Discovering causal relations among semantic factors is an emergent topic in representation learning. Most causal representation learning (CRL) methods are fully supervised, which is impractical due to costly labeling. To resolve this restriction, weakly supervised CRL methods were introduced. To evaluate CRL performance, four existing datasets, Pendulum, Flow, CelebA(BEARD) and CelebA(SMILE), are utilized. However, existing CRL datasets are limited to simple graphs with few generative factors. Thus we propose two new datasets with a larger number of diverse generative factors and more sophisticated causal graphs. In addition, current real datasets, CelebA(BEARD) and CelebA(SMILE), the originally proposed causal graphs are not aligned with the dataset distributions. Thus, we propose modifications to them.

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate. A-optimality is a widely used and easy-to-interpret criterion for Bayesian experimental design. This criterion seeks the optimal experimental design by minimizing the expected conditional variance, which is also known as the expected posterior variance. This study presents a novel likelihood-free approach to the A-optimal experimental design that does not require sampling or integrating the Bayesian posterior distribution. The expected conditional variance is obtained via the variance of the conditional expectation using the law of total variance, and we take advantage of the orthogonal projection property to approximate the conditional expectation. We derive an asymptotic error estimation for the proposed estimator of the expected conditional variance and show that the intractability of the posterior distribution does not affect the performance of our approach. We use an artificial neural network (ANN) to approximate the nonlinear conditional expectation in the implementation of our method. We then extend our approach for dealing with the case that the domain of experimental design parameters is continuous by integrating the training process of the ANN into minimizing the expected conditional variance. Through numerical experiments, we demonstrate that our method greatly reduces the number of observation model evaluations compared with widely used importance sampling-based approaches. This reduction is crucial, considering the high computational cost of the observational models. Code is available at https://github.com/vinh-tr-hoang/DOEviaPACE.

Traffic management systems play a vital role in ensuring safe and efficient transportation on roads. However, the use of advanced technologies in traffic management systems has introduced new safety challenges. Therefore, it is important to ensure the safety of these systems to prevent accidents and minimize their impact on road users. In this survey, we provide a comprehensive review of the literature on safety in traffic management systems. Specifically, we discuss the different safety issues that arise in traffic management systems, the current state of research on safety in these systems, and the techniques and methods proposed to ensure the safety of these systems. We also identify the limitations of the existing research and suggest future research directions.

Despite the strong predictive performance of deep learning models for traffic prediction, their widespread deployment in real-world intelligent transportation systems has been restrained by a lack of interpretability. Uncertainty quantification (UQ) methods provide an approach to induce probabilistic reasoning, improve decision-making and enhance model deployment potential. To gain a comprehensive picture of the usefulness of existing UQ methods for traffic prediction and the relation between obtained uncertainties and city-wide traffic dynamics, we investigate their application to a large-scale image-based traffic dataset spanning multiple cities and time periods. We compare two epistemic and two aleatoric UQ methods on both temporal and spatio-temporal transfer tasks, and find that meaningful uncertainty estimates can be recovered. We further demonstrate how uncertainty estimates can be employed for unsupervised outlier detection on changes in city traffic dynamics. We find that our approach can capture both temporal and spatial effects on traffic behaviour in a representative case study for the city of Moscow. Our work presents a further step towards boosting uncertainty awareness in traffic prediction tasks, and aims to highlight the value contribution of UQ methods to a better understanding of city traffic dynamics.

The unpredictability and volatility of the stock market render it challenging to make a substantial profit using any generalized scheme. Many previous studies tried different techniques to build a machine learning model, which can make a significant profit in the US stock market by performing live trading. However, very few studies have focused on the importance of finding the best features for a particular period for trading. Our top approach used the performance to narrow down the features from a total of 148 to about 30. Furthermore, the top 25 features were dynamically selected before each time training our machine learning model. It uses ensemble learning with four classifiers: Gaussian Naive Bayes, Decision Tree, Logistic Regression with L1 regularization and Stochastic Gradient Descent, to decide whether to go long or short on a particular stock. Our best model performed daily trade between July 2011 and January 2019, generating 54.35% profit. Finally, our work showcased that mixtures of weighted classifiers perform better than any individual predictor about making trading decisions in the stock market.

A major challenge in structured prediction is to represent the interdependencies within output structures. When outputs are structured as sequences, linear-chain conditional random fields (CRFs) are a widely used model class which can learn \textit{local} dependencies in the output. However, the CRF's Markov assumption makes it impossible for CRFs to represent distributions with \textit{nonlocal} dependencies, and standard CRFs are unable to respect nonlocal constraints of the data (such as global arity constraints on output labels). We present a generalization of CRFs that can enforce a broad class of constraints, including nonlocal ones, by specifying the space of possible output structures as a regular language $\mathcal{L}$. The resulting regular-constrained CRF (RegCCRF) has the same formal properties as a standard CRF, but assigns zero probability to all label sequences not in $\mathcal{L}$. Notably, RegCCRFs can incorporate their constraints during training, while related models only enforce constraints during decoding. We prove that constrained training is never worse than constrained decoding, and show empirically that it can be substantially better in practice. Additionally, we demonstrate a practical benefit on downstream tasks by incorporating a RegCCRF into a deep neural model for semantic role labeling, exceeding state-of-the-art results on a standard dataset.

For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. T o address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cram er-Rao lower bound as a benchmark. Index T erms--Bayesian filtering, counter-adversarial systems, extended Kalman filter, inverse filtering, non-linear processes.

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently, machine learning advances have enabled the creation of non-linear projection methods, such as Latent Space Dynamics Identification (LaSDI). LaSDI maps full-order PDE solutions to a latent space using autoencoders and learns the system of ODEs governing the latent space dynamics. By interpolating and solving the ODE system in the reduced latent space, fast and accurate ROM predictions can be made by feeding the predicted latent space dynamics into the decoder. In this paper, we introduce GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the ROM predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. We demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

We investigate the problem of compound estimation of normal means while accounting for the presence of side information. Leveraging the empirical Bayes framework, we develop a nonparametric integrative Tweedie (NIT) approach that incorporates structural knowledge encoded in multivariate auxiliary data to enhance the precision of compound estimation. Our approach employs convex optimization tools to estimate the gradient of the log-density directly, enabling the incorporation of structural constraints. We conduct theoretical analyses of the asymptotic risk of NIT and establish the rate at which NIT converges to the oracle estimator. As the dimension of the auxiliary data increases, we accurately quantify the improvements in estimation risk and the associated deterioration in convergence rate. The numerical performance of NIT is illustrated through the analysis of both simulated and real data, demonstrating its superiority over existing methods.

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.