GPR

Project.toml

@@ -4,10 +4,13 @@ authors = ["xKDR Forum, Sourish Das"]
 version = "0.1.0"
 
 [deps]
+Clustering = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 GLM = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
+GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9"
 HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 NLSolversBase = "d41bc354-129a-5804-8e4c-c37616107c6c"

src/CRRao.jl

@@ -1,11 +1,15 @@
 module CRRao
 
+
 using DataFrames, GLM, Turing, StatsModels, StatsBase
 using StatsBase, Distributions, LinearAlgebra
 using Optim, NLSolversBase, Random, HypothesisTests
+using GaussianProcesses, Distances, StatsModels
+
 import StatsBase: coef, coeftable, r2, adjr2, loglikelihood, aic, bic, predict, residuals, cooksdistance, fit
 import HypothesisTests: pvalue
 
+
 """
 ```julia
 LinearRegression
@@ -94,12 +98,37 @@ where
 """
 struct PoissonRegression end
 
+"""
+```julia
+GaussianProcessesRegression
+```
+Type representing the Gaussian Processes Regression model class.
+
+```math
+    y = f(X) + \\varepsilon,
+```
+where
+```math
+\\varepsilon \\sim N(0,\\sigma^2),
+```
+    + ``y`` is the response vector of size ``n``, representing the observed target values,
+    + ``X`` is the matrix of input variables of size ``n \\times p``, where ``n`` is the sample size and ``p`` is the number of input variables,
+    + ``f(X)`` is the latent function that represents the underlying unknown relationship between ``X`` and ``y``,
+    + ``\\varepsilon`` is the noise term that follows a Gaussian distribution with zero mean and variance ``\\sigma^2``.
+    + ``\\sigma`` is the standard deviation of the noise ``\\varepsilon``.
+
+The latent function `f(X)` is assumed to follow a Gaussian process, completely specified by its mean function and covariance function. The mean function provides the prior expectation of the latent function, and the covariance function captures the dependence structure between different input points.
+
+"""
+struct GaussianProcessesRegression end 
+
 """
 ```julia
 Boot_Residual
 ```
 Type representing Residual Bootstrap.
 """
+
 struct Boot_Residual end
 
 """
@@ -307,6 +336,8 @@ y_i \\sim D(\\mu_i,\\sigma), i=1,2,\\cdots,n
 """
 struct Prior_HorseShoe end
 
+
+
 """
 ```julia
 CRRaoLink
@@ -392,7 +423,7 @@ end
 
 Cauchit() = Cauchit(Cauchit_Link)
 
-export LinearRegression, LogisticRegression, PoissonRegression, NegBinomRegression, Boot_Residual
+export LinearRegression, LogisticRegression, PoissonRegression, NegBinomRegression, Boot_Residual, GaussianProcessesRegression
 export Prior_Ridge, Prior_Laplace, Prior_Cauchy, Prior_TDist, Prior_HorseShoe, Prior_Gauss
 export CRRaoLink, Logit, Probit, Cloglog, Cauchit, fit
 export coef, coeftable, r2, adjr2, loglikelihood, aic, bic, sigma, predict, residuals, cooksdistance, BPTest, pvalue
@@ -401,5 +432,5 @@ export FrequentistRegression, BayesianRegression
 include("random_number_generator.jl")
 include("general_stats.jl")
 include("fitmodel.jl")
-
+include("bayesian/gaussian_processes_regression.jl")
 end

src/bayesian/gaussian_processes_regression.jl

@@ -0,0 +1,132 @@
+
+"""
+```julia
+
+fit(formula, data::DataFrame, modelClass::GaussianProcessesRegression, IndexVar, mean, kern::Kernel, 
+   DistanceClass::Euclidean)
+```
+
+Fit a Gaussian Process Regression model on the input data with a Gaussian Process prior and user-specific mean and kernel functions.
+
+#Example
+
+```julia-repl
+
+julia> using CRRao, RDatasets, StatsModels, StatsPlots, GaussianProcesses, Distances
+julia> df = dataset("datasets", "mtcars")
+32×12 DataFrame
+ Row │ Model              MPG      Cyl    Disp     HP     DRat     WT       QSec     VS     AM     Gear   Carb  
+     │ String31           Float64  Int64  Float64  Int64  Float64  Float64  Float64  Int64  Int64  Int64  Int64 
+─────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────
+   1 │ Mazda RX4             21.0      6    160.0    110     3.9     2.62     16.46      0      1      4      4
+   2 │ Mazda RX4 Wag         21.0      6    160.0    110     3.9     2.875    17.02      0      1      4      4
+  ⋮  │         ⋮             ⋮       ⋮       ⋮       ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮      ⋮
+  31 │ Maserati Bora         15.0      8    301.0    335     3.54    3.57     14.6       0      1      5      8
+  32 │ Volvo 142E            21.4      4    121.0    109     4.11    2.78     18.6       1      1      4      2
+                                                                                             28 rows omitted
+
+julia> container=fit(@formula(MPG ~0+ HP),df,GaussianProcessesRegression(),[:MPG, :HP],MeanZero(), SE(0.0,0.0),Euclidean())
+
+Formula: MPG ~ 0 + HP
+Link: CRRao.Identity(CRRao.Identity_Link)
+Chain: GP Exact object:
+  Dim = 1
+  Number of observations = 32
+  Mean function:
+    Type: MeanZero, Params: Float64[]
+  Kernel:
+    Type: SEIso{Float64}, Params: [5.464908573213355, 3.3936838718120708]
+  Input observations = 
+[110.0 110.0 … 335.0 109.0]
+  Output observations = [21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2  …  15.2, 13.3, 19.2, 27.3, 26.0, 30.4, 15.8, 19.7, 15.0, 21.4]
+  Variance of observation noise = 9.667961411202336
+  Marginal Log-Likelihood = -89.745
+julia> plot(container.chain)
+```
+"""
+function fit(formula,
+     data::DataFrame, 
+     modelClass::GaussianProcessesRegression,
+     IndexVar, 
+     mean, 
+     kern::Kernel, 
+     DistanceClass::Euclidean)
+
+ formula = apply_schema(formula, schema(formula, data), RegressionModel)
+ select!(data, IndexVar)
+ y, X = modelcols(formula, data)
+ logObsNoise = -1.0
+ gp = GP(X', y, mean, kern, logObsNoise)
+ optimize!(gp)
+ return BayesianRegression(:GaussianProcessesRegression, gp, formula)
+
+end
+
+"""
+
+```julia
+
+fit(formula, data::DataFrame, modelClass::GaussianProcessesRegression, IndexVar, mean 
+   DistanceClass::Euclidean)
+```
+
+Fit a Gaussian Process Regression model on the input data with a Gaussian Process prior. The Zero Mean and Squared Exponential kernel function is implemented by default.
+
+#Example
+
+```julia-repl
+julia> using CRRao, RDatasets, StatsModels, StatsPlots, GaussianProcesses, Distances
+
+julia> df = dataset("datasets", "mtcars")
+32×12 DataFrame
+ Row │ Model              MPG      Cyl    Disp     HP     DRat     WT       QSec     VS     AM     Gear   Carb  
+     │ String31           Float64  Int64  Float64  Int64  Float64  Float64  Float64  Int64  Int64  Int64  Int64 
+─────┼──────────────────────────────────────────────────────────────────────────────────────────────────────────
+   1 │ Mazda RX4             21.0      6    160.0    110     3.9     2.62     16.46      0      1      4      4
+   2 │ Mazda RX4 Wag         21.0      6    160.0    110     3.9     2.875    17.02      0      1      4      4
+  ⋮  │         ⋮             ⋮       ⋮       ⋮       ⋮       ⋮        ⋮        ⋮       ⋮      ⋮      ⋮      ⋮
+  31 │ Maserati Bora         15.0      8    301.0    335     3.54    3.57     14.6       0      1      5      8
+  32 │ Volvo 142E            21.4      4    121.0    109     4.11    2.78     18.6       1      1      4      2
+                                                                                                 28 rows omitted
+
+julia> container=fit(@formula(MPG ~0+ HP),df,GaussianProcessesRegression(),[:MPG, :HP],Euclidean())
+
+Formula: MPG ~ 0 + HP
+Link: CRRao.Identity(CRRao.Identity_Link)
+Chain: GP Exact object:
+  Dim = 1
+  Number of observations = 32
+  Mean function:
+    Type: MeanZero, Params: Float64[]
+  Kernel:
+    Type: SEIso{Float64}, Params: [5.464908573213355, 3.3936838718120708]
+  Input observations = 
+[110.0 110.0 … 335.0 109.0]
+  Output observations = [21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2  …  15.2, 13.3, 19.2, 27.3, 26.0, 30.4, 15.8, 19.7, 15.0, 21.4]
+  Variance of observation noise = 9.667961411202336
+  Marginal Log-Likelihood = -89.745
+
+
+
+julia> plot(container.chain)
+```
+"""
+
+
+function fit(formula, 
+    data::DataFrame, 
+    modelClass::GaussianProcessesRegression,
+    IndexVar,
+    DistanceClass::Euclidean)
+
+ formula = apply_schema(formula, schema(formula, data), RegressionModel)
+ select!(data, IndexVar)
+ y, X = modelcols(formula, data)
+ logObsNoise = -1.0
+ mean= MeanZero()
+ kern=SE(0.0,0.0)
+ gp = GP(X', y, mean, kern, logObsNoise)
+ optimize!(gp)
+ return BayesianRegression(:GaussianProcessesRegression, gp, formula)
+
+end