Bayesian neural networks attempt to combine the strong predictive performance of neural networks with formal quantification of uncertainty associated with the predictive output in the Bayesian framework. However, it remains unclear how to endow the parameters of the network with a prior distribution that is meaningful when lifted into the output space of the network. A possible solution is proposed that enables the user to posit an appropriate covariance function for the task at hand. Our approach constructs a prior distribution for the parameters of the network, called a ridgelet prior, that approximates the posited covariance structure in the output space of the network. The approach is rooted in the ridgelet transform and we establish both finite-sample-size error bounds and the consistency of the approximation of the covariance function in a limit where the number of hidden units is increased. Our experimental assessment is limited to a proof-of-concept, where we demonstrate that the ridgelet prior can out-perform an unstructured prior on regression problems for which an informative covariance function can be a priori provided.

Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian Markov chain Monte Carlo (MCMC) simulation methods, which, however, are computationally expensive and do not scale well to large datasets. Variational Bayes (VB), a method from machine learning, addresses the shortcomings of MCMC by casting Bayesian estimation as an optimisation problem instead of a simulation problem. Considering all these advantages of VB, a VB method is derived for posterior inference in negative binomial models with unobserved parameter heterogeneity and spatial dependence. P\'olya-Gamma augmentation is used to deal with the non-conjugacy of the negative binomial likelihood and an integrated non-factorised specification of the variational distribution is adopted to capture posterior dependencies. The benefits of the proposed approach are demonstrated in a Monte Carlo study and an empirical application on estimating youth pedestrian injury counts in census tracts of New York City. The VB approach is around 45 to 50 times faster than MCMC on a regular eight-core processor in a simulation and an empirical study, while offering similar estimation and predictive accuracy. Conditional on the availability of computational resources, the embarrassingly parallel architecture of the proposed VB method can be exploited to further accelerate its estimation by up to 20 times.

We develop a goodness-of-fit (GOF) test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical experiments based on simulation and real-data validate our theory and demonstrate the proposed GS test's good performance.

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional data into low-dimensional spaces, which mitigates the effects of noise and uncovers latent relations. In order to make the learned representations inherit the structures in the original data, graph-regularization terms are often added to the loss function. However, the prior graph construction often fails to reflect the true network connectivity and the intrinsic relationships. In addition, many graph-regularized methods fail to take the dual spaces into account. Probabilistic models are often used to model the distribution of the representations, but most of previous methods often assume that the hidden variables are independent and identically distributed for simplicity. To this end, we propose a learnable graph-regularization model for matrix decomposition (LGMD), which builds a bridge between graph-regularized methods and probabilistic matrix decomposition models. LGMD learns two graphical structures (i.e., two precision matrices) in real-time in an iterative manner via sparse precision matrix estimation and is more robust to noise and missing entries. Extensive numerical results and comparison with competing methods demonstrate its effectiveness.

Expert search aims to find and rank experts based on a user's query. In academia, retrieving experts is an efficient way to navigate through a large amount of academic knowledge. Here, we study how different distributed representations of academic papers (i.e. embeddings) impact academic expert retrieval. We use the Microsoft Academic Graph dataset and experiment with different configurations of a document-centric voting model for retrieval. In particular, we explore the impact of the use of contextualized embeddings on search performance. We also present results for paper embeddings that incorporate citation information through retrofitting. Additionally, experiments are conducted using different techniques for assigning author weights based on author order. We observe that using contextual embeddings produced by a transformer model trained for sentence similarity tasks produces the most effective paper representations for document-centric expert retrieval. However, retrofitting the paper embeddings and using elaborate author contribution weighting strategies did not improve retrieval performance.

Despite the improvement of translation quality, neural machine translation (NMT) often suffers from the lack of diversity in its generation. In this paper, we propose to generate diverse translations by deriving a large number of possible models with Bayesian modelling and sampling models from them for inference. The possible models are obtained by applying concrete dropout to the NMT model and each of them has specific confidence for its prediction, which corresponds to a posterior model distribution under specific training data in the principle of Bayesian modeling. With variational inference, the posterior model distribution can be approximated with a variational distribution, from which the final models for inference are sampled. We conducted experiments on Chinese-English and English-German translation tasks and the results shows that our method makes a better trade-off between diversity and accuracy.

The interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose nodes represent microbial taxa and edges represent pairwise interactions. A microbial network is a weighted graph that is constructed from a sample-taxa count matrix, and can be used to model co-occurrences and/or interactions of the constituent members of a microbial community. The nodes in this graph represent microbial taxa and the edges represent pairwise associations amongst these taxa. A microbial network is typically constructed from a sample-taxa count matrix that is obtained by sequencing multiple biological samples and identifying taxa counts. From large-scale microbiome studies, it is evident that microbial community compositions and interactions are impacted by environmental and/or host factors. Thus, it is not unreasonable to expect that a sample-taxa matrix generated as part of a large study involving multiple environmental or clinical parameters can be associated with more than one microbial network. However, to our knowledge, microbial network inference methods proposed thus far assume that the sample-taxa matrix is associated with a single network.

We consider reinforcement learning (RL) in episodic Markov decision processes (MDPs) with linear function approximation under drifting environment. Specifically, both the reward and state transition functions can evolve over time, as long as their respective total variations, quantified by suitable metrics, do not exceed certain \textit{variation budgets}. We first develop the $\texttt{LSVI-UCB-Restart}$ algorithm, an optimistic modification of least-squares value iteration combined with periodic restart, and establish its dynamic regret bound when variation budgets are known. We then propose a parameter-free algorithm, $\texttt{Ada-LSVI-UCB-Restart}$, that works without knowing the variation budgets, but with a slightly worse dynamic regret bound. We also derive the first minimax dynamic regret lower bound for nonstationary MDPs to show that our proposed algorithms are near-optimal. As a byproduct, we establish a minimax regret lower bound for linear MDPs, which is unsolved by \cite{jin2020provably}. In addition, we provide numerical experiments to demonstrate the effectiveness of our proposed algorithms. As far as we know, this is the first dynamic regret analysis in nonstationary reinforcement learning with function approximation.

Bayesian inference without the access of likelihood, called likelihood-free inference, is highlighted in simulation to yield a more realistic simulation result. Recent research updates an approximate posterior sequentially with the cumulative simulation input-output pairs over inference rounds. This paper observes that previous algorithms with Monte-Carlo Markov Chain present low accuracy for inference on a simulation with a multi-modal posterior due to the mode collapse of MCMC. From the observation, we propose an implicit sampling method, Implicit Surrogate Proposal (ISP), to draw balanced simulation inputs at each round. The resolution of mode collapse comes from two mechanisms: 1) a flexible surrogate proposal density estimator and 2) a parallel explored samples to train the surrogate density model. We demonstrate that ISP outperforms the baseline algorithms in multi-modal simulations.

Machine learning models have traditionally been developed under the assumption that the training and test distributions match exactly. However, recent success in few-shot learning and related problems are encouraging signs that these models can be adapted to more realistic settings where train and test distributions differ. Unfortunately, there is severely limited theoretical support for these algorithms and little is known about the difficulty of these problems. In this work, we provide novel information-theoretic lower-bounds on minimax rates of convergence for algorithms that are trained on data from multiple sources and tested on novel data. Our bounds depend intuitively on the information shared between sources of data, and characterize the difficulty of learning in this setting for arbitrary algorithms. We demonstrate these bounds on a hierarchical Bayesian model of meta-learning, computing both upper and lower bounds on parameter estimation via maximum-a-posteriori inference.