Ryangineer

Machine Learning
Algorithms

My Machine Learning Projects

Data Preprocessing Template Iris Machine Learning Titanic Machine Learning Simple Linear Regression Multiple Linear Regression Polynomial Linear Regression Support Vector Regression Decision Tree Regression Random Forest Regression Logistic Regression

Support Vector Machine Kernel SVM Nonlinear Naive Bayes Classifier K-Nearest Neighbors K-Means Clustering Hierarchical Clustering Apriori Association Upper Confidence Bound Thompson Sampling

Noteworthy Machine Learning Algorithms

  Machine Learning   ⇒   software able to detect patterns, make decisions, predict outcomes, learn from mistakes & optimize own performance without being explicitly programmed to do so

Supervised Learning

  ↳ "learning a function that maps to an output based on the example of input-output pairs"

• Linear Regression | Predict Real Values

  Estimate or predict real values based on continuous variables -> establish relationship between independent variables (matrix of features) & dependent variable (output) by fitting a best line

• Homoscedasticity

  "Homoskedastic . . . refers to a condition in which the variance of the residual, or error term, [that is, the “noise” or random disturbance in the relationship between the independent variables and the dependent variable], in a regression model is constant. That is, the error term does not vary much as the value of the predictor variable changes." Investopedia

• Multicollinearity

  "[R]efers to predictors that are correlated [, that is, highly linearly related,] with other predictors. Multicollinearity occurs when your model includes multiple factors that are correlated not just to your response variable, but also to each other. In other words, it results when you have factors that are a bit redundant." Minitab

• No Free Lunch Theorems (NFL)

  "[S]tate that any one algorithm that searches for an optimal cost or fitness solution is not universally superior to any other algorithm. . . . 'If an algorithm performs better than random search on some class of problems then in must perform worse than random search on the remaining problems.'” Medium

• Parsimonious Model

  "Parsimonious models are simple models [with the least assumptions & variables but] with great explanatory predictive power. They explain data with a minimum number of parameters, or predictor variables. The idea behind parsimonious models stems from Occam's razor, or 'the law of briefness' (sometimes called lex parsimoniae in Latin)." Statistics How To

• Derivation of Line of Best Fit | Ordinary Least Squares method | Sum of Squares Residual

  SS_res = Σ(y - ŷ)² → min

• Simple Linear Regression

  Combining one variable in an equation to predict a single outcome

y = b₀ + b₁x₁

• Multiple Linear Regression

  Combining many variables in an equation to predict a single outcome

  $y_i \; =\; {\beta }_0 \; +\; {\beta }_1{x}_1{\mathrm{}}_i \; +\; {\beta }_2{x}_2{\mathrm{}}_i \; +\; {\beta }_3{x}_3{\mathrm{}}_i \; +\; {\epsilon }_i$

• Polynomial Linear Regression

  y = b₀ + b₁x₁ + b₂x₂² + . . . + b_nx_nⁿ

• R Squared | Goodness of Fit Parameter

  R² = 1 - SS_res/SS_tot
    ↳ where:
  

  ↳ SS_tot = Σ(y - y_avg)²

• Adjusted R Squared

  Adj R² = 1 - (1 - r²) * [(n - 1)/(n - p - 1)]
    ↳ where:
  

  ↳ p = number of regressors
  ↳ n = sample size

• Support Vector Regression | Classification

  Use as a regression method, maintaining all the main features that characterize the algorithm (maximal margin). The Support Vector Regression (SVR) uses the same principles as the SVM for classification, with only a few minor differences.

  • Epsilon-Insensitive Tube

    $\frac{1}{2}\parallel w\parallel \; +\; \mathrm{C\; }$Σ(ξ_i + ξ_i^*) → min

  • The Gaussian RBF Kernel

    $K(\mathrm{x⃗,\; }{\mathrm{l⃗}}^{\mathrm{ i}})=\exp (-\frac{\mathrm{\parallel \; x⃗,\; }{\mathrm{l⃗}}^{\mathrm{ i}}\parallel {\mathrm{}}^2}{2{\sigma }^2})$
    

• Logistic Regression | Classification

  Used to estimate discrete values, binary values (0/1, yes/no, true/false) based on given set of independent variables; predicts probability between 0 & 1 as output values.
    Logistic regression like its name is logarithmic. Its graph is curvilinear. If the dependent variable is binary, the graph is sigmoid. If not, the graph can be more pronounced, parabolic, etc.

  • Linear Regression | Sigmoid Function | Predicting Probability (p̂)

    y = b₀ + b₁x₁
    
    $\mathrm{ \; ↳p}=\frac{\mathrm{1\; }}{\mathrm{1\; \; +}{\mathrm{ \; e}}^{\mathrm{-y}}}$
    
    $\mathrm{ ↳ ln}\left(\frac{\mathrm{p\; }}{\mathrm{1\; -\; p}}\right)=b_0+b_{1}x$
    

• Decision Tree Regression

  Supervised learning algorithm used for classification problems; works for categorical & continuous variables

  • Standard Deviation Reduction

  F(T, X) = ΣP(c)S(c)

• Support Vector Machines | Discriminative Classifier

  Discriminative classifier formally defined by a separating hyperplane

  • Maximum Margin Hyperplane | Support Vectors

  {x_i, y_i} where i = 1 . . . L, y_i ∈ {-1, 1}, x ∈ ℝ^D

• Kernel SVM | Nonlinear

Mapping to a higher-dimensional space, applying the support vector algorithm & then projecting back to lower dimensional space resulting in a nonlinear separator

• Linearly Separable with Hyperplane in 3D

φ(x₁, x₂) ⇒ (x₁, x₂, z)

• The Gaussian or Radial Basis Function (RBF) Kernel

$K(\mathrm{x⃗,\; }{\mathrm{l⃗}}^{\mathrm{ i}})=\exp (-\frac{\mathrm{||\; x⃗,\; }{\mathrm{l⃗}}^{\mathrm{ i}}{\mathrm{||}}^2}{2{\sigma }^2})$


↳ where:


↳ K = function applied to two vectors
↳ x = point in datasets
↳ l = landmark

• Sigmoid Kernel

K(X, Y) = tanh(γ ˙ X^TY + r)

• Polynomial Kernel

K(X, Y) = tanh(γ ˙ X^TY + r)^d, γ > 0

• Naive Bayes Classification

  Probabilistic classifier based on Bayes Theorem with an assumption of independence between predictors (aka, features or independent variables)

  • Bayes Theorem ⇒ The probability of an event given prior knowledge of related events that occurred earlier

    $P(y\mid x_1,\dots ,x_n)=\frac{P(y)P(x_1,\dots ,x_n\mid y)}{P(x_1,\dots ,x_n)}$

• K-Nearest Neighbors

  Used for classification & regression; a simple algorithm that stores all available cases & classifies new cases by a "majority vote" of its K-nearest neighbors

  • Euclidean Distance

    $\mathrm{Between}{P}_1\&P_2=\sqrt{(x_2-x_1)2^{}+(y_2-y_1)2^{}}$

Unsupervised Learning

  ↳ "looks for previously undetected patterns in a data set with no pre-existing labels and with a minimum of human supervision"

• K-Means Clustering

Unsupervised algorithm which solves clustering problems; follows simple/easy way to classify a dataset through a certain number of clusters

• Within Cluster Sum of Squares (WCSS)| Quantifiable metric to evaluate how certain number of clusters performs compared to different number of clusters

WCSS = Σ distance(P_i, C₁)² + Σ distance(P_i, C₂)² +Σ distance(P_i, C₃)²

↳ where:


↳ distance = distance between each point inside cluster
↳ C = centroids, respectively


• Apriori Association

Analyzes the association of specific preferences in customer transactions (movies watched, items purchased in convenience store - beer & pampers urban myth) to discover relationships and how items are associated with each other

• Support

Movie recommendation example:
  ↳ where M = specific Movie

$\mathrm{Support(M)}=\frac{\mathrm{\#\; of\; user\; watchlists\; containing\; M}}{\mathrm{\#\; of\; user\; watchlists}}$

• Confidence

$\mathrm{Confidence}(M_1\to M_2)=\frac{\mathrm{\#\; of\; user\; watchlists\; containing}(M_1\to M_2)}{\mathrm{\#\; of\; user\; watchlists\; containing}(M_1)}$


• Lift → measuring the relevance of an associated rule & the improvement prediction

$\mathrm{Lift}(M_1\to M_2)=\frac{\mathrm{Confidence}(M_1\to M_2)}{\mathrm{Support}(M_2)}$

Reinforcement Learning

  ↳ "how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward"

• Upper Confidence Bound Algorithm | Deterministic Model

Modern application of Multi-Armed Bandit Problem (reference slot machine distributions)

• Advertising Model (requires update at every round)

Step 1: Each round n considers two numbers for each ad i:


  ↳ N_i(n) → # of times the ad i selected up to round n
  ↳ R_i(n) → Σ of rewards of ad i up to round n



Step 2: From these two numbers we compute:


  ↳ Average reward of ad i up to round n with:

        $\mathrm{r̄}(n)=\frac{R_{\mathrm{i}}(n)}{N_{\mathrm{i}}(n)}$


  ↳ Confidence interval [r̄_i(n) - △_i(n), r̄_i(n) + △_i(n)] at round n with:

        ${△}_{\mathrm{i}}(n)=\sqrt{\frac{3}{2}*\frac{\log (n)}{N_{\mathrm{i}}(n)}}$


Step 3: Select the ad i that has the maximum UCB r̄_i(n) + △_i(n)

• Thompson Sampling Algorithm | Probabilistic Model

Constructs distributions of where we think the actual expected value might lie; an auxiliary mechanism to solve the problem

• Advertising Model (can accomodate delayed feedback & has better empirical evidence than UCB)

Step 1: Each round n considers two numbers for each ad i:


  ↳ N_i¹(n) → # of times the ad i rewarded 1 up to round n
  ↳ N_i⁰(n) → # of times the ad i rewarded 0 up to round n



Step 2: For each ad i, we take a random draw from the distribution below:



θ_i(n) = β(N_i¹(n) + 1, N_i⁰(n + 1))




Step 3: Select the ad i that has highest θ_i(n)

• Random Forest Regression

Ensemble decision trees; a collection of decision trees (aka forest) to classify a new object based on attributes; each tree gives a classification & we say the tree "votes" for the class

• Dimensionality Reduction

Identifies highly significant variables when you have thousands

• Gradient Boosting

Ensemble of machine learning algorithms

My Neural Networks Projects

Artificial Neural Network | Regression Artificial Neural Network | Geodemographic Segmentation of Bank Clients Convolutional Neural Network | Boiler Plate Convolutional Neural Network | Facial Recognition

Convolutional Neural Network | Is it a Cat or Dog? Generative Adversarial Network | Neural Style Transfer Natural Language Processing Bidirectional Encoder Representations from Transformers

Lovely Deep Learning

About Ryan L Buchanan

I am re-skilling as a Data Analyst & Machine Learning Engineer.  I am currently enrolled in a Masters in Data Analytics.  I am also acquiring certifications as an ML Engineer & Algorithmic Trader from Udacity.   I have an MBA & an MS in Instructional Design.

I have a multi-displinary background including military intelligence, psychology, linguistics, economics, virtual reality & educational technology.  I have worked abroad for ten years with military, universities & vocational schools.   I have working knowledge of Arabic, Chinese & French.  I am very mobile, able to relocate quickly, adapt easily to diverse working conditions & have a current passport.

I have a passion for mathematics, statistics & artificial intelligence.  I am enthusiastic, highly self-motivated & enjoy presenting informative data to decision makers.  I am eager to work with dynamic teams to create high quality products & services.