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The idea of content-based recommendation is that instead of looking purely at a history of | |
how users interact with items where both users and items are considered as things we know | |
nothing about (other than their interactions), we can consider the features of the items. | |
By content here, we might consider actual textual descriptions, but we might also consider | |
more structured information about the objects like their color or whether they are shoes, | |
books or music. | |
If we look at the content associated with items, we can restate the user x item history as | |
a user x content-feature history. That is to say that we can look at what content features | |
our users interacted with as opposed to which items. Essentially, we are recommending features |
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Pragma version; | |
CREATE TABLE distributors ( | |
did integer CHECK (did > 100), | |
name varchar(40) | |
); | |
insert into distributors values (200, 'a'); | |
insert into distributors values (201, 'b'); | |
select min(columns('d.*')) from distributors; |
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x1 | x2 | x3 | |
---|---|---|---|
0.7231422916301575 | 0.819657781416707 | 0.6567508886461839 | |
0.4020425739176958 | 0.1549076251851813 | 0.4282647678658029 | |
0.4629109586444531 | 0.9094363294197141 | 0.1236688659876839 | |
0.747467460858015 | 0.2428975528400832 | 0.6360313817514556 |
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julia> A = 3 # this is \Alpha | |
3 | |
julia> Α = 4 # this is A | |
4 | |
julia> Α == A # they aren't the same | |
false | |
julia> x′ = rand(2,2) # this is x\prime |
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library (dplyr) | |
data = read.csv('median-error.csv') | |
png("max-error-uniform.png", width=1200, height=1000, pointsize=25) | |
i = -3.8 | |
boxplot(abs(error) ~ delta, (data %>% filter(n0==20)), ylim=c(0, 0.05), xlim=c(0.6,4.4), boxwex=0.1, at=(1:4)+i/11, xaxt='n', xlab=expression(delta), cex.lab=1.4) | |
axis(side=1, at=1:4, labels=c(50,100,200,500)) | |
for (nx in c(20, 50, 100, 1000, 10000, 100000)) { |
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# Analysis of how two t-digests see some sample data | |
png("figure.png", width=1200, height=1000, points=30) | |
# the first few actual data points with filler for the remainder | |
d = c(241, 543, 575, 702, 890, 1530, 1940, 2166, 2168, rep(3000,33)) | |
# the cumulative distribution function | |
f = ecdf(d) | |
# plot the actual CDF | |
plot(x=d, y=f(d), xlim = c(700, 2300), ylim = c(0.08, 0.25), type='s', | |
xlab="Sample value", ylab="Cumulative Distribution Function", | |
cex.lab=1.3) |
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using DifferentialEquations | |
using Plots | |
using Statistics | |
using LinearAlgebra | |
function lorenz!(du, u, p, t) | |
x, y, z = u | |
σ, ρ, β = p |
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### Draws a figure illustrating change detection in the distribution of synthetic data. | |
### Each dot represents a single time period with 1000 samples. Before the change, | |
### the data is sampled from a unit normal distribution. After the change, 20 samples | |
### in each time period are taken from N(3,1). Comparing counts with a chi^2 test that | |
### is robust to small expected counts robustly detects this shift. | |
### log-likelihood ratio test for multinomial data | |
llr = function(k) { | |
2 * sum(k) * (H(k) - H(rowSums(k)) - H(colSums(k))) | |
} |
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### This is a demonstration of a Monte Carlo Expectation Maximization | |
### algorithm that can recover the mean and standard deviation of | |
### truncated normally distributed data. We get 10,000 samples from | |
### a unit normal distribution, but every sample below 0.5 is truncated | |
### to that value. Every sample above 2.5 is truncated to that value. | |
### These choices were made to get quick and visually appealling convergence | |
### but the algorithm still converges for any choice. The converges | |
### could be very, very slow if there is little information in the samples | |
### and the final answer could have substantial uncertainty. For instance, | |
### if we truncated at 4 and 6, almost all samples would be piled up at |
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### This code builds a simple physical model of the range of an 85kWh Tesla Model S and | |
### compares it to real data. The data here is digitized from | |
### https://www.tesla.com/blog/model-s-efficiency-and-range | |
### The model here accounts for aerodynamic drag, viscous drag, constant | |
### friction and constant power drain | |
### First the digitized data | |
x = read.csv(text="v,range | |
10.22976354700292, 393.9005561997566 |
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