Relating to or involving variation; characterized by or expressing a process of change or adjustment, often with respect to a parameter or set of parameters, to optimize a specific objective. This frequently arises in optimization problems where one seeks to find the best values for certain variables. It implies a dynamic aspect, where the system or model explores different possibilities before converging towards a solution that minimizes or maximizes some function. The core concept lies in adapting and refining strategies based on observed differences or alterations within the data or system being analyzed.
Variational meaning with examples
- The algorithm employed a variational approach to refine the parameters of the neural network. It adjusted weights iteratively based on the loss function, seeking to minimize prediction errors. This variational learning allowed the model to adapt and improve over time by exploring different weight configurations, ensuring optimal performance on the training dataset.
- Researchers used variational inference to approximate the posterior distribution in their Bayesian model. By introducing a simpler, tractable distribution, they could estimate the complex relationships within the data through repeated adjustments. This variational method enabled them to draw inferences about the model's parameters despite computational challenges.
- In finance, the portfolio optimization strategy was variational. It constantly reevaluated the asset allocation based on changing market conditions, ensuring the portfolio remained aligned with the investor's risk tolerance and return objectives. This dynamic, adaptive strategy minimized exposure to fluctuations and improved financial performance.
- The control system for the robot employed a variational feedback loop. This process involved adjustments based on comparing desired and observed states. These adjustments, such as changing motor speeds, allowed the robot to compensate for external disturbances and achieve the targeted movements, resulting in smooth motions.