willtownes

---
title: "Poisson prediction interval"
author: "Will Townes"
output: html_document
---

Poisson prediction interval based on [Kim et al 2022](https://doi.org/10.1002/wics.1568)

```{r}
n<-100

willtownes

"""
From https://twitter.com/Al_Grigor/status/1357028887209902088
Most candidates cannot solve this interview problem:
* Input: "aaaabbbcca"
* Output: [("a", 4), ("b", 3), ("c", 2), ("a", 1)]
Write a function that converts the input to the output
I ask it in the screening interview and give it 25 minutes
How would you solve it?
"""

willtownes

from gpflow.conditionals import conditional
from gpflow.inducing_variables import SeparateIndependentInducingVariables
from gpflow.kernels import SeparateIndependent

#note: object 'm' is of type gpflow.models.svgp.SVGP

ind_conditional = conditional.dispatch(
    object, SeparateIndependentInducingVariables, SeparateIndependent, object)
gmu, gvar = ind_conditional(
    X,

willtownes

library(pdist)
n<-200
X<-matrix(10*runif(n),ncol=1)
y<-sin(X[,1])#+rnorm(n,sd=.2)
#plot(X[,1],y)
#xnew<-3

#span<-1

my_loess<-function(xnew,X,y,span=.75){

willtownes

#include <omp.h>
#include <stdio.h>
//clang++ -Xpreprocessor -fopenmp -lomp omptest.cpp -o omptest

int main() {
    #pragma omp parallel
    printf("Hello from thread %d, nthreads %d\n", omp_get_thread_num(), omp_get_num_threads());
}

willtownes

#Fuzzy version of Jaccard and Rand Indices
#based on Suleman: "Assessing a Fuzzy Extension of Rand Index and Related Measures"

L<-4 #number of clusters
N<-50 #number of objects
X<-gtools::rdirichlet(N,rep(.01,L)) #NxL soft random clustering
y<-apply(X,1,which.max) #hard cluster version of X
table(y)
Y<-model.matrix(~factor(y)-1) #hard cluster version of X
Z<-matrix(1/L,nrow=N,ncol=L) #perfect uncertainty soft clustering

willtownes

#gradient descent probabilistic PCA with missing data
#Will Townes

L<-2 #number of latent dimensions, more dims=more complexity
#tune these hyperparameters until get good results
penalty<- 1e-8
learn_rate<- .1
niter<-100000 #number of iterations

data(iris)

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#splatter experimenting with cell-specific dropouts
#pertains to https://github.com/Oshlack/splatter/issues/25
#devtools::install_github("Oshlack/splatter@dropout")
library(splatter)
data("sc_example_counts")
# Estimate parameters from example data
params <- splatEstimate(sc_example_counts)
# Simulate data using estimated parameters
sim1 <- splatSimulate(params, dropout.type = "experiment")
assay(sim1,"logcounts")<-log2(1+assay(sim1,"counts"))

willtownes

#compositional analysis
library(compositions)
x<-c(.1,.5,.4)
V<-t(ilrBase(x))
D<-rbind(c(1,0,-1),c(0,1,-1))
x_alr<-D%*%log(x)
x_ilr<-V%*%log(x)
x_alr
alr(x)
x_ilr

willtownes

### Adaptive Rejection Sampling
# by Will Townes

rexp_trunc<-function(n,slope=-1,lo=0,hi=Inf){
  #draw n samples from the truncated exponential distribution
  #the distribution is proportional to exp(slope*x)
  #default is standard exponential
  #slope cannot equal zero
  #lo is lower truncation point, can be -Inf
  #hi is upper truncation point, can be +Inf