This study employs Bayesian methodologies to explore the influence of player or positional factors in predicting the probability of a shot resulting in a goal, measured by the expected goals (xG) metric. Utilising publicly available data from StatsBomb, Bayesian hierarchical logistic regressions are constructed, analysing approximately 10,000 shots from the English Premier League to ascertain whether positional or player-level effects impact xG. The findings reveal positional effects in a basic model that includes only distance to goal and shot angle as predictors, highlighting that strikers and attacking midfielders exhibit a higher likelihood of scoring. However, these effects diminish when more informative predictors are introduced. Nevertheless, even with additional predictors, player-level effects persist, indicating that certain players possess notable positive or negative xG adjustments, influencing their likelihood of scoring a given chance. The study extends its analysis to data from Spain's La Liga and Germany's Bundesliga, yielding comparable results. Additionally, the paper assesses the impact of prior distribution choices on outcomes, concluding that the priors employed in the models provide sound results but could be refined to enhance sampling efficiency for constructing more complex and extensive models feasibly.

Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the importance of an input to the network. We observe that there are two dominant strategies: static sampling, where the scores are determined before training, and dynamic sampling, where the scores can depend on the model weights. Static algorithms are computationally inexpensive but less effective than their dynamic counterparts, which can cause end-to-end slowdown due to their need to explicitly compute losses. To address this problem, we propose a novel sampling distribution based on nonparametric kernel regression that learns an effective importance score as the neural network trains. However, nonparametric regression models are too computationally expensive to accelerate end-to-end training. Therefore, we develop an efficient sketch-based approximation to the Nadaraya-Watson estimator. Using recent techniques from high-dimensional statistics and randomized algorithms, we prove that our Nadaraya-Watson sketch approximates the estimator with exponential convergence guarantees. Our sampling algorithm outperforms the baseline in terms of wall-clock time and accuracy on four datasets.

This paper presents a comprehensive evaluation of three distinct computational algorithms applied to the decision-making process of real estate purchases. Specifically, we analyze the efficacy of Linear Regression from Scikit-learn library, Gaussian Elimination with partial pivoting, and LU Decomposition in predicting the advisability of buying a house in the State of Connecticut based on a set of financial and market-related parameters. The algorithms' performances were compared using a dataset encompassing town-specific details, yearly data, interest rates, and median sale ratios. Our results demonstrate significant differences in predictive accuracy, with Linear Regression and LU Decomposition providing the most reliable recommendations and Gaussian Elimination showing limitations in stability and performance. The study's findings emphasize the importance of algorithm selection in predictive analytic and offer insights into the practical applications of computational methods in real estate investment strategies. By evaluating model efficacy through metrics such as R-squared scores and Mean Squared Error, we provide a nuanced understanding of each method's strengths and weaknesses, contributing valuable knowledge to the fields of real estate analysis and predictive modeling.

This optimization paradigm can naturally be used to formulate fundamental problems in interpretable supervised learning (e.g., sparse regression and decision trees), in unsupervised learning (e.g., clustering), and beyond; BackboneLearn solves the aforementioned problems faster than exact methods and with higher accuracy than commonly used heuristics. The package is built in Python and is user-friendly and easily extensible: users can directly implement a backbone algorithm for their MIO problem at hand.

Robotic capacities in object manipulation are incomparable to those of humans. Besides years of learning, humans rely heavily on the richness of information from physical interaction with the environment. In particular, tactile sensing is crucial in providing such rich feedback. Despite its potential contributions to robotic manipulation, tactile sensing is less exploited; mainly due to the complexity of the time series provided by tactile sensors. In this work, we propose a method for assessing grasp stability using tactile sensing. More specifically, we propose a methodology to extract task-relevant features and design efficient classifiers to detect object slippage with respect to individual fingertips. We compare two classification models: support vector machine and logistic regression. We use highly sensitive Uskin tactile sensors mounted on an Allegro hand to test and validate our method. Our results demonstrate that the proposed method is effective in slippage detection in an online fashion.

In this work, we contribute the first visual open-source empirical study on human behaviour during the COVID-19 pandemic, in order to investigate how compliant a general population is to mask-wearing-related public-health policy. Object-detection-based convolutional neural networks, regression analysis and multilayer perceptrons are combined to analyse visual data of the Viennese public during 2020. We find that mask-wearing-related government regulations and public-transport announcements encouraged correct mask-wearing-behaviours during the COVID-19 pandemic. Importantly, changes in announcement and regulation contents led to heterogeneous effects on people's behaviour. Comparing the predictive power of regression analysis and neural networks, we demonstrate that the latter produces more accurate predictions of population reactions during the COVID-19 pandemic. Our use of regression modelling also allows us to unearth possible causal pathways underlying societal behaviour. Since our findings highlight the importance of appropriate communication contents, our results will facilitate more effective non-pharmaceutical interventions to be developed in future. Adding to the literature, we demonstrate that regression modelling and neural networks are not mutually exclusive but instead complement each other.

Do neural networks, trained on well-understood algorithmic tasks, reliably rediscover known algorithms for solving those tasks? Several recent studies, on tasks ranging from group arithmetic to in-context linear regression, have suggested that the answer is yes. Using modular addition as a prototypical problem, we show that algorithm discovery in neural networks is sometimes more complex. Small changes to model hyperparameters and initializations can induce discovery of qualitatively different algorithms from a fixed training set, and even parallel implementations of multiple such algorithms. Some networks trained to perform modular addition implement a familiar Clock algorithm (previously described by Nanda et al. [1]); others implement a previously undescribed, less intuitive, but comprehensible procedure we term the Pizza algorithm, or a variety of even more complex procedures. Our results show that even simple learning problems can admit a surprising diversity of solutions, motivating the development of new tools for characterizing the behavior of neural networks across their algorithmic phase space.

Bayesian predictive synthesis (BPS) provides a method for combining multiple predictive distributions based on agent/expert opinion analysis theory and encompasses a range of existing density forecast pooling methods. The key ingredient in BPS is a ``synthesis'' function. This is typically specified parametrically as a dynamic linear regression. In this paper, we develop a nonparametric treatment of the synthesis function using regression trees. We show the advantages of our tree-based approach in two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area's Survey of Professional Forecasters. The second combines density forecasts of US inflation produced by many regression models involving different predictors. Both applications demonstrate the benefits -- in terms of improved forecast accuracy and interpretability -- of modeling the synthesis function nonparametrically.

Moore Law states that transistor density will double every two years, which is sustained until today due to continuous multi-directional innovations, such as extreme ultraviolet lithography, novel patterning techniques etc., leading the semiconductor industry towards 3nm node and beyond. For any patterning scheme, the most important metric to evaluate the quality of printed patterns is EPE, with overlay being its largest contribution. Overlay errors can lead to fatal failures of IC devices such as short circuits or broken connections in terms of P2P electrical contacts. Therefore, it is essential to develop effective overlay analysis and control techniques to ensure good functionality of fabricated semiconductor devices. In this work we have used an imec N14 BEOL process flow using LELE patterning technique to print metal layers with minimum pitch of 48nm with 193i lithography. FF structures are decomposed into two mask layers (M1A and M1B) and then the LELE flow is carried out to make the final patterns. Since a single M1 layer is decomposed into two masks, control of overlay between the two masks is critical. The goal of this work is of two-fold as, (a) to quantify the impact of overlay on capacitance and (b) to see if we can predict the final capacitance measurements with selected machine learning models at an early stage. To do so, scatterometry spectra are collected on these electrical test structures at (a)post litho, (b)post TiN hardmask etch, and (c)post Cu plating and CMP. Critical Dimension and overlay measurements for line-space pattern are done with SEM post litho, post etch and post Cu CMP. Various machine learning models are applied to do the capacitance prediction with multiple metrology inputs at different steps of wafer processing. Finally, we demonstrate that by using appropriate machine learning models we are able to do better prediction of electrical results.

Overlapping asymmetric datasets are common in data science and pose questions of how they can be incorporated together into a predictive analysis. In healthcare datasets there is often a small amount of information that is available for a larger number of patients such as an electronic health record, however a small number of patients may have had extensive further testing. Common solutions such as missing data imputation can often be unwise if the smaller cohort is significantly different in scale to the larger sample, therefore the aim of this research is to develop a new method which can model the smaller cohort against a particular response, whilst considering the larger cohort also. Motivated by non-parametric models, and specifically flexible smoothing techniques via generalized additive models, we model a twice penalized P-Spline approximation method to firstly prevent over/under-fitting of the smaller cohort and secondly to consider the larger cohort. This second penalty is created through looking at discrepancies in the marginal value of covariates that exist in both the smaller and larger cohorts. Through a series of data simulations, penalty parameter tunings and model adaptations to consider both a continuous and binary response, we find that our twice penalized approach offers an enhanced model fit over a linear B-Spline model and once penalized P-Spline approximation method. Applying our twice penalized method to a real-life healthcare dataset relating to an individual's risk of developing Non-Alcoholic Steatohepatitis, we see an improved model fit performance of over 65% as opposed to linear and once penalized methods. Areas for future work within this space include adapting our method to not require dimensionality reduction and also consider parametric modelling methods. However, to our knowledge this is the first work to propose additional marginal penalties in a flexible regression of which we can report a vastly improved model fit that is able to consider asymmetric datasets, without the need for missing data imputation.