scikit-learn : VC (Vapnik-Chervonenkis) Dimension and Shatter
VC (Vapnik-Chervonenkis) dimension is a measure of the capacity or complexity of a space of functions that can be learned by a classification algorithm (more specifically, hypothesis). It is defined as the most points the hypothesis can shatter.
How many points can a linear boundary classify?
1-D : 2 points
2-D : 3 points
3-D : 4 points
n-D : n+1 points
Picture source: wiki - VC dimension and Advanced Introduction to Machine Learning, CMU-10715
Parameters may not contribute degrees of freedom. For example, we may have 4 1-D perceptrons in our model with 4 parameters (the step values) and 4 weights while still the VC dimension remains 2.
Picture source: Lecture 07 - The VC Dimension
VC dimension measures the effective number of parameters.
In practice, the number of data sets for training ($N$) is proportional to VC dimension($d_{VC}$):
$$N \propto d_{VC} $$The rule of thumb:
$$ N \ge 10 d_{VC}$$Machine Learning with scikit-learn
scikit-learn installation
scikit-learn : Features and feature extraction - iris dataset
scikit-learn : Machine Learning Quick Preview
scikit-learn : Data Preprocessing I - Missing / Categorical data
scikit-learn : Data Preprocessing II - Partitioning a dataset / Feature scaling / Feature Selection / Regularization
scikit-learn : Data Preprocessing III - Dimensionality reduction vis Sequential feature selection / Assessing feature importance via random forests
Data Compression via Dimensionality Reduction I - Principal component analysis (PCA)
scikit-learn : Data Compression via Dimensionality Reduction II - Linear Discriminant Analysis (LDA)
scikit-learn : Data Compression via Dimensionality Reduction III - Nonlinear mappings via kernel principal component (KPCA) analysis
scikit-learn : Logistic Regression, Overfitting & regularization
scikit-learn : Supervised Learning & Unsupervised Learning - e.g. Unsupervised PCA dimensionality reduction with iris dataset
scikit-learn : Unsupervised_Learning - KMeans clustering with iris dataset
scikit-learn : Linearly Separable Data - Linear Model & (Gaussian) radial basis function kernel (RBF kernel)
scikit-learn : Decision Tree Learning I - Entropy, Gini, and Information Gain
scikit-learn : Decision Tree Learning II - Constructing the Decision Tree
scikit-learn : Random Decision Forests Classification
scikit-learn : Support Vector Machines (SVM)
scikit-learn : Support Vector Machines (SVM) II
Flask with Embedded Machine Learning I : Serializing with pickle and DB setup
Flask with Embedded Machine Learning II : Basic Flask App
Flask with Embedded Machine Learning III : Embedding Classifier
Flask with Embedded Machine Learning IV : Deploy
Flask with Embedded Machine Learning V : Updating the classifier
scikit-learn : Sample of a spam comment filter using SVM - classifying a good one or a bad one
Machine learning algorithms and concepts
Batch gradient descent algorithmSingle Layer Neural Network - Perceptron model on the Iris dataset using Heaviside step activation function
Batch gradient descent versus stochastic gradient descent
Single Layer Neural Network - Adaptive Linear Neuron using linear (identity) activation function with batch gradient descent method
Single Layer Neural Network : Adaptive Linear Neuron using linear (identity) activation function with stochastic gradient descent (SGD)
Logistic Regression
VC (Vapnik-Chervonenkis) Dimension and Shatter
Bias-variance tradeoff
Maximum Likelihood Estimation (MLE)
Neural Networks with backpropagation for XOR using one hidden layer
minHash
tf-idf weight
Natural Language Processing (NLP): Sentiment Analysis I (IMDb & bag-of-words)
Natural Language Processing (NLP): Sentiment Analysis II (tokenization, stemming, and stop words)
Natural Language Processing (NLP): Sentiment Analysis III (training & cross validation)
Natural Language Processing (NLP): Sentiment Analysis IV (out-of-core)
Locality-Sensitive Hashing (LSH) using Cosine Distance (Cosine Similarity)
Artificial Neural Networks (ANN)
[Note] Sources are available at Github - Jupyter notebook files1. Introduction
2. Forward Propagation
3. Gradient Descent
4. Backpropagation of Errors
5. Checking gradient
6. Training via BFGS
7. Overfitting & Regularization
8. Deep Learning I : Image Recognition (Image uploading)
9. Deep Learning II : Image Recognition (Image classification)
10 - Deep Learning III : Deep Learning III : Theano, TensorFlow, and Keras
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