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The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising the need to explore the patterns behind them further. To this end, we propose a hypothesis-driven statistical framework. We use a Bayesian network to implement a hypothesis about how a task (in our example, natural language inference) is solved, and its internal states are translated into natural language with templates. Those explanations are then compared to LLM-generated free-text explanations using automatic and human evaluations. This allows us to judge how similar the LLM's and the Bayesian network's decision processes are. We demonstrate the usage of our framework with an example hypothesis and two realisations in Bayesian networks. The resulting models do not exhibit a strong similarity to GPT-3.5. We discuss the implications of this as well as the framework's potential to approximate LLM decisions better in future work.

This study investigates the asymptotic dynamics of alternating minimization applied to optimize a bilinear non-convex function with normally distributed covariates. We employ the replica method from statistical physics in a multi-step approach to precisely trace the algorithm's evolution. Our findings indicate that the dynamics can be described effectively by a two--dimensional discrete stochastic process, where each step depends on all previous time steps, revealing a memory dependency in the procedure. The theoretical framework developed in this work is broadly applicable for the analysis of various iterative algorithms, extending beyond the scope of alternating minimization.

This paper presents a new method for combining (or aggregating or ensembling) multivariate probabilistic forecasts, considering dependencies between quantiles and marginals through a smoothing procedure that allows for online learning. We discuss two smoothing methods: dimensionality reduction using Basis matrices and penalized smoothing. The new online learning algorithm generalizes the standard CRPS learning framework into multivariate dimensions. It is based on Bernstein Online Aggregation (BOA) and yields optimal asymptotic learning properties. The procedure uses horizontal aggregation, i.e., aggregation across quantiles. We provide an in-depth discussion on possible extensions of the algorithm and several nested cases related to the existing literature on online forecast combination. We apply the proposed methodology to forecasting day-ahead electricity prices, which are 24-dimensional distributional forecasts. The proposed method yields significant improvements over uniform combination in terms of continuous ranked probability score (CRPS). We discuss the temporal evolution of the weights and hyperparameters and present the results of reduced versions of the preferred model. A fast C++ implementation of the proposed algorithm is provided in the open-source R-Package profoc on CRAN.

We study inference on the long-term causal effect of a continual exposure to a novel intervention, which we term a long-term treatment, based on an experiment involving only short-term observations. Key examples include the long-term health effects of regularly-taken medicine or of environmental hazards and the long-term effects on users of changes to an online platform. This stands in contrast to short-term treatments or ``shocks," whose long-term effect can reasonably be mediated by short-term observations, enabling the use of surrogate methods. Long-term treatments by definition have direct effects on long-term outcomes via continual exposure, so surrogacy conditions cannot reasonably hold. We connect the problem with offline reinforcement learning, leveraging doubly-robust estimators to estimate long-term causal effects for long-term treatments and construct confidence intervals.

This paper introduces and investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally dependent dimensions, assess the advantages of each test statistic, examine their respective null distributions, and present a fast chi-square-based testing procedure. The resulting tests are non-parametric and applicable to both Euclidean distance and the Gaussian kernel as the underlying metric. To better understand the practical use cases of the proposed tests, we evaluate the empirical performance of the maximum distance correlation, average distance correlation, and the original distance correlation across various multivariate dependence scenarios, as well as conduct a real data experiment to test the presence of various cancer types and peptide levels in human plasma.

This paper introduces an innovative guidance and control method for simultaneously capturing and stabilizing a fast-spinning target satellite, such as a spin-stabilized satellite, using a spinning-base servicing satellite equipped with a robotic manipulator, joint locks, and reaction wheels (RWs). The method involves controlling the RWs of the servicing satellite to replicate the spinning motion of the target satellite, while locking the manipulator's joints to achieve spin-matching. This maneuver makes the target stationary with respect to the rotating frame of the servicing satellite located at its center-of-mass (CoM), simplifying the robot capture trajectory planning and eliminating post-capture trajectory planning entirely. In the next phase, the joints are unlocked, and a coordination controller drives the robotic manipulator to capture the target satellite while maintaining zero relative rotation between the servicing and target satellites. The spin stabilization phase begins after completing the capture phase, where the joints are locked to form a single tumbling rigid body consisting of the rigidly connected servicing and target satellites. An optimal controller applies negative control torques to the RWs to dampen out the tumbling motion of the interconnected satellites as quickly as possible, subject to the actuation torque limit of the RWs and the maximum torque exerted by the manipulator's end-effector.

This paper introduces a novel numerical approach to achieving smooth lane-change trajectories in autonomous driving scenarios. Our trajectory generation approach leverages particle swarm optimization (PSO) techniques, incorporating Neural Network (NN) predictions for trajectory refinement. The generation of smooth and dynamically feasible trajectories for the lane change maneuver is facilitated by combining polynomial curve fitting with particle propagation, which can account for vehicle dynamics. The proposed planning algorithm is capable of determining feasible trajectories with real-time computation capability. We conduct comparative analyses with two baseline methods for lane changing, involving analytic solutions and heuristic techniques in numerical simulations. The simulation results validate the efficacy and effectiveness of our proposed approach.

This paper discusses two approaches to the diachronic normalization of Polish texts: a rule-based solution that relies on a set of handcrafted patterns, and a neural normalization model based on the text-to-text transfer transformer architecture. The training and evaluation data prepared for the task are discussed in detail, along with experiments conducted to compare the proposed normalization solutions. A quantitative and qualitative analysis is made. It is shown that at the current stage of inquiry into the problem, the rule-based solution outperforms the neural one on 3 out of 4 variants of the prepared dataset, although in practice both approaches have distinct advantages and disadvantages.

This paper investigates truck-involved crashes to determine the statistically significant factors that contribute to injury severity under different weather conditions. The analysis uses crash data from the state of Ohio between 2011 and 2015 available from the Highway Safety Information System. To determine if weather conditions should be considered separately for truck safety analyses, parameter transferability tests are conducted; the results suggest that weather conditions should be modeled separately with a high level of statistical confidence. To this end, three separate mixed logit models are estimated for three different weather conditions: normal, rain and snow. The estimated models identify a variety of statistically significant factors influencing the injury severity. Different weather conditions are found to have different contributing effects on injury severity in truck-involved crashes. Rural, rear-end and sideswipe crash parameters were found to have significantly different levels of impact on injury severity. Based on the findings of this study, several countermeasures are suggested: 1) safety and enforcement programs should focus on female truck drivers, 2) a variable speed limit sign should be used to lower speeds of trucks during rainy condition, and 3) trucks should be restricted or prohibited on non-interstates during rainy and snowy conditions. These countermeasures could reduce the number and severity of truck-involved crashes under different weather conditions.

This paper explores the use of unstructured, multimodal data, namely text and images, in causal inference and treatment effect estimation. We propose a neural network architecture that is adapted to the double machine learning (DML) framework, specifically the partially linear model. An additional contribution of our paper is a new method to generate a semi-synthetic dataset which can be used to evaluate the performance of causal effect estimation in the presence of text and images as confounders. The proposed methods and architectures are evaluated on the semi-synthetic dataset and compared to standard approaches, highlighting the potential benefit of using text and images directly in causal studies. Our findings have implications for researchers and practitioners in economics, marketing, finance, medicine and data science in general who are interested in estimating causal quantities using non-traditional data.