Comprehending how consumers react to advertising inputs is essential for marketers aiming to optimize advertising strategies and improve campaign effectiveness. This study examines the complex nature of consumer behaviour by applying theoretical frameworks derived from physics and social psychology. We present an innovative equation that captures the relation between spending on advertising and consumer response, using concepts such as symmetries, scaling laws, and phase transitions. By validating our equation against well-known models such as the Michaelis-Menten and Hill equations, we prove its effectiveness in accurately representing the complexity of consumer response dynamics. The analysis emphasizes the importance of key model parameters, such as marketing effectiveness, response sensitivity, and behavioural sensitivity, in influencing consumer behaviour. The work explores the practical implications for advertisers and marketers, as well as discussing the limitations and future research directions. In summary, this study provides a thorough framework for comprehending and forecasting consumer reactions to advertising, which has implications for optimizing advertising strategies and allocating resources.

We study the problem of distributed and rate-adaptive feature compression for linear regression. A set of distributed sensors collect disjoint features of regressor data. A fusion center is assumed to contain a pretrained linear regression model, trained on a dataset of the entire uncompressed data. At inference time, the sensors compress their observations and send them to the fusion center through communication-constrained channels, whose rates can change with time. Our goal is to design a feature compression {scheme} that can adapt to the varying communication constraints, while maximizing the inference performance at the fusion center. We first obtain the form of optimal quantizers assuming knowledge of underlying regressor data distribution. Under a practically reasonable approximation, we then propose a distributed compression scheme which works by quantizing a one-dimensional projection of the sensor data. We also propose a simple adaptive scheme for handling changes in communication constraints. We demonstrate the effectiveness of the distributed adaptive compression scheme through simulated experiments.

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this work, we tackle model shifts in the presence of covariate shifts in the high-dimensional regression setting. Specifically, we propose a two-step method with a novel fused-regularizer that effectively leverages samples from source tasks to improve the learning performance on a target task with limited samples. Nonasymptotic bound is provided for the estimation error of the target model, showing the robustness of the proposed method to covariate shifts. We further establish conditions under which the estimator is minimax-optimal. Additionally, we extend the method to a distributed setting, allowing for a pretraining-finetuning strategy, requiring just one round of communication while retaining the estimation rate of the centralized version. Numerical tests validate our theory, highlighting the method's robustness to covariate shifts.

Linear models are ubiquitous in data science, but are particularly prone to overfitting and data memorization in high dimensions. To guarantee the privacy of training data, differential privacy can be used. Many papers have proposed optimization techniques for high-dimensional differentially private linear models, but a systematic comparison between these methods does not exist. We close this gap by providing a comprehensive review of optimization methods for private high-dimensional linear models. Empirical tests on all methods demonstrate robust and coordinate-optimized algorithms perform best, which can inform future research. Code for implementing all methods is released online.

Social media data has been used for detecting users with mental disorders, such as depression. Despite the global significance of cross-cultural representation and its potential impact on model performance, publicly available datasets often lack crucial metadata related to this aspect. In this work, we evaluate the generalization of benchmark datasets to build AI models on cross-cultural Twitter data. We gather a custom geo-located Twitter dataset of depressed users from seven countries as a test dataset. Our results show that depression detection models do not generalize globally. The models perform worse on Global South users compared to Global North. Pre-trained language models achieve the best generalization compared to Logistic Regression, though still show significant gaps in performance on depressed and non-Western users. We quantify our findings and provide several actionable suggestions to mitigate this issue.

Advances in machine learning and increased computational power have driven progress in energy-related research. However, limited access to private energy data from buildings hinders traditional regression models relying on historical data. While generative models offer a solution, previous studies have primarily focused on short-term generation periods (e.g., daily profiles) and a limited number of meters. Thus, the study proposes a conditional diffusion model for generating high-quality synthetic energy data using relevant metadata. Using a dataset comprising 1,828 power meters from various buildings and countries, this model is compared with traditional methods like Conditional Generative Adversarial Networks (CGAN) and Conditional Variational Auto-Encoders (CVAE). It explicitly handles long-term annual consumption profiles, harnessing metadata such as location, weather, building, and meter type to produce coherent synthetic data that closely resembles real-world energy consumption patterns. The results demonstrate the proposed diffusion model's superior performance, with a 36% reduction in Frechet Inception Distance (FID) score and a 13% decrease in Kullback-Leibler divergence (KL divergence) compared to the following best method. The proposed method successfully generates high-quality energy data through metadata, and its code will be open-sourced, establishing a foundation for a broader array of energy data generation models in the future.

This study examines the effects of macroeconomic policies on financial markets using a novel approach that combines Machine Learning (ML) techniques and causal inference. It focuses on the effect of interest rate changes made by the US Federal Reserve System (FRS) on the returns of fixed income and equity funds between January 1986 and December 2021. The analysis makes a distinction between actively and passively managed funds, hypothesizing that the latter are less susceptible to changes in interest rates. The study contrasts gradient boosting and linear regression models using the Double Machine Learning (DML) framework, which supports a variety of statistical learning techniques. Results indicate that gradient boosting is a useful tool for predicting fund returns; for example, a 1% increase in interest rates causes an actively managed fund's return to decrease by -11.97%. This understanding of the relationship between interest rates and fund performance provides opportunities for additional research and insightful, data-driven advice for fund managers and investors

Transfer learning is a critical part of real-world machine learning deployments and has been extensively studied in experimental works with overparameterized neural networks. However, even in the simplest setting of linear regression a notable gap still exists in the theoretical understanding of transfer learning. In-distribution research on high-dimensional linear regression has led to the identification of a phenomenon known as \textit{benign overfitting}, in which linear interpolators overfit to noisy training labels and yet still generalize well. This behavior occurs under specific conditions on the source covariance matrix and input data dimension. Therefore, it is natural to wonder how such high-dimensional linear models behave under transfer learning. We prove the first non-asymptotic excess risk bounds for benignly-overfit linear interpolators in the transfer learning setting. From our analysis, we propose a taxonomy of \textit{beneficial} and \textit{malignant} covariate shifts based on the degree of overparameterization. We follow our analysis with empirical studies that show these beneficial and malignant covariate shifts for linear interpolators on real image data, and for fully-connected neural networks in settings where the input data dimension is larger than the training sample size.

Additive Gaussian Processes (GPs) are popular approaches for nonparametric feature selection. The common training method for these models is Bayesian Back-fitting. However, the convergence rate of Back-fitting in training additive GPs is still an open problem. By utilizing a technique called Kernel Packets (KP), we prove that the convergence rate of Back-fitting is no faster than $(1-\mathcal{O}(\frac{1}{n}))^t$, where $n$ and $t$ denote the data size and the iteration number, respectively. Consequently, Back-fitting requires a minimum of $\mathcal{O}(n\log n)$ iterations to achieve convergence. Based on KPs, we further propose an algorithm called Kernel Multigrid (KMG). This algorithm enhances Back-fitting by incorporating a sparse Gaussian Process Regression (GPR) to process the residuals after each Back-fitting iteration. It is applicable to additive GPs with both structured and scattered data. Theoretically, we prove that KMG reduces the required iterations to $\mathcal{O}(\log n)$ while preserving the time and space complexities at $\mathcal{O}(n\log n)$ and $\mathcal{O}(n)$ per iteration, respectively. Numerically, by employing a sparse GPR with merely 10 inducing points, KMG can produce accurate approximations of high-dimensional targets within 5 iterations.

Price prediction algorithms propose prices for every product or service according to market trends, projected demand, and other characteristics, including government rules, international transactions, and speculation and expectation. As the dependent variable in price prediction, it is affected by several independent and correlated variables which may challenge the price prediction. To overcome this challenge, machine learning algorithms allow more accurate price prediction without explicitly modeling the relatedness between variables. However, as inputs increase, it challenges the existing machine learning approaches regarding computing efficiency and prediction effectiveness. Hence, this study introduces a novel decision level fusion approach to select informative variables in price prediction. The suggested metaheuristic algorithm balances two competitive objective functions, which are defined to improve the prediction utilized variables and reduce the error rate simultaneously. To generate Pareto optimal solutions, an Elastic net approach is employed to eliminate unrelated and redundant variables to increase the accuracy. Afterward, we propose a novel method for combining solutions and ensuring that a subset of features is optimal. Two various real datasets evaluate the proposed price prediction method. The results support the suggested superiority of the model concerning its relative root mean square error and adjusted correlation coefficient.