using LinearAlgebra, Zygote, ForwardDiff, Printf

using CSV$,$ DataFrames

using StatsBase: mean

using Parameters

using Distributions

using Random

using BSON

### Below you will implement your linear regression object from scratch.

###

### you will also imply some penalty methods as well.

#### $----$ ###

### Before getting started you should write your student$\_$number in integer format

const student$\_$number: :Int$64=0,$## replace $$ by your student$\_$number

### $----$ ###

### This hw is a bit harder than the usual ones, so you may want to

### take a look at$--$Julia official website

## Before you get started, $...$ you gotta look at do end syntax of Julia

## Instead of mean square loss we shall use Huber loss which

## sometimes performs better when your dataset contains some out of distribution points

### We split it into two parts the first one is for scalars the second one is for vectors

## remember that you will multiple dispatch!!!

function huber$\_$loss$($y$\_$pred::T$,$ y$\_$true::T; $$::$F$ loat$64=0\mathrm{.}1)$ where $T$ : Real

return nothing

end

function huber$\_$loss$($y$\_$pred: :AbstractArray $\{T\},y_{-}$true:$\frac{\text{:}}{A}bs$ tractArray$\{T\})$ where $T$ : Real

return nothing

end

function unit$\_$test$\_$huber$\_$loss$()$ : :Bool

Random.seed! $()$

@assert huber$\_$loss $(1\mathrm{.}0,1\mathrm{.}0)==0\mathrm{.}0$

@assert huber$\_$loss $(1\mathrm{.}0,2\mathrm{.}0$;$=0\mathrm{.}9)==0\mathrm{.}49500000000000005$

Qassert isapprox$($huber$\_$loss$($randn$(100,100),$ randn$(100,100)),0\mathrm{.}10791842,$ atol $=1$e$-2)$

@assert isapprox$($huber$\_$loss$($randn$(100),$ randn$(100)),0\mathrm{.}107945,$ atol $=1$e$-2)$

@info "You can not stop now comrade!!! jump to the next exercise!!!"

return $1$function unit$\_$test$\_$huber$\_$loss$()$::Bool

Random.seed! $()$

@assert huber$\_$loss $(1\mathrm{.}0,1\mathrm{.}0)==0\mathrm{.}0$

@assert huber$\_$loss $(1\mathrm{.}0,2\mathrm{.}0$;$=0\mathrm{.}9)=0\mathrm{.}49500000000000005$

Qassert isapprox$($huber$\_$loss$($randn $(100,100),$randn$(100,100),$ atol $=1$e$-2)$

@assert isapprox$($huber$\_$loss$($randn$(100),$ randn$(100)),0\mathrm{.}107945,$ atol $=1$e$-2)$

@info "You can not stop now comrade!!! jump to the next exercise!!!""

return $1$

end

## See you have implemented huber$\_$loss$()$ well??

unit$\_$test$\_$huber$\_$loss$()$

### create a roof for the Logistic regression Logisticclassifier

abstract type LinearRegression end

mutable struct linear$\_$regression $$: LinearRegression

## This part is given to you!!!

# Realize that we have fields: $8$ and bias.

$$: : AbstractVector

bias: : Real

linear$\_$regression $,$ zero$(1))$

end

## write the forwardpass function

function $(1$r::Linear$\_$regression$)($X: Matrix $\{T\}$ where $T$:Real

# This dude is the forward pass function!!!

return nothing

end

function unit$\_$test$\_$forward$\_$pass$()$ : :Bool

try

linear$\_$regression $(20)(randn(10,20))$

catch ERROR

error$("$SEG$-$FAULT!!!!!"$)$

end

@info "Real test started!!!!!"

for $i$ in ProgressBar $(1$:$10000)$

sleed$(0\mathrm{.}0001)$function unit$\_$test$\_$forward$\_$pass $()$::Bool

try

linear$\_$regression $(20)(randn(10,20))$

catch ERROR

error$("$SEG$-$FAULT! $!!!")$

end

@info "Real test started!!!!"

for $i$ in ProgressBar $(1$:$10000)$

sleep $(0\mathrm{.}0001)$

lr $=$ linear$\_$regression$(3)$

$x=$randn$(2,3)$

@assert $lr(x)==x**lr*.+lr.$ bias

end

@info "Oki doki!!!"

return $1$

end

### Let's give a try!!!!!!!

unit$\_$test$\_$forward$\_$pass $()$

## we shall now implement fit! method!!!!

## before we get ready run the next $5$ lines to see in this setting grad function returns a dictionary:

#$=$

Lr $=$ Linear$\_$regression$(10)$

val, grad $=$ Zygote.withgradient $(Lr)$ do $Lr$

end

$=$#

function update$\_$grads!$(1$r::LinearRegression, learning$\_$rate::Float$64,$ grads$)$

## Here you will implement update$\_$grads, this function returns nothing.

## Search for setfield! and getfield functions.

## $x-=$ learning$\_$rate$*$grads will happen here!!!

return nothing

end

function fit!$($lr:: Linear$\_$regression,

$x$ : :AbstractMatrix,

y: :AbstractVector;

$1$nunnina natn..ElnntaA $-$ A agah$1$function update$\_$grads!$($lr::LinearRegression, learning$\_$rate::Float$64,$ grads$)$

## Here you will implement update grads, this function returns nothing.

## Search for setfield! and getfield functions.

## $x-=$ learning rate$*$grads will happen here!!!

return nothing

end

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