Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better uncertainty quantification. For the success of BNN, search an appropriate architecture of the neural networks is an important task, and various algorithms to find good sparse neural networks have been proposed. In this paper, we propose a new node-sparse BNN model which has good theoretical properties and is computationally feasible. We prove that the posterior concentration rate to the true model is near minimax optimal and adaptive to the smoothness of the true model. In particular the adaptiveness is the first of its kind for node-sparse BNNs. In addition, we develop a novel MCMC algorithm which makes the Bayesian inference of the node-sparse BNN model feasible in practice.

Many scientific models are composed of multiple discrete components, and scien tists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model components, but defining prior distributions over model components and developing associated inference schemes has been challenging. We approach this problem in an amortized simulation-based inference framework: We define implicit model priors over a fixed set of candidate components and train neural networks to infer joint probability distributions over both, model components and associated parameters from simulations. To represent distributions over model components, we introduce a conditional mixture of multivariate binary distributions in the Grassmann formalism. Our approach can be applied to any compositional stochastic simulator without requiring access to likelihood evaluations. We first illustrate our method on a simple time series model with redundant components and show that it can retrieve joint posterior distribution over a set of symbolic expressions and their parameters while accurately capturing redundancy with strongly correlated posteriors. We then apply our approach to drift-diffusion models, a commonly used model class in cognitive neuroscience. After validating the method on synthetic data, we show that our approach explains experimental data as well as previous methods, but that our fully probabilistic approach can help to discover multiple data-consistent model configurations, as well as reveal non-identifiable model components and parameters. Our method provides a powerful tool for data-driven scientific inquiry which will allow scientists to systematically identify essential model components and make uncertainty-informed modelling decisions.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum likelihood estimation as an optimization problem: namely, as the minimization of a free energy functional. One way to solve this problem is to consider the discretization of a gradient flow associated with the free energy. We study one such approach, which resembles an extension of the popular Stein variational gradient descent algorithm. In particular, we establish a descent lemma for this algorithm, which guarantees that the free energy decreases at each iteration. This method, and any other obtained as the discretization of the gradient flow, will necessarily depend on a learning rate which must be carefully tuned by the practitioner in order to ensure convergence at a suitable rate. With this in mind, we also propose another algorithm for optimizing the free energy which is entirely learning rate free, based on coin betting techniques from convex optimization. We validate the performance of our algorithms across a broad range of numerical experiments, including several high-dimensional settings. Our results are competitive with existing particle-based methods, without the need for any hyperparameter tuning.

Autonomous exploration has many important applications. However, classic information gain-based or frontier-based exploration only relies on the robot current state to determine the immediate exploration goal, which lacks the capability of predicting the value of future states and thus leads to inefficient exploration decisions. This paper presents a method to learn how "good" states are, measured by the state value function, to provide a guidance for robot exploration in real-world challenging environments. We formulate our work as an off-policy evaluation (OPE) problem for robot exploration (OPERE). It consists of offline Monte-Carlo training on real-world data and performs Temporal Difference (TD) online adaptation to optimize the trained value estimator. We also design an intrinsic reward function based on sensor information coverage to enable the robot to gain more information with sparse extrinsic rewards. Results show that our method enables the robot to predict the value of future states so as to better guide robot exploration. The proposed algorithm achieves better prediction and exploration performance compared with the state-of-the-arts. To the best of our knowledge, this work for the first time demonstrates value function prediction on real-world dataset for robot exploration in challenging subterranean and urban environments. More details and demo videos can be found at https://jeffreyyh.github.io/opere/.

The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose a transformation, called the Wasserstein Gaussianization transformation, that uses a Wasserstein gradient flow to approximately transform the distribution of the summary statistics into a Gaussian distribution. BSL also implicitly requires compatibility between simulated summary statistics under the working model and the observed summary statistics. A robust BSL variant which achieves this has been developed in the recent literature. We combine the Wasserstein Gaussianization transformation with robust BSL, and an efficient Variational Bayes procedure for posterior approximation, to develop a highly efficient and reliable approximate Bayesian inference method for likelihood-free problems.

In a multi-agent environment, In order to overcome and alleviate the non-stationarity of the multi-agent environment, the mainstream method is to adopt the framework of Centralized Training Decentralized Execution (CTDE). This thesis is based on the framework of CTDE, and studies the cooperative decision-making of multi-agent based on the Multi-Agent Proximal Policy Optimization (MAPPO) algorithm for multi-agent proximal policy optimization. In order to alleviate the non-stationarity of the multi-agent environment, a multi-agent communication mechanism based on weight scheduling and attention module is introduced. Different agents can alleviate the non-stationarity caused by local observations through information exchange between agents, assisting in the collaborative decision-making of agents. The specific method is to introduce a communication module in the policy network part. The communication module is composed of a weight generator, a weight scheduler, a message encoder, a message pool and an attention module. Among them, the weight generator and weight scheduler will generate weights as the selection basis for communication, the message encoder is used to compress and encode communication information, the message pool is used to store communication messages, and the attention module realizes the interactive processing of the agent's own information and communication information. This thesis proposes a Multi-Agent Communication and Global Information Optimization Proximal Policy Optimization(MCGOPPO)algorithm, and conducted experiments in the SMAC and the MPE. The experimental results show that the improvement has achieved certain effects, which can better alleviate the non-stationarity of the multi-agent environment, and improve the collaborative decision-making ability among the agents.

The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass functional deep neural network (mfDNN) classifier as an innovative data mining and classification tool. Specifically, we consider sparse deep neural network architecture with rectifier linear unit (ReLU) activation function and minimize the cross-entropy loss in the multiclass classification setup. This neural network architecture allows us to employ modern computational tools in the implementation. The convergence rates of the misclassification risk functions are also derived for both fully observed and discretely observed multidimensional functional data. We demonstrate the performance of mfDNN on simulated data and several benchmark datasets from different application domains.

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author's semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shan-non's MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon's MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks' latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development.

In this paper, we present Deep Functional Factor Model (DF2M), a Bayesian nonparametric model for analyzing high-dimensional functional time series. The DF2M makes use of the Indian Buffet Process and the multi-task Gaussian Process with a deep kernel function to capture non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, the DF2M provides an explainable way to use neural networks by constructing a factor model and incorporating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm for inferring the DF2M. Empirical results from four real-world datasets demonstrate that the DF2M offers better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.