Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold representing similarity. We propose a Bayesian approach to multidimensional scaling when the low-dimensional manifold is hyperbolic. Using hyperbolic space facilitates representing tree-like structures common in many settings (e.g. text or genetic data with hierarchical structure). A Bayesian approach provides regularization that minimizes the impact of measurement error in the observed data and assesses uncertainty. We also propose a case-control likelihood approximation that allows for efficient sampling from the posterior distribution in larger data settings, reducing computational complexity from approximately $O(n^2)$ to $O(n)$. We evaluate the proposed method against state-of-the-art alternatives using simulations, canonical reference datasets, Indian village network data, and human gene expression data.

We propose OCDaf, a novel order-based method for learning causal graphs from observational data. We establish the identifiability of causal graphs within multivariate heteroscedastic noise models, a generalization of additive noise models that allow for non-constant noise variances. Drawing upon the structural similarities between these models and affine autoregressive normalizing flows, we introduce a continuous search algorithm to find causal structures. Our experiments demonstrate state-of-the-art performance across the Sachs and SynTReN benchmarks in Structural Hamming Distance (SHD) and Structural Intervention Distance (SID). Furthermore, we validate our identifiability theory across various parametric and nonparametric synthetic datasets and showcase superior performance compared to existing baselines.

Standard online change point detection (CPD) methods tend to have large false discovery rates as their detections are sensitive to outliers. To overcome this drawback, we propose Greedy Online Change Point Detection (GOCPD), a computationally appealing method which finds change points by maximizing the probability of the data coming from the (temporal) concatenation of two independent models. We show that, for time series with a single change point, this objective is unimodal and thus CPD can be accelerated via ternary search with logarithmic complexity. We demonstrate the effectiveness of GOCPD on synthetic data and validate our findings on real-world univariate and multivariate settings.

This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a very general and more realistic setup in which the comparison graph consists of hyper-edges of possible heterogeneous sizes and the number of comparisons can be as low as one for a given hyper-edge. Such a setting is pervasive in real applications, circumventing the need to specify the graph randomness and the restrictive homogeneous sampling assumption imposed in the commonly-used Bradley-Terry-Luce (BTL) or Plackett-Luce (PL) models. Furthermore, in the scenarios when the BTL or PL models are appropriate, we unravel the relationship between the spectral estimator and the Maximum Likelihood Estimator (MLE). We discover that a two-step spectral method, where we apply the optimal weighting estimated from the equal weighting vanilla spectral method, can achieve the same asymptotic efficiency as the MLE. Given the asymptotic distributions of the estimated preference scores, we also introduce a comprehensive framework to carry out both one-sample and two-sample ranking inferences, applicable to both fixed and random graph settings. It is noteworthy that it is the first time effective two-sample rank testing methods are proposed. Finally, we substantiate our findings via comprehensive numerical simulations and subsequently apply our developed methodologies to perform statistical inferences on statistics journals and movie rankings.

Semantic communications are expected to accomplish various semantic tasks with relatively less spectrum resource by exploiting the semantic feature of source data. To simultaneously serve both the data transmission and semantic tasks, joint data compression and semantic analysis has become pivotal issue in semantic communications. This paper proposes a deep separate source-channel coding (DSSCC) framework for the joint task and data oriented semantic communications (JTD-SC) and utilizes the variational autoencoder approach to solve the rate-distortion problem with semantic distortion. First, by analyzing the Bayesian model of the DSSCC framework, we derive a novel rate-distortion optimization problem via the Bayesian inference approach for general data distributions and semantic tasks. Next, for a typical application of joint image transmission and classification, we combine the variational autoencoder approach with a forward adaption scheme to effectively extract image features and adaptively learn the density information of the obtained features. Finally, an iterative training algorithm is proposed to tackle the overfitting issue of deep learning models. Simulation results reveal that the proposed scheme achieves better coding gain as well as data recovery and classification performance in most scenarios, compared to the classical compression schemes and the emerging deep joint source-channel schemes.

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.

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.