In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to assess their effectiveness in predicting the 20-day variation in the pairs' daily returns. Our analysis involves the implementation of Exponentially Weighted Moving Average (EWMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Implied Volatility (IV) models. To evaluate their performance, we compare the accuracy of their predictions using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. We delve into the intricacies of GARCH models, examining their statistical characteristics when applied to the provided dataset. Our findings suggest the existence of asymmetric returns in the EUR/GBP pair, while such evidence is inconclusive for the GBP/USD pair. Additionally, we observe that GARCH-type models better fit the data when assuming residuals follow a standard t-distribution rather than a standard normal distribution. Furthermore, we investigate the efficacy of different forecasting techniques within GARCH-type models. Comparing rolling window forecasts to expanding window forecasts, we find no definitive superiority in either approach across the tested scenarios. Our experiments reveal that for the GBP/USD pair, the most accurate volatility forecasts stem from the utilization of GARCH models employing a rolling window methodology. Conversely, for the EUR/GBP pair, optimal forecasts are derived from GARCH models and Ordinary Least Squares (OLS) models incorporating the annualized implied volatility of the exchange rate as an independent variable. Keywords: Euro, Exponentially Weighted Moving Average, Generalized Autoregressive Conditional Heteroskedasticity, Great Britain Pound, Implied Volatility, United States Dollar 1. Introduction As defined by the [1], a volatility of a financial asset is simply how much its price changes over time.

Simultaneous Localization and Mapping (SLAM) presents a formidable challenge in robotics, involving the dynamic construction of a map while concurrently determining the precise location of the robotic agent within an unfamiliar environment. This intricate task is further compounded by the inherent "chicken-and-egg" dilemma, where accurate mapping relies on a dependable estimation of the robot's location, and vice versa. Moreover, the computational intensity of SLAM adds an additional layer of complexity, making it a crucial yet demanding topic in the field. In our research, we address the challenges of SLAM by adopting the Particle Filter SLAM method. Our approach leverages encoded data and fiber optic gyro (FOG) information to enable precise estimation of vehicle motion, while lidar technology contributes to environmental perception by providing detailed insights into surrounding obstacles. The integration of these data streams culminates in the establishment of a Particle Filter SLAM framework, representing a key endeavor in this paper to effectively navigate and overcome the complexities associated with simultaneous localization and mapping in robotic systems.

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in both deterministic and stochastic settings. We conduct extensive convergence analysis and show that by choosing the inexactness tolerances appropriately, the inexact schemes admit an $O(k^{-1})$ convergence rate in terms of the (expected) residue norm. Our results relax the state-of-the-art inexactness conditions employed in the literature while sharing the same competitive convergence properties. We then demonstrate how the proposed methods can be applied for solving two classes of data-driven Wasserstein distributionally robust optimization problems that admit convex-concave min-max optimization reformulations. We highlight its capability of performing inexact computations for distributionally robust learning with stochastic first-order methods.

Recently, deep reinforcement learning has shown promising results for learning fast heuristics to solve routing problems. Meanwhile, most of the solvers suffer from generalizing to an unseen distribution or distributions with different scales. To address this issue, we propose a novel architecture, called Invariant Nested View Transformer (INViT), which is designed to enforce a nested design together with invariant views inside the encoders to promote the generalizability of the learned solver. It applies a modified policy gradient algorithm enhanced with data augmentations. We demonstrate that the proposed INViT achieves a dominant generalization performance on both TSP and CVRP problems with various distributions and different problem scales.

The US Census Bureau has collected two rounds of experimental data from the Commodity Flow Survey, providing shipment-level characteristics of nationwide commodity movements, published in 2012 (i.e., Public Use Microdata) and in 2017 (i.e., Public Use File). With this information, data-driven methods have become increasingly valuable for understanding detailed patterns in freight logistics. In this study, we used the 2017 Commodity Flow Survey Public Use File data set to explore building a high-performance freight mode choice model, considering three main improvements: (1) constructing local models for each separate commodity/industry category; (2) extracting useful geographical features, particularly the derived distance of each freight mode between origin/destination zones; and (3) applying additional ensemble learning methods such as stacking or voting to combine results from local and unified models for improved performance. The proposed method achieved over 92% accuracy without incorporating external information, an over 19% increase compared to directly fitting Random Forests models over 10,000 samples. Furthermore, SHAP (Shapely Additive Explanations) values were computed to explain the outputs and major patterns obtained from the proposed model. The model framework could enhance the performance and interpretability of existing freight mode choice models.

We present a novel approach for differentially private data synthesis of protected tabular datasets, a relevant task in highly sensitive domains such as healthcare and government. Current state-of-the-art methods predominantly use marginal-based approaches, where a dataset is generated from private estimates of the marginals. In this paper, we introduce PrivPGD, a new generation method for marginal-based private data synthesis, leveraging tools from optimal transport and particle gradient descent. Our algorithm outperforms existing methods on a large range of datasets while being highly scalable and offering the flexibility to incorporate additional domain-specific constraints.

Transformer models have achieved remarkable results in a wide range of applications. However, their scalability is hampered by the quadratic time and memory complexity of the self-attention mechanism concerning the sequence length. This limitation poses a substantial obstacle when dealing with long documents or high-resolution images. In this work, we study the self-attention mechanism by analyzing the distribution of the attention matrix and its concentration ability. Furthermore, we propose instruments to measure these quantities and introduce a novel self-attention mechanism, Linear Log-Normal Attention, designed to emulate the distribution and concentration behavior of the original self-attention. Our experimental results on popular natural language benchmarks reveal that our proposed Linear Log-Normal Attention outperforms other linearized attention alternatives, offering a promising avenue for enhancing the scalability of transformer models.

We study the asymptotic behavior of second-order algorithms mixing Newton's method and inertial gradient descent in non-convex landscapes. We show that, despite the Newtonian behavior of these methods, they almost always escape strict saddle points. We also evidence the role played by the hyper-parameters of these methods in their qualitative behavior near critical points. The theoretical results are supported by numerical illustrations.

However, a decision-makers often take identical actions in limitation of CP is that the prediction intervals provide valid contexts with identical predicted outcomes. Conformal coverage only marginally, averaged across all possible contexts prediction helps decision-makers quantify - where'context' refers to the information available for outcome uncertainty for actions, allowing for better decision-making. Thus, for a specific context, CP intervals risk management. Inspired by this perspective, may not accurately capture the true outcome variability, leading we introduce self-consistent conformal prediction, to unreliable and potentially harmful decision-making which yields both Venn-Abers calibrated predictions (van Calster et al., 2019; Lloyd-Jones et al., 2019).

Human Activity Recognition (HAR) has been studied for decades, from data collection, learning models, to post-processing and result interpretations. However, the inherent hierarchy in the activities remains relatively under-explored, despite its significant impact on model performance and interpretation. In this paper, we propose H-HAR, by rethinking the HAR tasks from a fresh perspective by delving into their intricate global label relationships. Rather than building multiple classifiers separately for multi-layered activities, we explore the efficacy of a flat model enhanced with graph-based label relationship modeling. Being hierarchy-aware, the graph-based label modeling enhances the fundamental HAR model, by incorporating intricate label relationships into the model. We validate the proposal with a multi-label classifier on complex human activity data. The results highlight the advantages of the proposal, which can be vertically integrated into advanced HAR models to further enhance their performances.