variational inference enabling large scale BNNs. However, BNNs remain brittle and hard to train, especially: (1) when using deep architectures consisting of many hidden layers and (2) in situations with large weight variances. We use signal propagation theory to quantify these challenges and propose self-stabilising priors. This is achieved by a reformulation of the ELBO to allow the prior to influence network signal propagation. Then, we develop a stabilising prior, where the…

深度函数因子模型：通过贝叶斯非参数因子化进行高维函数时间序列的预测

Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization

本文提出DF2M模型，通过贝叶斯非参数因子化方法提升高维函数时间序列预测的可解释性和准确性。