We derive the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated approximate posterior over the weights at all layers in a Bayesian neural network. We extend this approach to deep Gaussian processes, unifying inference in the two model classes. Our approximate posterior uses learned "global" inducing points, which are defined only at the input layer and propagated through the network to obtain inducing inputs at subsequent layers. By contrast, standard, "local", inducing point methods from the deep Gaussian process literature optimize a separate set of inducing inputs at every layer, and thus do not model correlations across layers. Our method gives state-of-the-art performance for a variational Bayesian method, without data augmentation or tempering, on CIFAR-10 of $86.7\%$.

Neural Tensor Networks (NTNs), which are structured to encode the degree of relationship among pairs of entities, are used in Logic Tensor Networks (LTNs) to facilitate Statistical Relational Learning (SRL) in first-order logic. In this paper, we propose Randomly Weighted Tensor Networks (RWTNs), which incorporate randomly drawn, untrained tensors into an NTN encoder network with a trained decoder network. We show that RWTNs meet or surpass the performance of traditionally trained LTNs for Semantic Image Interpretation (SII) tasks that have been used as a representative example of how LTNs utilize reasoning over first-order logic to exceed the performance of solely data-driven methods. We demonstrate that RWTNs outperform LTNs for the detection of the relevant part-of relations between objects, and we show that RWTNs can achieve similar performance as LTNs for object classification while using fewer parameters for learning. Furthermore, we demonstrate that because the randomized weights do not depend on the data, several decoder networks can share a single NTN, giving RWTNs a unique economy of spatial scale for simultaneous classification tasks.

In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy estimations. We approach the problem from the perspective of importance-sampling theory, and advocate the use of the likelihood ratio to guide the search algorithm towards regions of the input space where the objective function to be minimized assumes abnormally small values. The likelihood ratio acts as a sampling weight and can be computed at each iteration without severely deteriorating the overall efficiency of the algorithm. In particular, it can be approximated in a way that makes the approach tractable in high dimensions. The "likelihood-weighted" acquisition functions introduced in this work are found to outperform their unweighted counterparts in a number of applications.

This paper briefly analyzes the advantages and problems of AI mainstream technology and puts forward: To achieve stronger Artificial Intelligence, the end-to-end function calculation must be changed and adopt the technology system centered on scene fitting. It also discusses the concrete scheme named Dynamic Cognitive Network model (DC Net). Discussions : The knowledge and data in the comprehensive domain are uniformly represented by using the rich connection heterogeneous Dynamic Cognitive Network constructed by conceptualized elements; A network structure of two dimensions and multi layers is designed to achieve unified implementation of AI core processing such as combination and generalization; This paper analyzes the implementation differences of computer systems in different scenes, such as open domain, closed domain, significant probability and non-significant probability, and points out that the implementation in open domain and significant probability scene is the key of AI, and a cognitive probability model combining bidirectional conditional probability, probability passing and superposition, probability col-lapse is designed; An omnidirectional network matching-growth algorithm system driven by target and probability is designed to realize the integration of parsing, generating, reasoning, querying, learning and so on; The principle of cognitive network optimization is proposed, and the basic framework of Cognitive Network Learning algorithm (CNL) is designed that structure learning is the primary method and parameter learning is the auxiliary. The logical similarity of implementation between DC Net model and human intelligence is analyzed in this paper.

Leveraging well-established MCMC strategies, we propose MCMC-interactive variational inference (MIVI) to not only estimate the posterior in a time constrained manner, but also facilitate the design of MCMC transitions. Constructing a variational distribution followed by a short Markov chain that has parameters to learn, MIVI takes advantage of the complementary properties of variational inference and MCMC to encourage mutual improvement. On one hand, with the variational distribution locating high posterior density regions, the Markov chain is optimized within the variational inference framework to efficiently target the posterior despite a small number of transitions. On the other hand, the optimized Markov chain with considerable flexibility guides the variational distribution towards the posterior and alleviates its underestimation of uncertainty. Furthermore, we prove the optimized Markov chain in MIVI admits extrapolation, which means its marginal distribution gets closer to the true posterior as the chain grows. Therefore, the Markov chain can be used separately as an efficient MCMC scheme. Experiments show that MIVI not only accurately and efficiently approximates the posteriors but also facilitates designs of stochastic gradient MCMC and Gibbs sampling transitions.

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models with various underlying structures in the latent space. We represent the inductive bias in the form of mask variables to model the dependency structure in the graphical model and extend the theory of multivariate information bottleneck to enforce it. Our model provides a principled approach to learn a set of semantically meaningful latent factors that reflect various types of desired structures like capturing correlation or encoding invariance, while also offering the flexibility to automatically estimate the dependency structure from data. We show that our framework unifies many existing generative models and can be applied to a variety of tasks including multi-modal data modeling, algorithmic fairness, and invariant risk minimization.

ParaMonte::Python (standing for Parallel Monte Carlo in Python) is a serial and MPI-parallelized library of (Markov Chain) Monte Carlo (MCMC) routines for sampling mathematical objective functions, in particular, the posterior distributions of parameters in Bayesian modeling and analysis in data science, Machine Learning, and scientific inference in general. In addition to providing access to fast high-performance serial/parallel Monte Carlo and MCMC sampling routines, the ParaMonte::Python library provides extensive post-processing and visualization tools that aim to automate and streamline the process of model calibration and uncertainty quantification in Bayesian data analysis. Furthermore, the automatically-enabled restart functionality of ParaMonte::Python samplers ensure seamless fully-deterministic into-the-future restart of Monte Carlo simulations, should any interruptions happen. The ParaMonte::Python library is MIT-licensed and is permanently maintained on GitHub at https://github.com/cdslaborg/paramonte/tree/master/src/interface/Python.

Background: Catastrophic forgetting is the notorious vulnerability of neural networks to the changes in the data distribution during learning. This phenomenon has long been considered a major obstacle for using learning agents in realistic continual learning settings. A large body of continual learning research assumes that task boundaries are known during training. However, only a few works consider scenarios in which task boundaries are unknown or not well defined -- task agnostic scenarios. The optimal Bayesian solution for this requires an intractable online Bayes update to the weights posterior. Contributions: We aim to approximate the online Bayes update as accurately as possible. To do so, we derive novel fixed-point equations for the online variational Bayes optimization problem, for multivariate Gaussian parametric distributions. By iterating the posterior through these fixed-point equations, we obtain an algorithm (FOO-VB) for continual learning which can handle non-stationary data distribution using a fixed architecture and without using external memory (i.e. without access to previous data). We demonstrate that our method (FOO-VB) outperforms existing methods in task agnostic scenarios. FOO-VB Pytorch implementation will be available online.

AI planning can be cast as inference in probabilistic models, and probabilistic programming was shown to be capable of policy search in partially observable domains. Prior work introduces policy search through Markov chain Monte Carlo in deterministic domains, as well as adapts black-box variational inference to stochastic domains, however not in the strictly Bayesian sense. In this work, we cast policy search in stochastic domains as a Bayesian inference problem and provide a scheme for encoding such problems as nested probabilistic programs. We argue that probabilistic programs for policy search in stochastic domains should involve nested conditioning, and provide an adaption of Lightweight Metropolis-Hastings (LMH) for robust inference in such programs. We apply the proposed scheme to stochastic domains and show that policies of similar quality are learned, despite a simpler and more general inference algorithm. We believe that the proposed variant of LMH is novel and applicable to a wider class of probabilistic programs with nested conditioning.

We propose to distinguish between deterministic conditioning, that is, conditioning on a sample from the joint data distribution, and stochastic conditioning, that is, conditioning on the distribution of the observable variable. Mostly, probabilistic programs follow the Bayesian approach by choosing a prior distribution of parameters and conditioning on observations. In a basic setting, individual observations are In a basic setting, individual observations are samples from the joint data distribution. However, observations may also be independent samples from marginal data distributions of each observable variable, summary statistics, or even data distributions themselves . These cases naturally appear in real life scenarios: samples from marginal distributions arise when different observations are collected by different parties, summary statistics (mean, variance, and quantiles) are often used to represent data collected over a large population, and data distributions may represent uncertainty during inference about future states of the world, that is, in planning. Probabilistic programming languages and frameworks which support conditioning on samples from the joint data distribution are not directly capable of expressing such models. We define the notion of stochastic conditioning and describe extensions of known general inference algorithms to probabilistic programs with stochastic conditioning. In case studies we provide probabilistic programs for several problems of statistical inference which are impossible or difficult to approach otherwise, perform inference on the programs, and analyse the results.