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In this paper we obtain quantitative Bernstein-von Mises type bounds on the normal approximation of the posterior distribution in exponential family models when centering either around the posterior mode or around the maximum likelihood estimator. Our bounds, obtained through a version of Stein's method, are non-asymptotic, and data dependent; they are of the correct order both in the total variation and Wasserstein distances, as well as for approximations for expectations of smooth functions of the posterior. All our results are valid for univariate and multivariate posteriors alike, and do not require a conjugate prior setting. We illustrate our findings on a variety of exponential family distributions, including Poisson, multinomial and normal distribution with unknown mean and variance. The resulting bounds have an explicit dependence on the prior distribution and on sufficient statistics of the data from the sample, and thus provide insight into how these factors may affect the quality of the normal approximation. The performance of the bounds is also assessed with simulations.

In recent years, deep learning has been a topic of interest in almost all disciplines due to its impressive empirical success in analyzing complex data sets, such as imaging, genetics, climate, and medical data. While most of the developments are treated as black-box machines, there is an increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning is proven to be promising in this regard. However, the recent developments do not address the situations of ultra-high dimensional and highly correlated feature selection in addition to the high noise level. In this article, we propose a novel screening and cleaning strategy with the aid of deep learning for the cluster-level discovery of highly correlated predictors with a controlled error rate. A thorough empirical evaluation over a wide range of simulated scenarios demonstrates the effectiveness of the proposed method by achieving high power while having a minimal number of false discoveries. Furthermore, we implemented the algorithm in the riboflavin (vitamin $B_2$) production dataset in the context of understanding the possible genetic association with riboflavin production. The gain of the proposed methodology is illustrated by achieving lower prediction error compared to other state-of-the-art methods.

\cite{rohe2016co} proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary directed graph data in network studies. However, ScBM completely ignores node weight, and is unable to explain the block structure of directed weighted network which appears in various areas, such as biology, sociology, physiology and computer science. Here, to model directed weighted network, we introduce a Directed Distribution-Free model by releasing ScBM's distribution restriction. We also build an extension of the proposed model by considering variation of node degree. Our models do not require a specific distribution on generating elements of adjacency matrix but only a block structure on the expected adjacency matrix. Spectral algorithms with theoretical guarantee on consistent estimation of node label are presented to identify communities. Our proposed methods are illustrated by simulated and empirical examples.

Feature transformation aims to extract a good representation (feature) space by mathematically transforming existing features. It is crucial to address the curse of dimensionality, enhance model generalization, overcome data sparsity, and expand the availability of classic models. Current research focuses on domain knowledge-based feature engineering or learning latent representations; nevertheless, these methods are not entirely automated and cannot produce a traceable and optimal representation space. When rebuilding a feature space for a machine learning task, can these limitations be addressed concurrently? In this extension study, we present a self-optimizing framework for feature transformation. To achieve a better performance, we improved the preliminary work by (1) obtaining an advanced state representation for enabling reinforced agents to comprehend the current feature set better; and (2) resolving Q-value overestimation in reinforced agents for learning unbiased and effective policies. Finally, to make experiments more convincing than the preliminary work, we conclude by adding the outlier detection task with five datasets, evaluating various state representation approaches, and comparing different training strategies. Extensive experiments and case studies show that our work is more effective and superior.

Assigning weights to a large pool of objects is a fundamental task in a wide variety of applications. In this article, we introduce the concept of structured high-dimensional probability simplexes, in which most components are zero or near zero and the remaining ones are close to each other. Such structure is well motivated by (i) high-dimensional weights that are common in modern applications, and (ii) ubiquitous examples in which equal weights -- despite their simplicity -- often achieve favorable or even state-of-the-art predictive performance. This particular structure, however, presents unique challenges partly because, unlike high-dimensional linear regression, the parameter space is a simplex and pattern switching between partial constancy and sparsity is unknown. To address these challenges, we propose a new class of double spike Dirichlet priors to shrink a probability simplex to one with the desired structure. When applied to ensemble learning, such priors lead to a Bayesian method for structured high-dimensional ensembles that is useful for forecast combination and improving random forests, while enabling uncertainty quantification. We design efficient Markov chain Monte Carlo algorithms for implementation. Posterior contraction rates are established to study large sample behaviors of the posterior distribution. We demonstrate the wide applicability and competitive performance of the proposed methods through simulations and two real data applications using the European Central Bank Survey of Professional Forecasters data set and a data set from the UC Irvine Machine Learning Repository (UCI).

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

Recent years have witnessed significant advances in technologies and services in modern network applications, including smart grid management, wireless communication, cybersecurity as well as multi-agent autonomous systems. Considering the heterogeneous nature of networked entities, emerging network applications call for game-theoretic models and learning-based approaches in order to create distributed network intelligence that responds to uncertainties and disruptions in a dynamic or an adversarial environment. This paper articulates the confluence of networks, games and learning, which establishes a theoretical underpinning for understanding multi-agent decision-making over networks. We provide an selective overview of game-theoretic learning algorithms within the framework of stochastic approximation theory, and associated applications in some representative contexts of modern network systems, such as the next generation wireless communication networks, the smart grid and distributed machine learning. In addition to existing research works on game-theoretic learning over networks, we highlight several new angles and research endeavors on learning in games that are related to recent developments in artificial intelligence. Some of the new angles extrapolate from our own research interests. The overall objective of the paper is to provide the reader a clear picture of the strengths and challenges of adopting game-theoretic learning methods within the context of network systems, and further to identify fruitful future research directions on both theoretical and applied studies.

Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.