Black Box Variational Inference is a method that allows for quick and efficient approximation of posterior distributions in complex latent variable models without requiring detailed model-specific analysis. The method uses stochastic optimization to maximize the Evidence Lower Bound (ELBO), where gradients are estimated using Monte Carlo samples from the variational distribution. Variance reduction techniques, such as Rao-Blackwellization and control variates, are employed to improve the efficiency and convergence of the algorithm. The method is evaluated against sampling-based techniques and shown to achieve better predictive likelihoods faster. It is demonstrated that Black Box Variational Inference can be applied to a wide range of models, including longitudinal healthcare data, enabling rapid exploration and evaluation of different modeling assumptions. The algorithm is implemented using stochastic optimization, with adaptive learning rates and subsampling to enhance scalability and performance. The method is shown to be effective in various applications, including hierarchical Bayesian models and non-conjugate models, where traditional variational inference techniques are difficult to apply. The key advantage of Black Box Variational Inference is its ability to work with a wide variety of models with minimal analytical effort, making it a powerful tool for probabilistic modeling.Black Box Variational Inference is a method that allows for quick and efficient approximation of posterior distributions in complex latent variable models without requiring detailed model-specific analysis. The method uses stochastic optimization to maximize the Evidence Lower Bound (ELBO), where gradients are estimated using Monte Carlo samples from the variational distribution. Variance reduction techniques, such as Rao-Blackwellization and control variates, are employed to improve the efficiency and convergence of the algorithm. The method is evaluated against sampling-based techniques and shown to achieve better predictive likelihoods faster. It is demonstrated that Black Box Variational Inference can be applied to a wide range of models, including longitudinal healthcare data, enabling rapid exploration and evaluation of different modeling assumptions. The algorithm is implemented using stochastic optimization, with adaptive learning rates and subsampling to enhance scalability and performance. The method is shown to be effective in various applications, including hierarchical Bayesian models and non-conjugate models, where traditional variational inference techniques are difficult to apply. The key advantage of Black Box Variational Inference is its ability to work with a wide variety of models with minimal analytical effort, making it a powerful tool for probabilistic modeling.