A WRM incorporates an adversarial policy that exploits the model to generate a data distribution that weakens the model's

Recently, a provocative claim was published that number sense spontaneously emerges in a deep neural network trained merely for visual object recognition.

We consider the problem of partial identification, the estimation of bounds on the treatment effects from observational data.

We perform a random search [43] for hyperparameter optimization over the search ranges in Table 6.

Motivated by the great success of Bayesian additive regression trees (BART) on regression, we propose a nonparametric Bayesian approach for the function-on-scalar regression problem, termed as Functional BART (FBART). Utilizing spline-based function representation and tree-based domain partition model, FBART offers great flexibility in characterizing the complex and heterogeneous relationship between the response curve and scalar covariates. We devise a tailored Bayesian backfitting algorithm for estimating the parameters in the FBART model. Furthermore, we introduce an FBART model with shape constraints on the response curve, enhancing estimation and prediction performance when prior shape information of response curves is available. By incorporating a shape-constrained prior, we ensure that the posterior samples of the response curve satisfy the required shape constraints (e.g., monotonicity and/or convexity). Our proposed FBART model and its shape-constrained version are the new advances of BART models for functional data. Under certain regularity conditions, we derive the posterior convergence results for both FBART and its shape-constrained version. Finally, the superiority of the proposed methods over other competitive counterparts is validated through simulation experiments under various settings and analyses of two real datasets.

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.