Category: Blog

  • Normalizing flows for probability distribution reconstruction

    Tutorial Tutorial Visualizing the target distribution Setting up the normalizing flow Training the normalizing flow Sampling from the trained normalizing flow Acknowledgements Author Normalizing flows can approximate complex probability distributions by applying a sequence of invertible transformations to a simpler base distribution, such as a multivariate Gaussian. If the base distribution has a joint probability…

  • A primer on the normal distribution

    normal.md A primer on the normal distribution Introduction Why is the normal distribution so important? Where does the (68.3,95.4,99.7)(68.3, 95.4, 99.7)(68.3,95.4,99.7) rule comes from? Integrating the normal distribution The standard normal Error function Conclusion Introduction New students in science and mathematics may have seen a figure such as the one below. This figure illustrates the…

  • Krylov Matrix Exponential

    Welcome file The Matrix exponential Consider a vector-valued function v⃗(t)\vec{v}(t)v(t) whose total derivative with respect to its argument is given explicitly by a linear operator AAA (which we’ll represent as a matrix): dv⃗(t)dt=v⃗(t)A.\frac{d\vec{v}(t)}{dt} = \vec{v}(t) A .dtdv(t)​=v(t)A. Suppose at some ttt we know the function’s value v⃗(0)\vec{v}(0)v(0). (N.B. We’ve chosen t=0t=0t=0 here without losing generality;…