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For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.

Directed Acyclic Graphs (DAGs) provide a powerful framework to model causal relationships among variables in multivariate settings; in addition, through the do-calculus theory, they allow for the identification and estimation of causal effects between variables also from pure observational data. In this setting, the process of inferring the DAG structure from the data is referred to as causal structure learning or causal discovery. We introduce BCDAG, an R package for Bayesian causal discovery and causal effect estimation from Gaussian observational data, implementing the Markov chain Monte Carlo (MCMC) scheme proposed by Castelletti & Mascaro (2021). Our implementation scales efficiently with the number of observations and, whenever the DAGs are sufficiently sparse, with the number of variables in the dataset. The package also provides functions for convergence diagnostics and for visualizing and summarizing posterior inference. In this paper, we present the key features of the underlying methodology along with its implementation in BCDAG. We then illustrate the main functions and algorithms on both real and simulated datasets.

Reinforcement learning (RL) applications, where an agent can simply learn optimal behaviors by interacting with the environment, are quickly gaining tremendous success in a wide variety of applications from controlling simple pendulums to complex data centers. However, setting the right hyperparameters can have a huge impact on the deployed solution performance and reliability in the inference models, produced via RL, used for decision-making. Hyperparameter search itself is a laborious process that requires many iterations and computationally expensive to find the best settings that produce the best neural network architectures. In comparison to other neural network architectures, deep RL has not witnessed much hyperparameter tuning, due to its algorithm complexity and simulation platforms needed. In this paper, we propose a distributed variable-length genetic algorithm framework to systematically tune hyperparameters for various RL applications, improving training time and robustness of the architecture, via evolution. We demonstrate the scalability of our approach on many RL problems (from simple gyms to complex applications) and compared with Bayesian approach. Our results show that with more generations, optimal solutions that require fewer training episodes and are computationally cheap while being more robust for deployment. Our results are imperative to advance deep reinforcement learning controllers for real-world problems.

Deep models trained in supervised mode have achieved remarkable success on a variety of tasks. When labeled samples are limited, self-supervised learning (SSL) is emerging as a new paradigm for making use of large amounts of unlabeled samples. SSL has achieved promising performance on natural language and image learning tasks. Recently, there is a trend to extend such success to graph data using graph neural networks (GNNs). In this survey, we provide a unified review of different ways of training GNNs using SSL. Specifically, we categorize SSL methods into contrastive and predictive models. In either category, we provide a unified framework for methods as well as how these methods differ in each component under the framework. Our unified treatment of SSL methods for GNNs sheds light on the similarities and differences of various methods, setting the stage for developing new methods and algorithms. We also summarize different SSL settings and the corresponding datasets used in each setting. To facilitate methodological development and empirical comparison, we develop a standardized testbed for SSL in GNNs, including implementations of common baseline methods, datasets, and evaluation metrics.

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty. The past decade has seen major advances in many perception tasks such as visual object recognition and speech recognition using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. In recent years, Bayesian deep learning has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models. In this general framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in turn, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a comprehensive introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, control, etc. Besides, we also discuss the relationship and differences between Bayesian deep learning and other related topics such as Bayesian treatment of neural networks.

Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor fine-tuning when training the model. One of the two essential components of a PBDN is the development of a special infinite-wide single-hidden-layer neural network, whose number of active hidden units can be inferred from the data. The other one is the construction of a greedy layer-wise learning algorithm that uses a forward model selection criterion to determine when to stop adding another hidden layer. We develop both Gibbs sampling and stochastic gradient descent based maximum a posteriori inference for PBDNs, providing state-of-the-art classification accuracy and interpretable data subtypes near the decision boundaries, while maintaining low computational complexity for out-of-sample prediction.

We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.

Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.