Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of a collocation grid and customized loss functions are proposed to fine tune the ODE trajectories and Laplace approximation. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions, the Susceptible-Infectious-Removed (SIR) model for infectious diseases, based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.

Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we apply a generalization of the Metropolis Hastings algorithm that allows us to restrict the evaluation of the likelihood to small mini-batches in a Bayesian inference context. Since it requires the computation of a so-called "noise penalty" determined by the variance of the training loss function over the mini-batches, we refer to this data subsampling strategy as Penalty Bayesian Neural Networks - PBNNs. Its implementation on top of MCMC is straightforward, as the variance of the loss function merely reduces the acceptance probability. Comparing to other samplers, we empirically show that PBNN achieves good predictive performance for a given mini-batch size. Varying the size of the mini-batches enables a natural calibration of the predictive distribution and provides an inbuilt protection against overfitting. We expect PBNN to be particularly suited for cases when data sets are distributed across multiple decentralized devices as typical in federated learning.

Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen domains after fine-tuning on multiple training domains. However, maximally exploiting a zoo of PTMs is challenging since fine-tuning all possible combinations of PTMs is computationally prohibitive while accurate selection of PTMs requires tackling the possible data distribution shift for OoD tasks. In this work, we propose ZooD, a paradigm for PTMs ranking and ensemble with feature selection. Our proposed metric ranks PTMs by quantifying inter-class discriminability and inter-domain stability of the features extracted by the PTMs in a leave-one-domain-out cross-validation manner. The top-K ranked models are then aggregated for the target OoD task. To avoid accumulating noise induced by model ensemble, we propose an efficient variational EM algorithm to select informative features. We evaluate our paradigm on a diverse model zoo consisting of 35 models for various OoD tasks and demonstrate: (i) model ranking is better correlated with fine-tuning ranking than previous methods and up to 9859x faster than brute-force fine-tuning; (ii) OoD generalization after model ensemble with feature selection outperforms the state-of-the-art methods and the accuracy on most challenging task DomainNet is improved from 46.5\% to 50.6\%. Furthermore, we provide the fine-tuning results of 35 PTMs on 7 OoD datasets, hoping to help the research of model zoo and OoD generalization. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/zood.

In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure learning algorithms cannot orientate all edges from purely observational data. Moreover, latent confounders can lead to false positive edges. Relatively few methods have been proposed to address these issues. In this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data that involves an observational data set and one or more interventional data sets. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG). Structure learning relies on a hybrid approach and a novel Bayesian scoring paradigm that calculates the posterior probability of each directed edge being added to the learnt graph. Experimental results based on well-known networks of up to 109 variables and 10k sample size show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.

Decision tree models such as CART (Breiman et al., 1984) and their ensembles such as Random Forests (Breiman, 2001) and Gradient Boosted Trees (Chen & Guestrin, 2016; Friedman, 2001) have proved to be enormously successful supervised learning algorithms, because they are able to combine non-parametric model fitting with implicit dimension reduction. It is often difficult to quantify the uncertainty of their predictions and due to their greedy local splitting criteria, there is no guarantee for the optimality of the constructed decision trees. An alternative approach is to construct the decision trees in a Bayesian manner (H. A. Chipman et al., 1998; Denison et al., 1998; Wu et al., 2007) To address these issues, H. A. Chipman et al., 1998 proposed a Bayesian adaptation of CART, Bayesian CART, and later, a sum of Bayesian CART trees, which they called Bayesian Additive Regression Trees (BART) (H. A. Chipman et al., 2010). One perspective views these algorithms as non-greedy stochastic versions of their deterministic equivalents, where the randomness inside the fitting process allows the algorithm to explore the space of possible decision trees in ways the CART algorithm cannot. An alternative perspective views these algorithms as Bayesian non-parametric regression models, in which we put a prior on the space of decision trees, assume a likelihood for the observed data, and then obtain a posterior distribution over the possible decision trees based on the training data. The posterior distribution can be used to provide posterior predictive credible intervals and other forms of uncertainty quantification.

Neural Networks (NNs) have been widely {used in supervised learning} due to their ability to model complex nonlinear patterns, often presented in high-dimensional data such as images and text. However, traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs (BNNS) could help measure the uncertainty by considering the distributions of the NN model parameters. Besides, domain knowledge is commonly available and could improve the performance of BNNs if it can be appropriately incorporated. In this work, we propose a novel Posterior-Regularized Bayesian Neural Network (PR-BNN) model by incorporating different types of knowledge constraints, such as the soft and hard constraints, as a posterior regularization term. Furthermore, we propose to combine the augmented Lagrangian method and the existing BNN solvers for efficient inference. The experiments in simulation and two case studies about aviation landing prediction and solar energy output prediction have shown the knowledge constraints and the performance improvement of the proposed model over traditional BNNs without the constraints.

We propose a general framework to design posterior sampling methods for model-based RL. We show that the proposed algorithms can be analyzed by reducing regret to Hellinger distance in conditional probability estimation. We further show that optimistic posterior sampling can control this Hellinger distance, when we measure model error via data likelihood. This technique allows us to design and analyze unified posterior sampling algorithms with state-of-the-art sample complexity guarantees for many model-based RL settings. We illustrate our general result in many special cases, demonstrating the versatility of our framework.

The cooperative Multi-A gent R einforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL problem is lacking due to the curse of many agents and the limited exploration of the relational reasoning in existing works. In this paper, we verify that the transformer implements complex relational reasoning, and we propose and analyze model-free and model-based offline MARL algorithms with the transformer approximators. We prove that the suboptimality gaps of the model-free and model-based algorithms are independent of and logarithmic in the number of agents respectively, which mitigates the curse of many agents. These results are consequences of a novel generalization error bound of the transformer and a novel analysis of the Maximum Likelihood Estimate (MLE) of the system dynamics with the transformer. Our model-based algorithm is the first provably efficient MARL algorithm that explicitly exploits the permutation invariance of the agents. Our improved generalization bound may be of independent interest and is applicable to other regression problems related to the transformer beyond MARL.

Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to the posterior approximation's error. Meanwhile, alternatives to MC integration tend to be more expensive or biased. In this work, we experimentally show that the key to good MC-approximated predictive distributions is the quality of the approximate posterior itself. However, previous methods for obtaining accurate posterior approximations are expensive and non-trivial to implement. We, therefore, propose to refine Gaussian approximate posteriors with normalizing flows. When applied to last-layer BNNs, it yields a simple \emph{post hoc} method for improving pre-existing parametric approximations. We show that the resulting posterior approximation is competitive with even the gold-standard full-batch Hamiltonian Monte Carlo.

Speakers repeat constructions frequently in dialogue. Due to their peculiar information-theoretic properties, repetitions can be thought of as a strategy for cost-effective communication. In this study, we focus on the repetition of lexicalised constructions -- i.e., recurring multi-word units -- in English open-domain spoken dialogues. We hypothesise that speakers use construction repetition to mitigate information rate, leading to an overall decrease in utterance information content over the course of a dialogue. We conduct a quantitative analysis, measuring the information content of constructions and that of their containing utterances, estimating information content with an adaptive neural language model. We observe that construction usage lowers the information content of utterances. This facilitating effect (i) increases throughout dialogues, (ii) is boosted by repetition, (iii) grows as a function of repetition frequency and density, and (iv) is stronger for repetitions of referential constructions.