In many cases of crimes involving a firearm, police investigators need to know how far the firearm was held from the victim when it was discharged. Knowing this distance, vital questions regarding the re-construction of the crime scene can be known. Often, the original firearm used in commission of a suspected crime is not available for testing or is damaged. Crime laboratories require the original firearm in order to conduct distance determination tests. However, no empirical research has ever been conducted to determine if same make and model firearms produce different results in distance determination testing. It was the purpose of this study to determine if there are significant differences between the same make and model of firearms in distance determination testing. The findings indicate no significant differences; furthermore they imply that if the original firearm is not available, another firearm of the same make and model may be used.

Sorting out data into partitions is increasing becoming complex as the constituents of data is growing outward everyday. Mixed data comprises continuous, categorical, directional functional and other types of variables. Clustering mixed data is based on special dissimilarities of the variables. Some data types may influence the clustering solution. Assigning appropriate weight to the functional data may improve the performance of the clustering algorithm. In this paper we use the extension of the Gower coefficient with judciously chosen weight for the L2 to cluster mixed data.The benefits of weighting are demonstrated both in in applications to the Buoy data set as well simulation studies. Our studies show that clustering algorithms with application of proper weight give superior recovery level when a set of data with mixed continuous, categorical directional and functional attributes is clustered. We discuss open problems for future research in clustering mixed data.

<p>Although deep learning models continue to gain momentum, their robustness and interpretability have always been a big concern because of the complexity of such models. In this dissertation, we studied several topics on the robustness and interpretability of convolutional neural networks (CNNs) and graph neural networks (GNNs). We first identified the structural problem of deep convolutional neural networks that leads to the adversarial examples and defined DNN uncertainty regions. We also argued that the generalization error, the large sample theoretical guarantee established for DNN, cannot adequately capture the phenomenon of adversarial examples. Secondly, we studied the dropout in GNNs, which is an effective regularization approach to prevent overfitting. Contrary to CNN, GNN usually has a shallow structure because a deep GNN normally sees performance degradation. We studied different dropout schemes and established a connection between dropout and over-smoothing in GNNs. Therefore we developed layer-wise compensation dropout, which allows GNN to go deeper without suffering performance degradation. We also developed a heteroscedastic dropout which effectively deals with a large number of missing node features due to heavy experimental noise or privacy issues. Lastly, we studied the interpretability of graph neural networks. We developed a self-interpretable GNN structure that denoises useless edges or features, leading to a more efficient message-passing process. The GNN prediction and explanation accuracy were boosted compared with baseline models. </p>

Sig sigma is a methodology where companies strive to reproduce results ending up having a 99.9996% chance their product will be void of defects. In order for companies to reach six sigma, statistical process control (SPC) needs to be introduced. SPC has many different tools associated with it, control charts being one of them. Control charts play a vital role in managing how a process is behaving. Control charts allow users to identify special causes, or shifts, and can therefore change the process to keep producing good products, free of defects. There are many factories and manufacturing facilities having implemented some sort of statistical process control. St. Jude Medical implemented control charts to monitor different tools on the manufacturing line. How the data is entered and stored poses a difficult situation for the person monitoring the processes. The program used to keep the control charts is not user friendly and difficult to use. Another program can be produced to provide a greater level of efficiency. The goals of this project are to stress how important control charts are in the manufacturing world, what problems are currently seen for operators and supervisors, and how a new and improved program can help fix the current situation. This paper goes into the reasons for the change as well has what has been improved.

<p dir="ltr">The research focuses on improving natural language processing (NLP) models by integrating the hierarchical structure of language, which is essential for understanding and generating human language. The main contributions of the study are:</p><ol><li><b>Hierarchical RNN Model:</b> Development of a deep Recurrent Neural Network model that captures both explicit and implicit hierarchical structures in language.</li><li><b>Hierarchical Attention Mechanism:</b> Use of a multi-level attention mechanism to help the model prioritize relevant information at different levels of the hierarchy.</li><li><b>Latent Indicators and Efficient Training:</b> Integration of latent indicators using the Expectation-Maximization algorithm and reduction of computational complexity with Bootstrap sampling and layered training strategies.</li><li><b>Sequence-to-Sequence Model for Translation:</b> Extension of the model to translation tasks, including a novel pre-training technique and a hierarchical decoding strategy to stabilize latent indicators during generation.</li></ol><p dir="ltr">The study claims enhanced performance in various NLP tasks with results comparable to larger models, with the added benefit of increased interpretability.</p>

<p dir="ltr">Bandit and optimization represent prominent areas of machine learning research. Despite extensive prior research on these topics in various contexts, modern challenges, such as deal- ing with highly unsmooth nonlinear reward objectives and incorporating federated learning, have sparked new discussions. The X-armed bandit problem is a specialized case where bandit algorithms and blackbox optimization techniques join forces to address noisy reward functions within continuous domains to minize the regret. This thesis concentrates on the X -armed bandit problem in a modern setting. In the first chapter, we introduce an optimal statistical collaboration framework for the single-client X -armed bandit problem, expanding the range of objectives by considering more general smoothness assumptions and empha- sizing tighter statistical error measures to expedite learning. The second chapter addresses the federated X-armed bandit problem, providing a solution for collaboratively optimizing the average global objective while ensuring client privacy. In the third chapter, we confront the more intricate personalized federated X -armed bandit problem. An enhanced algorithm facilitating the simultaneous optimization of all local objectives is proposed.</p>

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability. In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based upon general trends in the data, we recommend potential actions the company could take. Additionally, we examine how a company can utilize predictive modeling to help them adapt their decision-making process as the trends identified from the initial analysis of the data evolve over time.

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<p><em>Image-to-image regression is an important computer vision research topic. Previous</em></p> <p><em>research works have been concentrating on task-dependent end-to-end regression models. In</em></p> <p><em>this dissertation, we focus on a generative regression framework based on score matching.</em></p> <p><em>Such generative models are called score-based generative models, which learn the data score</em></p> <p><em>functions by gradually adding noise to data using a diffusion process. Images can be generated</em></p> <p><em>with learned score functions through a time-reversal sampling process.</em></p> <p><em>First, we propose a conditional score matching regression framework which targets the</em></p> <p><em>conditional score functions in regression problems. The framework can perform diverse inferences</em></p> <p><em>about conditional distribution by generating samples. We demonstrate its advantages</em></p> <p><em>with various image-to-image regression applications.</em></p> <p><em>Second, we propose a score-based regression model that applies the diffusion process to</em></p> <p><em>both input and response images simultaneously. The proposed method, called synchronized</em></p> <p><em>diffusion, can help stabilize model parameter learning and increase model robustness. In</em></p> <p><em>addition, we develop an effective prediction algorithm based on the Expectation-Maximization</em></p> <p><em>(EM) algorithm which can improve accuracy and computation speed. We illustrate the efficacy</em></p> <p><em>of our proposed approach on high-resolution image datasets.</em></p> <p><em>The last part of the dissertation focuses on analyzing the score-based generative modeling</em></p> <p><em>framework. We conduct a theoretical analysis of the variance exploding behavior observed in</em></p> <p><em>training score-based generative models with denoising score matching objective functions. We</em></p> <p><em>explain the large variance problem from a nonparametric estimation perspective. Furthermore,</em></p> <p><em>we propose a solution to the general score function estimation problem based on Simulation-</em></p> <p><em>Extrapolation (SIMEX), which was originally developed in the measurement error model</em></p> <p><em>literature. We validate our theoretical findings and the effectiveness of the proposed solution</em></p> <p><em>on both synthesized and real datasets.</em></p>

Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected by the author and friends and investigate how that data is different from Minimax optimal play.