Finding Pareto Frontier Problem statement Given $N$ points $x_i$ in $d$ dimensional space, find the set of points such that you cannot make improvement on any dimension without decreasing other dimensions. In other words, these sets of point do not dominate each other.
https://towardsdatascience.com/understanding-compositional-pattern-producing-networks-810f6bef1b88 CPPN Images or sound could be thought of as a continuous function over space, $I[x,y]$. As such this function could be modelled by a neural network! The basic idea of CPPN is simple, it’s just input $x,y$ coordinates as input to a neural network and output patterns. Thus, this idea is quite general: Regress images or voxels or sequence onto the underlying spatial / temporal grid (e.g. meshgrid).
Max Flow Min Cut Theorem https://en.wikipedia.org/wiki/Cederbaum%27s_maximum_flow_theorem https://en.wikipedia.org/wiki/Max-flow_min-cut_theorem https://en.wikipedia.org/wiki/Graph_cuts_in_computer_vision
Note on Geodesic and Curvature on Manifold
Fitting Linear Nonlinear Poisson Model Poisson Likelihood We know that the Poisson distribution reads $$ Pr(X=k\mid\lambda)=\frac{\lambda^ke^{-\lambda}}{k!}\\ \log Pr(X=k\mid\lambda)=k\log \lambda -\lambda -\log k! $$ Here we have a bunch of discrete data like spike counts $y_i$ and paired input data $x_i$. We have assumed a functional form to transform $x$ into the rate $f(x)$. Given the data, how can we write down a loss function to optimize?
Reference VC_dimension
Motivation Generating and rendering random shapes may be of interest to visual coding experiment or computer vision. In this note we introduce a few easy way to generate smooth “random” objects from matlab.
Image Prior Reading Note Content Aware Image Prior 2010 CVPR
Distance Matrix Based Regression Distance Based Mean and Median