Skip to content

新鲜事

pclasso

Refer to pcLasso: a new method for sparse regression

set.seed(1234)
n = 100; p = 10
X = matrix(rnorm(n * p), nrow = n)
y = rnorm(n)
library(pcLasso)
fit <- pcLasso(X, y, theta = 10)

predict(fit, X[1:3, ])[, 5]

groups = list(1:5, 6:10)
fit = pcLasso(X, y, theta = 10, groups = groups)

fit = cv.pcLasso(X, y, theta = 10)
predict(fit, X[1:3,], s = "lambda.min")

Emojis in scatterplot

References:

  1. Using emojis as scatterplot points
  2. dill/emoGG
library(ggplot2)
library(emoGG)
data("ToothGrowth")
p1 <- geom_emoji(data = subset(ToothGrowth, supp == "OJ"), 
                aes(dose + runif(sum(ToothGrowth$supp == "OJ"), min = -0.2, max = 0.2), 
                   len), emoji = "1f34a")
p2 <- geom_emoji(data = subset(ToothGrowth, supp == "VC"), 
                 aes(dose + runif(sum(ToothGrowth$supp == "OJ"), min = -0.2, max = 0.2), 
                     len), emoji = "1f48a")

ggplot() +
    p1 + p2 +
    labs(x = "Dose (mg/day)", y = "Tooth length")

Medians in high dimensions

Refer to Medians in high dimensions

  • marginal median
  • geometric median
  • medoid
  • centerpoint
  • Tukey median

Laplace distribution as a mixture of normal distributions

Refer to Laplace distribution as a mixture of normals

\int_0^\infty f_{X\mid W=w}(x)f_W(w)dw=\frac{1}{2b}\exp\Big(-\frac{\vert x\vert}{b}\Big)\,.

Gradient descent as a minimization problem

Refer to Gradient descent as a minimization problem

put gradient decent into the optimization framework, then derive

  • projected gradient descent
  • proximal gradient methods

Coordinate descent doesn’t always work for convex functions

Refer to Coordinate descent doesn’t always work for convex functions

A counterexample:

z=\max(x,y)+\vert x-y\vert

Solution to a sgn equation

Refer to Soft-thresholding and the sgn function

Give a proof of the solution of

ax-b+c\mathrm{sgn}(x)=0

where a>0 and c\ge 0.

Horvitz–Thompson estimator

Refer to Horvitz–Thompson estimator

Perform an inverse probability weighting to (unbiasedly) estimate the total T=\sum X_i.

Illustration of SCAD penalty

Refer to The SCAD penalty

The dotted line is the y=x line. The line in black represents soft-thresholding (LASSO estimates) while the line in red represents the SCAD estimates.

Leverage in Linear regression

Refer to Bounds/constraints on leverage in linear regression

The leverage of data point i is the i-th diagonal entry of the hat matrix.

Modification to fundamental sampling formula

Refer to Inverse transform sampling for truncated distributions

We can draw sample X\sim F conditional on X\ge t.

Borel’s Paradox

Retire Statistical Significance

A petition

EM estimation for Weibull distribution

f_k(x) = k x^{k-1} e^{-x^k} \quad x >0

Refer to EM maximum likelihood estimation for Weibull distribution

A little confused about the answer

Power method for top eigenvector

Power method for obtaining the top eigenvector