Discussing the article: "Overcoming The Limitation of Machine Learning (Part 4): Overcoming Irreducible Error Using Multiple Forecast Horizons"
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Check out the new article: Overcoming The Limitation of Machine Learning (Part 4): Overcoming Irreducible Error Using Multiple Forecast Horizons.
Machine learning is often viewed through statistical or linear algebraic lenses, but this article emphasizes a geometric perspective of model predictions. It demonstrates that models do not truly approximate the target but rather map it onto a new coordinate system, creating an inherent misalignment that results in irreducible error. The article proposes that multi-step predictions, comparing the model’s forecasts across different horizons, offer a more effective approach than direct comparisons with the target. By applying this method to a trading model, the article demonstrates significant improvements in profitability and accuracy without changing the underlying model.
In our related series on self-optimizing expert advisors, we discussed how linear regression models could be constructed using matrix factorization, introduced the OpenBLAS library, and explained singular value decomposition (SVD). Readers unfamiliar with that discussion should review it, as this article builds on that foundation, a link is provided, here.
For returning readers, recall that SVD factorizes a matrix into three smaller matrices: U, S and VT. Each has special geometric properties. U and VT are orthogonal matrices, meaning they represent rotations or reflections of the original data — and crucially, they do not stretch vectors, they only change direction. S, the middle matrix, is diagonal and scales the data values.
Taken together, SVD can be understood as a sequence of rotation, scaling, and rotation applied to the data. This is how linear regression models embed images of the target onto the space of the inputs. Therefore, if we strip linear regression down to its geometric essence, it is simply rotating, scaling, and rotating again. Nothing more. That’s it. Rotate, scale, rotate. Studying geometry will teach you to see it this way, but once you do so, a provocative question emerges: where is all the “learning” truly happening?
Author: Gamuchirai Zororo Ndawana