Machine Learning Strategies
Machine Learning Strategies
A Practical Guide to Automatic Differentiation in Python: Operator Overloading from Scratch and other implementation strategies
Welcome back, gradient enthusiasts! If you caught my last article on Differentiation Techniques, you already know how crucial gradients are for optimizing machine learning models. [Link to First Article]. Today, we’re diving deeper into the fascinating world of Automatic Differentiation (AD) — the unsung hero that powers much of modern machine learning and deep learning.
So, what exactly is Automatic Differentiation? In simple terms, AD is a set of techniques that allows us to compute the derivatives of complex functions specified by computer programs with incredible precision and efficiency. Unlike numerical differentiation, which approximates derivatives and can be prone to errors, or symbolic differentiation, which can become unwieldy with complicated expressions, AD strikes the perfect balance by leveraging the exactness of symbolic methods without the associated complexity...
Continue to read: https://medium.com/@souvikat/a-practical-guide-to-automatic-differentiation-in-python-operator-overloading-from-scratch-and-6cb5393343db
Cracking the Gradient Code: Exploring Differentiation Techniques for Machine Learning - Souvik
When it comes to Machine Learning and other data-driven optimization techniques, the ultimate goal is often to optimize a loss function to find its minimum. This process is essential because it helps models learn by adjusting their parameters to minimize errors. Among the various methods available, Gradient Descent stands out as the most widely embraced approach for optimizing loss functions. But here’s the kicker — any gradient-based optimization method hinges on one crucial step: calculating those gradients first. It might sound obvious, but this fundamental computation is what drives the entire optimization process forward...
Nonlinear Parameter Identification Using Optimization Based Prediction Error Method - Souvik
In the world of dynamic system modeling, accurately identifying system parameters is essential for building models that not only represent real-world behaviors but also enable effective prediction, control, and optimization. In the previous article, we explored how optimization-based parameter identification, particularly using the Prediction Error Method (PEM), effectively handles linear systems, offering improvements over traditional techniques like Ordinary Least Squares (OLS). However, real-world systems are rarely purely linear. From mechanical oscillators to chemical reactors and biological networks, most systems exhibit nonlinear dynamics that demand more sophisticated identification approaches.
Nonlinear parameter identification introduces new layers of complexity that go beyond the challenges encountered in linear systems. While linear models benefit from well-defined cost landscapes and closed-form solutions, nonlinear models often involve complex cost functions riddled with multiple local minima, sensitivity to initial conditions, and increased computational demands. These challenges make parameter estimation in nonlinear systems a far more intricate task, where traditional optimization methods can fall short...
An Introduction to Linear Model Identification: Ordinary Least Squares (OLS) with Python
In the realm of dynamic systems modeling — particularly in engineering, control theory, and systems biology — the State Space Model provides a robust framework for analyzing how systems evolve over time. This approach enables a structured way to model complex systems using a set of linear equations that describe the behavior of internal states, inputs, and outputs over discrete time steps.
A special case of state space models is the Linear Time-Invariant (LTI) model, where the relationships between input and output remain constant over time. This makes the LTI model especially useful for systems that exhibit predictable, time-invariant behavior, which is common in many engineering applications.
The Linear Time Invariant State Space Model consists of three primary components...
Continue to read: https://medium.com/@souvikat/an-introduction-to-linear-model-identification-ordinary-least-squares-ols-with-python-4e358e70d642
Numerical Solutions of ODEs with Python: Euler, Runge Kutta and Beyond - Souvik
Solving Ordinary Differential Equations (ODEs) lies at the core of modeling dynamic systems in engineering. From predicting chemical reactions to simulating mechanical oscillations, numerical solutions to ODEs are crucial for understanding time-dependent processes. While some simple systems have closed-form solutions, most real-world scenarios — especially in chemical engineering — are too complex for analytical approaches. This is where numerical methods come in...
Continue to read: https://medium.com/@souvikat/numerical-solutions-of-odes-with-python-euler-runge-kutta-and-beyond-421d4926d1fd
