Research Notes and Blog Posts

2024

Heterogeneity and Hierarchical Models: Understanding Pooled, Unpooled, and Hierarchical Approaches

4 minute read

Published:

Hierarchical models are powerful tools in statistical modeling and machine learning, enabling us to represent data with complex dependency structures. These models are particularly useful in contexts where data is naturally grouped or exhibits multi-level variability. A critical aspect of hierarchical models lies in their hyperparameters, which control the relationships between different levels of the model.

2022

Matrix Derivative of Frobenius norm involving Hadamard Product

less than 1 minute read

Published:

Problem: Solve $\frac{\partial\left|\boldsymbol{A}\circ (\boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right|_ {F}^{2}}{\partial\boldsymbol{W}}$ and $\frac{\partial\left|\boldsymbol{A}\circ ( \boldsymbol{Y}-\boldsymbol{W}^\top\boldsymbol{X})\right|_{F}^{2}}{\partial\boldsymbol{X}}$, where $\circ$ denotes the Hadamard product, and all variables are matrices.