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)

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.

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.

We study reinforcement learning in factored Markov decision processes (FMDPs) in the non-episodic setting. We focus on regret analyses providing both upper and lower bounds. We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a frequentist regret bound respectively, both of which reduce to the near-optimal bound $\widetilde{O}(DS\sqrt{AT})$ for standard non-factored MDPs. Our lower bound depends on the span of the bias vector rather than the diameter $D$ and we show via a simple Cartesian product construction that FMDPs with a bounded span can have an arbitrarily large diameter, which suggests that bounds with a dependence on diameter can be extremely loose. We, therefore, propose another algorithm that only depends on span but relies on a computationally stronger oracle. Our algorithms outperform the previous near-optimal algorithms on computer network administrator simulations.

In many cases, neural network classifiers are likely to be exposed to input data that is outside of their training distribution data. Samples from outside the distribution may be classified as an existing class with high probability by softmax-based classifiers; such incorrect classifications affect the performance of the classifiers and the applications/systems that depend on them. Previous research aimed at distinguishing training distribution data from out-of-distribution data (OOD) has proposed detectors that are external to the classification method. We present Gaussian isolation machine (GIM), a novel hybrid (generative-discriminative) classifier aimed at solving the problem arising when OOD data is encountered. The GIM is based on a neural network and utilizes a new loss function that imposes a distribution on each of the trained classes in the neural network's output space, which can be approximated by a Gaussian. The proposed GIM's novelty lies in its discriminative performance and generative capabilities, a combination of characteristics not usually seen in a single classifier. The GIM achieves state-of-the-art classification results on image recognition and sentiment analysis benchmarking datasets and can also deal with OOD inputs. We also demonstrate the benefits of incorporating part of the GIM's loss function into standard neural networks as a regularization method.

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.

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.