Evaluating the Role of Stochastic Optimization in Parameter Estimation for Complex Statistical Models

Posted: Jul 22, 2018

• Isla Hayes
• Jasmine Reed
• Jason Powell

Abstract

The estimation of parameters in complex statistical models represents a fundamental challenge in computational statistics and machine learning. Traditional optimization methods, including gradient-based approaches and expectation-maximization algorithms, frequently encounter limitations when applied to high-dimensional parameter spaces characterized by non-convex likelihood surfaces and complex dependency structures. These challenges are particularly pronounced in Bayesian hierarchical models, mixture distributions, and time-series models where the parameter space exhibits multiple local optima and complex correlation patterns. The conventional wisdom in statistical computing has largely favored deterministic optimization techniques due to their theoretical guarantees and predictable convergence behavior. However, this preference comes at the cost of computational efficiency and practical applicability in increasingly complex modeling scenarios. Stochastic optimization offers a promising alternative framework that embraces randomness as a computational resource rather than treating it as a nuisance. The core premise of stochastic optimization lies in its ability to efficiently explore complex parameter spaces through controlled randomization, potentially escaping local optima and discovering globally optimal solutions. Despite these theoretical advantages, the application of stochastic optimization to statistical parameter estimation remains underexplored, with existing literature primarily focusing on simplified model structures or specific algorithm classes. This research gap is particularly significant given the growing complexity of statistical models employed in contemporary data science applications. This paper addresses several critical research questions that have received limited attention in the existing literature. First, we investigate whether stochastic optimization techniques can consistently outperform traditional deterministic methods across diverse statistical model families. Second, we examine the conditions under which stochastic optimization provides the greatest benefits, considering factors such as model complexity, sample size, and parameter dimensionality. Third, we develop novel hybrid approaches that combine elements of stochastic and deterministic optimization to leverage the strengths of both.