Types of Machine Learning¶
Supervised learning¶
Popular Machine Learning Packages in Julia:
Flux.jl (Deep learning, flexible):
- Powerful and flexible framework for building and training various neural network architectures.
- Offers automatic differentiation for efficient gradient calculations.
- Similar to PyTorch in functionality and community, but with a more concise syntax.
MLJ.jl (General-purpose, user-friendly):
- General-purpose machine learning library with familiar algorithms for classification, regression, and dimensionality reduction.
- Provides a user-friendly interface with clear documentation.
- Similar to scikit-learn in offering established algorithms and a user-friendly API, but with a focus on Julia's performance.
XGBoost¶
- XGBoost (eXtreme Gradient Boosting) is a powerful machine learning algorithm excelling for regression and cassification
- It's particularly well-suited for handling tabular data
- XGBoost is known for accuracy, efficiency, and scalability to large datasets
- XGBoost uses gradient boosting to combine weak decision trees into a strong learner.
- Julia users can leverage XGBoost through the XGBoost.jl package, providing a convenient interface to this powerful algorithm within the Julia ecosystem.
We use the simulated data from the MAGIC telescope.
The MAGIC telescope is a Cherenkov telescope situated on La Palma, one of the Canary Islands. The MAGIC machine learning dataset can be obtained from UC Irvine Machine Learning Repository.
Our task is to separate signal events (gamma showers) and background events (hadron showers) based on the features of a measured Cherenkov shower.
Classification of air showers¶
Features of the measured air showers¶
The features of a shower are:
1. fLength: continuous # major axis of ellipse [mm]
2. fWidth: continuous # minor axis of ellipse [mm]
3. fSize: continuous # 10-log of sum of content of all pixels [in #phot]
4. fConc: continuous # ratio of sum of two highest pixels over fSize [ratio]
5. fConc1: continuous # ratio of highest pixel over fSize [ratio]
6. fAsym: continuous # distance from highest pixel to center, projected onto major axis [mm]
7. fM3Long: continuous # 3rd root of third moment along major axis [mm]
8. fM3Trans: continuous # 3rd root of third moment along minor axis [mm]
9. fAlpha: continuous # angle of major axis with vector to origin [deg]
10. fDist: continuous # distance from origin to center of ellipse [mm]
11. class: g,h # gamma (signal), hadron (background)g = gamma (signal): 12332 h = hadron (background): 6688
For technical reasons, the number of h events is underestimated. In the real data, the h class represents the majority of the events.
In [1]:
using CSV, DataFrames, XGBoost, MLUtils, Plots
ENV["DATAFRAMES_ROWS"] = 10;
In [2]:
magic_data = CSV.read(joinpath("data", "magic04_data.txt"), DataFrame)
magic_data.class = (l -> l == "g" ? 1 : 0).(magic_data.class)
magic_data
19020×11 DataFrame
19010 rows omitted
| Row | fLength | fWidth | fSize | fConc | fConc1 | fAsym | fM3Long | fM3Trans | fAlpha | fDist | class |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Float64 | Int64 | |
| 1 | 28.7967 | 16.0021 | 2.6449 | 0.3918 | 0.1982 | 27.7004 | 22.011 | -8.2027 | 40.092 | 81.8828 | 1 |
| 2 | 31.6036 | 11.7235 | 2.5185 | 0.5303 | 0.3773 | 26.2722 | 23.8238 | -9.9574 | 6.3609 | 205.261 | 1 |
| 3 | 162.052 | 136.031 | 4.0612 | 0.0374 | 0.0187 | 116.741 | -64.858 | -45.216 | 76.96 | 256.788 | 1 |
| 4 | 23.8172 | 9.5728 | 2.3385 | 0.6147 | 0.3922 | 27.2107 | -6.4633 | -7.1513 | 10.449 | 116.737 | 1 |
| 5 | 75.1362 | 30.9205 | 3.1611 | 0.3168 | 0.1832 | -5.5277 | 28.5525 | 21.8393 | 4.648 | 356.462 | 1 |
| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
| 19016 | 21.3846 | 10.917 | 2.6161 | 0.5857 | 0.3934 | 15.2618 | 11.5245 | 2.8766 | 2.4229 | 106.826 | 0 |
| 19017 | 28.9452 | 6.702 | 2.2672 | 0.5351 | 0.2784 | 37.0816 | 13.1853 | -2.9632 | 86.7975 | 247.456 | 0 |
| 19018 | 75.4455 | 47.5305 | 3.4483 | 0.1417 | 0.0549 | -9.3561 | 41.0562 | -9.4662 | 30.2987 | 256.517 | 0 |
| 19019 | 120.513 | 76.9018 | 3.9939 | 0.0944 | 0.0683 | 5.8043 | -93.5224 | -63.8389 | 84.6874 | 408.317 | 0 |
| 19020 | 187.181 | 53.0014 | 3.2093 | 0.2876 | 0.1539 | -167.312 | -168.456 | 31.4755 | 52.731 | 272.317 | 0 |
In [3]:
# y = value to predict, X = features
# Convert DataFrame to tuple of arrays
X = Matrix(magic_data[:, 1:end-1]) # Features
y = magic_data[:, :class]; # Target
In [4]:
# Shuffle observations
shuffled_indices = shuffleobs(1:size(X, 1)) # Shuffle row indices
X_shuffled = X[shuffled_indices, :]
y_shuffled = y[shuffled_indices, :];
In [5]:
# Split shuffled data into training and test sets,
# 80% training, 20% testing
train_indices, test_indices = splitobs(1:size(X, 1), at = 0.8)
train_X = X_shuffled[train_indices, :]
train_y = vec(y_shuffled[train_indices, :])
test_X = X_shuffled[test_indices, :]
test_y = vec(y_shuffled[test_indices, :]);
In [6]:
bst = xgboost((train_X, train_y), num_round=1000, objective="binary:logistic")
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train-logloss:0.00484130405699632 └ @ XGBoost /Users/reygers/.julia/packages/XGBoost/nqMqQ/src/booster.jl:451 ┌ Info: Training rounds complete. └ @ XGBoost /Users/reygers/.julia/packages/XGBoost/nqMqQ/src/booster.jl:603
Booster()
Evaluate model on test data
In [7]:
predictions = predict(bst, test_X);
Plot predicted probabilities for the test sample for signal and background events:
In [8]:
signal_indicees = findall(test_y .== 1);
backgr_indecees = findall(test_y .!= 1);
stephist(predictions[signal_indicees], normalize=true, label="signal", bins=100, size=(400,300))
stephist!(predictions[backgr_indecees], normalize=true, label="backgr", bins=100)
Accuracy (fraction of correctly classified instances):
In [9]:
# Calculate evaluation metric (e.g., accuracy)
threshold = 0.8
predicted_labels = Int64.(predictions .> threshold)
acc = sum(predicted_labels .== test_y) / length(test_y)
println("accuracy = $(acc)")
accuracy = 0.867770767613039
MNIST classification using Flux¶
See here for more information on the https://en.wikipedia.org/wiki/MNIST_database.
Convolutional Neural Networks (CNNs)¶
Layers of a CNN¶
The following code is from the course Julia for Optimization and Learning.
In [21]:
using MLDatasets
T = Float32
X_train, y_train = MLDatasets.MNIST(T, :train)[:]
X_test, y_test = MLDatasets.MNIST(T, :test)[:];
In [22]:
using Plots
# Choose some random indices to plot
indices_to_plot = rand(1:size(X_train)[3])
heatmap(X_train[:, :, indices_to_plot]', color=:grays, axis=false, c=:greys, legend=false, size=(200, 200))
In [12]:
function reshape_data(X::AbstractArray{<:Real, 3})
s = size(X)
return reshape(X, s[1], s[2], 1, s[3])
end
reshape_data (generic function with 1 method)
In [13]:
using Flux
using Flux: onehotbatch, onecold
function load_data(dataset; T=Float32, onehot=false, classes=0:9)
X_train, y_train = dataset(T, :train)[:]
X_test, y_test = dataset(T, :test)[:]
X_train = reshape_data(X_train)
X_test = reshape_data(X_test)
if onehot
y_train = onehotbatch(y_train, classes)
y_test = onehotbatch(y_test, classes)
end
return X_train, y_train, X_test, y_test
end
load_data (generic function with 1 method)
In [23]:
X_train, y_train, X_test, y_test =
load_data(MLDatasets.MNIST; T=T, onehot=true);
In [15]:
using Random
using Flux: flatten
Random.seed!(31)
m = Chain(
Conv((2,2), 1=>16, relu),
MaxPool((2,2)),
Conv((2,2), 16=>8, relu),
MaxPool((2,2)),
flatten,
Dense(288, size(y_train,1)),
softmax,
)
Chain( Conv((2, 2), 1 => 16, relu), # 80 parameters MaxPool((2, 2)), Conv((2, 2), 16 => 8, relu), # 520 parameters MaxPool((2, 2)), Flux.flatten, Dense(288 => 10), # 2_890 parameters NNlib.softmax, ) # Total: 6 arrays, 3_490 parameters, 14.711 KiB.
Define the loss function
In [16]:
using Flux: crossentropy
L(X, y) = crossentropy(m(X), y)
L (generic function with 1 method)
In [17]:
using Flux.Data: DataLoader
batchsize = 32
batches = DataLoader((X_train, y_train); batchsize, shuffle = true)
1875-element DataLoader(::Tuple{Array{Float32, 4}, OneHotArrays.OneHotMatrix{UInt32, Vector{UInt32}}}, shuffle=true, batchsize=32)
with first element:
(28×28×1×32 Array{Float32, 4}, 10×32 OneHotMatrix(::Vector{UInt32}) with eltype Bool,)
In [18]:
using BSON
using Flux: params
function train_model!(m, L, X, y;
opt = Descent(0.1),
batchsize = 128,
n_epochs = 10,
file_name = "")
batches = DataLoader((X, y); batchsize, shuffle = true)
for _ in 1:n_epochs
Flux.train!(L, params(m), batches, opt)
end
!isempty(file_name) && BSON.bson(file_name, m=m)
return
end
train_model! (generic function with 1 method)
In [19]:
file_name = "mnist_simple.bson"
train_model!(m, L, X_train, y_train; n_epochs=10, file_name=file_name)
In [20]:
using Statistics
accuracy(x, y) = mean(onecold(m(x)) .== onecold(y))
"Test accuracy = " * string(accuracy(X_test, y_test))
"Test accuracy = 0.9753"