Mathematical models of system dynamics are a core technology in most model-based engineered systems acting and interacting with their environment. Examples include GPS, autonomous vehicles, passenger aircraft and robotics, to name just a few. The remarkable utility of mathematical models stems from the fact that, inter alia, they enable decision making based on prediction of system behaviour under new scenarios, accelerate the analysis and design processes, are fundamental to detecting faults or changes, and they are capable of handling uncertainty that is present in data, assumptions and algorithms. Motivated by the broad applicability and utility of modelling, the scientific community has devoted significant research attention towards learning dynamical models from data. Importantly, for dynamic systems, the sequence or ordering of the data must be maintained as future outcomes are deemed to be fundamentally related to the past. This is sometimes called sequence learning (Sun and Giles, 2001) or system identification (Ljung, 1999). In essence, these approaches search over a space of models and determine the model that best (in some sense) fits the data while maintaining the time ordering. The current paper is directed towards solving this important problem. To make these ideas more concrete, here we assume that data from the system of interest is available in the form of a data record y 1:T {y 1,...,y T }, where each measurementy k is potentially multidimensional and the number of available measurements is denoted as T 0. We further assume that the data may be adequately described as an instance from a joint distribution that is parametrized by an unknown vectorθ (called the parameter vector), that is (with abuse of notation)

Here, we report that the depth and the width of a neural network are dual from two perspectives. First, we employ the partially separable representation to determine the width and depth. Second, we use the De Morgan law to guide the conversion between a deep network and a wide network. Furthermore, we suggest the generalized De Morgan law to promote duality to network equivalency.

Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving infinite-length sequences from a recurrent language model when using common decoding algorithms. To analyze this issue, we first define inconsistency of a decoding algorithm, meaning that the algorithm can yield an infinite-length sequence that has zero probability under the model. We prove that commonly used incomplete decoding algorithms - greedy search, beam search, top-k sampling, and nucleus sampling - are inconsistent, despite the fact that recurrent language models are trained to produce sequences of finite length. Based on these insights, we propose two remedies which address inconsistency: consistent variants of top-k and nucleus sampling, and a self-terminating recurrent language model. Empirical results show that inconsistency occurs in practice, and that the proposed methods prevent inconsistency.

Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles, are defined on spaces with more complex geometries, such as tori or spheres. In this paper, we propose and compare expressive and numerically stable flows on such spaces. Our flows are built recursively on the dimension of the space, starting from flows on circles, closed intervals or spheres.

An ideal cognitively-inspired memory system would compress and organize incoming items. The Kanerva Machine (Wu et al., 2018b;a) is a Bayesian model that naturally implements online memory compression. However, the organization of the Kanerva Machine is limited by its use of a single Gaussian random matrix for storage. Here we introduce the Product Kanerva Machine, which dynamically combines many smaller Kanerva Machines. Its hierarchical structure provides a principled way to abstract invariant features and gives scaling and capacity advantages over single Kanerva Machines. We show that it can exhibit unsupervised clustering, find sparse and combinatorial allocation patterns, and discover spatial tunings that approximately factorize simple images by object.

Despite the wide implementation of machine learning (ML) techniques in traffic flow modeling recently, those data-driven approaches often fall short of accuracy in the cases with a small or noisy dataset. To address this issue, this study presents a new modeling framework, named physics regularized machine learning (PRML), to encode classical traffic flow models (referred as physical models) into the ML architecture and to regularize the ML training process. More specifically, a stochastic physics regularized Gaussian process (PRGP) model is developed and a Bayesian inference algorithm is used to estimate the mean and kernel of the PRGP. A physical regularizer based on macroscopic traffic flow models is also developed to augment the estimation via a shadow GP and an enhanced latent force model is used to encode physical knowledge into stochastic processes. Based on the posterior regularization inference framework, an efficient stochastic optimization algorithm is also developed to maximize the evidence lowerbound of the system likelihood. To prove the effectiveness of the proposed model, this paper conducts empirical studies on a real-world dataset which is collected from a stretch of I-15 freeway, Utah. Results show the new PRGP model can outperform the previous compatible methods, such as calibrated pure physical models and pure machine learning methods, in estimation precision and input robustness.

Large uncertainties in many phenomena of interest have challenged the reliability of pertaining decisions. Collecting additional information to better characterize involved uncertainties is among decision alternatives. Value of information (VoI) analysis is a mathematical decision framework that quantifies expected potential benefits of new data and assists with optimal allocation of resources for information collection. However, a primary challenge facing VoI analysis is the very high computational cost of the underlying Bayesian inference especially for equality-type information. This paper proposes the first surrogate-based framework for VoI analysis. Instead of modeling the limit state functions describing events of interest for decision making, which is commonly pursued in surrogate model-based reliability methods, the proposed framework models system responses. This approach affords sharing equality-type information from observations among surrogate models to update likelihoods of multiple events of interest. Moreover, two knowledge sharing schemes called model and training points sharing are proposed to most effectively take advantage of the knowledge offered by costly model evaluations. Both schemes are integrated with an error rate-based adaptive training approach to efficiently generate accurate Kriging surrogate models. The proposed VoI analysis framework is applied for an optimal decision-making problem involving load testing of a truss bridge. While state-of-the-art methods based on importance sampling and adaptive Kriging Monte Carlo simulation are unable to solve this problem, the proposed method is shown to offer accurate and robust estimates of VoI with a limited number of model evaluations. Therefore, the proposed method facilitates the application of VoI for complex decision problems.

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process leading to a decision, which is a major issue in life-critical applications. Probabilistic logic reasoning allows to exploit both statistical regularities and specific domain expertise to perform reasoning under uncertainty, but its scalability and brittle integration with the layers processing the sensory data have greatly limited its applications. For these reasons, combining deep architectures and probabilistic logic reasoning is a fundamental goal towards the development of intelligent agents operating in complex environments. This paper presents Relational Neural Machines, a novel framework allowing to jointly train the parameters of the learners and of a First--Order Logic based reasoner. A Relational Neural Machine is able to recover both classical learning from supervised data in case of pure sub-symbolic learning, and Markov Logic Networks in case of pure symbolic reasoning, while allowing to jointly train and perform inference in hybrid learning tasks. Proper algorithmic solutions are devised to make learning and inference tractable in large-scale problems. The experiments show promising results in different relational tasks.

Causality has traditionally been a scientific way to generate knowledge by relating causes to effects. From an imaginery point of view, causal graphs are a helpful tool for representing and infering new causal information. In previous works, we have generated automatically causal graphs associated to a given concept by analyzing sets of documents and extracting and representing the found causal information in that visual way. The retrieved information shows that causality is frequently imperfect rather than exact, feature gathered by the graph. In this work we will attempt to go a step further modelling the uncertainty in the graph through probabilistic improving the management of the imprecision in the quoted graph.

CausalNex is a Python library that allows data scientists and domain experts to co-develop models that go beyond correlation and consider causal relationships. 'CasualNex' provides a practical'what if' library which is deployed to test scenarios using Bayesian Networks (BNs). 'CasualNex' prepares practitioners to understand structural relationships from data and helps in the verification for accuracy of the relationships between different data sets. Apart from practitioners understanding the structural relationship from data, it also enables domain experts to fit conditional probability distributions and study the effect of potential interventions. 'CasualNex' helps to simplify the following steps: CausalNex is a Python package.