We unify empirical Bayes and variational Bayes for approximating unnormalized densities. This framework, named unnormalized variational Bayes (UVB), is based on formulating a latent variable model for the random variable $Y=X+N(0,\sigma^2 I_d)$ and using the evidence lower bound (ELBO), computed by a variational autoencoder, as a parametrization of the energy function of $Y$ which is then used to estimate $X$ with the empirical Bayes least-squares estimator. In this intriguing setup, the $\textit{gradient}$ of the ELBO with respect to noisy inputs plays the central role in learning the energy function. Empirically, we demonstrate that UVB has a higher capacity to approximate energy functions than the parametrization with MLPs as done in neural empirical Bayes (DEEN). We especially showcase $\sigma=1$, where the differences between UVB and DEEN become visible and qualitative in the denoising experiments. For this high level of noise, the distribution of $Y$ is very smoothed and we demonstrate that one can traverse in a single run $-$ without a restart $-$ all MNIST classes in a variety of styles via walk-jump sampling with a fast-mixing Langevin MCMC sampler. We finish by probing the encoder/decoder of the trained models and confirm UVB $\neq$ VAE.

The aim of improvements in data driven exercises in insurance has led to the desire to gather additional data than traditionally available. In addition to underwriting characteristics such as age, gender and address, technology now allows the collection of many more variables. Examples include dynamic data from sensors for driving behaviour in vehicles, appliance and electrical usage in homes and static data from external databases on traffic violations, crime scores or credit scores. High dimensional models arise if modelling sensor data at multiple time points and the individual variables that comprise summary scores. Reasoning with a large number of variables can become unnecessarily complex without any actuarial judgment. For example, it may not be necessary to include hundreds of rating factors as predictors if many of them are known to be related or unnecessary. This discussion proposes the use of graph theory as a means of translating intuitive reasoning to mathematical properties. This is done via graphical models, which involve the use of graph theory to formulate probabilistic models (Lauritzen, 1996). The approach has been used in applications such as medical expert systems (Franklin et al., 1989), natural language processing (Blei et al., 2003), image processing, bioinformatics and others (Wainwright and Jordan, 2008).

The implementation of robust, stable, and user-centered data analytics and machine learning models is confronted by numerous challenges in production and manufacturing. Therefore, a systematic approach is required to develop, evaluate, and deploy such models. The data-driven knowledge discovery framework provides an orderly partition of the data-mining processes to ensure the practical implementation of data analytics and machine learning models. However, the practical application of robust industry-specific data-driven knowledge discovery models faces multiple data-- and model-development--related issues. These issues should be carefully addressed by allowing a flexible, customized, and industry-specific knowledge discovery framework; in our case, this takes the form of the cross-industry standard process for data mining (CRISP-DM). This framework is designed to ensure active cooperation between different phases to adequately address data- and model-related issues. In this paper, we review several extensions of CRISP-DM models and various data-robustness-- and model-robustness--related problems in machine learning, which currently lacks proper cooperation between data experts and business experts because of the limitations of data-driven knowledge discovery models.

A central capability of a long-lived reinforcement learning (RL) agent is to incrementally adapt its behavior as its environment changes, and to incrementally build upon previous experiences to facilitate future learning in real-world scenarios. In this paper, we propose LifeLong Incremental Reinforcement Learning (LLIRL), a new incremental algorithm for efficient lifelong adaptation to dynamic environments. We develop and maintain a library that contains an infinite mixture of parameterized environment models, which is equivalent to clustering environment parameters in a latent space. The prior distribution over the mixture is formulated as a Chinese restaurant process (CRP), which incrementally instantiates new environment models without any external information to signal environmental changes in advance. During lifelong learning, we employ the expectation maximization (EM) algorithm with online Bayesian inference to update the mixture in a fully incremental manner. In EM, the E-step involves estimating the posterior expectation of environment-to-cluster assignments, while the M-step updates the environment parameters for future learning. This method allows for all environment models to be adapted as necessary, with new models instantiated for environmental changes and old models retrieved when previously seen environments are encountered again. Experiments demonstrate that LLIRL outperforms relevant existing methods, and enables effective incremental adaptation to various dynamic environments for lifelong learning.

In multimedia forensics, learning-based methods provide state-of-the-art performance in determining origin and authenticity of images and videos. However, most existing methods are challenged by out-of-distribution data, i.e., with characteristics that are not covered in the training set. This makes it difficult to know when to trust a model, particularly for practitioners with limited technical background. In this work, we make a first step toward redesigning forensic algorithms with a strong focus on reliability. To this end, we propose to use Bayesian neural networks (BNN), which combine the power of deep neural networks with the rigorous probabilistic formulation of a Bayesian framework. Instead of providing a point estimate like standard neural networks, BNNs provide distributions that express both the estimate and also an uncertainty range. We demonstrate the usefulness of this framework on a classical forensic task: resampling detection. The BNN yields state-of-the-art detection performance, plus excellent capabilities for detecting out-of-distribution samples. This is demonstrated for three pathologic issues in resampling detection, namely unseen resampling factors, unseen JPEG compression, and unseen resampling algorithms. We hope that this proposal spurs further research toward reliability in multimedia forensics.

Cloud computing (CC) is a centralized computing paradigm that accumulates resources centrally and provides these resources to users through Internet. Although CC holds a large number of resources, it may not be acceptable by real-time mobile applications, as it is usually far away from users geographically. On the other hand, edge computing (EC), which distributes resources to the network edge, enjoys increasing popularity in the applications with low-latency and high-reliability requirements. EC provides resources in a decentralized manner, which can respond to users' requirements faster than the normal CC, but with limited computing capacities. As both CC and EC are resource-sensitive, several big issues arise, such as how to conduct job scheduling, resource allocation, and task offloading, which significantly influence the performance of the whole system. To tackle these issues, many optimization problems have been formulated. These optimization problems usually have complex properties, such as non-convexity and NP-hardness, which may not be addressed by the traditional convex optimization-based solutions. Computational intelligence (CI), consisting of a set of nature-inspired computational approaches, recently exhibits great potential in addressing these optimization problems in CC and EC. This paper provides an overview of research problems in CC and EC and recent progresses in addressing them with the help of CI techniques. Informative discussions and future research trends are also presented, with the aim of offering insights to the readers and motivating new research directions.

The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the symbolic reasoning module and thus converge slowly with sparse rewards. In this paper, we address these issues and close the loop of neural-symbolic learning by (1) introducing the \textbf{grammar} model as a \textit{symbolic prior} to bridge neural perception and symbolic reasoning, and (2) proposing a novel \textbf{back-search} algorithm which mimics the top-down human-like learning procedure to propagate the error through the symbolic reasoning module efficiently. We further interpret the proposed learning framework as maximum likelihood estimation using Markov chain Monte Carlo sampling and the back-search algorithm as a Metropolis-Hastings sampler. The experiments are conducted on two weakly-supervised neural-symbolic tasks: (1) handwritten formula recognition on the newly introduced HWF dataset; (2) visual question answering on the CLEVR dataset. The results show that our approach significantly outperforms the RL methods in terms of performance, converging speed, and data efficiency. Our code and data are released at \url{https://liqing-ustc.github.io/NGS}.

One of the primary goals of systems neuroscience is to relate the structure of neural circuits to their function, yet patterns of connectivity are difficult to establish when recording from large populations in behaving organisms. Many previous approaches have attempted to estimate functional connectivity between neurons using statistical modeling of observational data, but these approaches rely heavily on parametric assumptions and are purely correlational. Recently, however, holographic photostimulation techniques have made it possible to precisely target selected ensembles of neurons, offering the possibility of establishing direct causal links. A naive method for inferring functional connections is to stimulate each individual neuron multiple times and observe the responses of cells in the local network, but this approach scales poorly with the number of neurons. Here, we propose a method based on noisy group testing that drastically increases the efficiency of this process in sparse networks. By stimulating small ensembles of neurons, we show that it is possible to recover binarized network connectivity with a number of tests that grows only logarithmically with population size under minimal statistical assumptions. Moreover, we prove that our approach, which reduces to an efficiently solvable convex optimization problem, is equivalent to Variational Bayesian inference on the binary connection weights, and we derive rigorous bounds on the posterior marginals. This allows us to extend our method to the streaming setting, where continuously updated posteriors allow for optional stopping, and we demonstrate the feasibility of inferring connectivity for networks of up to tens of thousands of neurons online.

Such a phenomenon is summed up in the manifold distribution hypothesis, and can be exploited in probabilistic learning. Here we present normal-bundle bootstrap (NBB), a method that generates new data which preserve the geometric structure of a given data set. Inspired by algorithms for manifold learning and concepts in differential geometry, our method decomposes the underlying probability measure into a marginalized measure on a learned data manifold and conditional measures on the normal spaces. The algorithm estimates the data manifold as a density ridge, and constructs new data by bootstrapping projection vectors and adding them to the ridge. We apply our method to the inference of density ridge and related statistics, and data augmentation to reduce overfitting.

Prior probability models are a central component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided state-of-the-art solutions for problems such as denoising, which implicitly rely on a prior probability model of natural images. Here, we develop a robust and general methodology for making use of this implicit prior. We rely on a little-known statistical result due to Miyasawa (1961), who showed that the least-squares solution for removing additive Gaussian noise can be written directly in terms of the gradient of the log of the noisy signal density. We use this fact to develop a stochastic coarse-to-fine gradient ascent procedure for drawing high-probability samples from the implicit prior embedded within a CNN trained to perform blind (i.e., unknown noise level) least-squares denoising. A generalization of this algorithm to constrained sampling provides a method for using the implicit prior to solve any linear inverse problem, with no additional training. We demonstrate this general form of transfer learning in multiple applications, using the same algorithm to produce high-quality solutions for deblurring, super-resolution, inpainting, and compressive sensing.