New nonlinear least squares solvers in R with {gslnls}

Introduction Solving a nonlinear least squares problem consists of minimizing a least squares objective function made up of residuals $g_1(\boldsymbol{\theta}), \ldots, g_n(\boldsymbol{\theta})$ that are nonlinear functions of the parameters of interest $\boldsymbol{\theta} = (\theta_1,\ldots, \theta_p)'$: $$ \boldsymbol{\theta}^* \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \Vert g(\boldsymbol{\theta}) \Vert^2 $$ In the context of regression, this problem is usually formulated as: $$ \begin{align} \boldsymbol{\theta}^* & \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \Vert \boldsymbol{y} - f(\boldsymbol{\theta}) \Vert^2 \\ & \ = \ \arg \min_{\boldsymbol{\theta}} \frac{1}{2} \sum_{i = 1}^n (y_i - f_i(\boldsymbol{\theta}))^2 \end{align} $$

Continue reading

Kustomize Best Practices

Introduction In recent years, Kubernetes has become a renowned solution for orchestrating cloud-independent infrastructure. Open Analytics supports the data analysis process end to end. This includes infrastructure that underpins the data science platforms we build. Since we exclusively work with open technology, it should come as no surprise that we adopted Kubernetes early on in our technology stack. As Kubernetes rose in popularity and maturity, it became an essential backbone to deliver fully open-source data science platforms.

Continue reading