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Predictive Analytics - Coggle Diagram

- - - - more aggregate, more accurate
    - - higher update frequency, more accurate
    - - the shorter term the prediction, more accurate
  - - - Dependent upon expert opinions
    - - Classical Decomposition
        
        Multiplicative
        
        Multiplication of trend, seasonality and irregularity
        (2.2 p11)
        
        Increasing or decreasing seasonal variation
        (2.2 p3)
        
        Manual method
        (2.2 p16-27)
        
        Additive
        
        Addition of trend, seasonality and irregularity
        (2.2 p13)
        
        Constant seasonal variation
        (2.2 p3)
        
        Manual method
        (2.2 p28-31)
        
        Use if time series exhibit both trend and seasonal effects
      - Use of statistic
      - Smoothing
        
        Exponential
        (3.1 p8-13)
        
        Unequal weighting
        
        Simple exponential
        (3.1 p14)
        
        Only capture level
        
        Holt’s method
        (double exponential)
        (3.1 p15-17)
        
        Capture level and trend
        
        Holt Winter’s Method
        (triple exponential)
        (3.1 p18)
        
        Capture level, trend, seasonality)
        
        Simple
        (3.1 p3-4)
        
        Moving Averages
        (3.1 p3-7)
      - Box Jenkins Methods
        (ARIMA / SARIMA)
        
        Time series must be stationary
        (3.2 p4-9)
        
        mean, variance and co-variance are constant over time
        
        Test for stationarity
        (3.3 p12)
        
        Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test
        
        stationary when p−value > 0.05
        
        Augmented Dickey-Fuller (ADF) Test
        
        stationary when p−value ≤ 0.05 or critical value < -3
        
        Achieving stationarity
        
        Perform differencing
        (3.2 p7-9)
        
        unlikely need more than two orders
        
        Autocorrelation
        (3.2 p11-13)
        
        how a time series is related to itself over time
        
        Partial Autocorrelation
        (3.2 p14)
        
        Autocorrelation with all the influence of the lag in between removed
        
        Auto Regression (AR)
        (3.2 p17-23)
        
        Use linear regression for predicting the future observation using one or more past observations
        
        ACF dies down, PACF cuts off
        
        Moving Average (MA)
        (3.2 p25-26)
        
        Use past forecast errors in a regression-like model
        
        ACF cuts off, PACF dies down
        
        ARIMA / SARIMA
        (3.3 p4-11)
        
        Integrate AR and MA
        
        ACF and PACF dies down
        
        ARIMA(p, d, q)
        p = order of the autoregressive part
        d = order of integration
        q = order of the moving average part
        
        Diagnostic Checking
        
        Residual Analysis
        (3.3 p15-17)
        
        ACF and PACF of the residuals are insignificant
        
        p-value > 0.05
        
        Residual autocorrelations as a group should be consistent with those produced by random errors.
        
        Portmanteau test
        
        If insignificant, i.e. p-vale > 0.05 , the model is adequate
        
        Model Selection Criteria
        
        AIC and SBC to be as small as possible
      - Time Series Regression
        (2.1 p34-35)
      - Evaluation metrics
        
        RMSE
        Root Mean Squared Error
        
        As low as possible
        
        Representation of how forecasted values differ from actual
        
        MAPE
        Mean Absolute Percentage Error
        
        As low as possible
        
        Measure of how accurate a forecast system is
- - - - Max gain = most informative
      - Entropy before splitting - Entropy after splitting
    - - Measurement of impurities or randomness in the data points
      - between 0 and 1
        0 when all observations belong to 1 class
        1 when observations split equally b/w the classes
    - - between 0 and 1
      - least gini index is preferred as root node
      - computes the degree of probability of a specific variable that is wrongly being classified when chosen randomly
  - - - decreases the variance and helps to avoid overfitting
      - Build several models from different bootstrap samples and average the results
    - - attempts to build a strong classifier from the number of weak classifiers
    - - Enhanced version of bagging
      - the tree to use only a random subset of its available predictors to split on in the growing phase
- - - - MSE for Regression
      - quantifies gap between the prediction and the ground truth.
      - Binary cross entropy (BCE) for Classification
    - - Learning mechanism that allows the MLP to iteratively adjust the weights in the network, with the goal of minimizing the cost function
      - Stochastic Gradient Descent (SGD)
      - Adam
    - - Sigmoid
      - Rectified Linear Unit (ReLU)
- - - - Steps
        (1.1 p37)
        
        Evaluation of model
        
        Check multicollinearity
        
        All variables are Continuous
        
        VIF
        (1.1 p53)
        
        If 1 < VIF < 5, moderately correlated
        
        If VIF = 1, no multicollinearity
        
        If multiple variables with VIF > 5, drop the variable with the highest VIF, run the multi regression, get the VIF and drop the next highest VIF.
        
        If VIF > 5, highly correlated with the other variables
        
        Correlation matrix
        
        eliminate variables which are highly correlated keeping the one with highest correlation with y
        
        Contains Categorical variables
        
        Continuous-Categorical
        
        1 Categorical
        
        1 more item...
        
        2 Categorical
        
        1 more item...
        
        Perform one-hot encoding
        (5.1 p6-14)
        
        Categorical-Categorical
        
        Chi-Square
        (5.1 p17)
        
        If the predictor variables are highly correlated
        
        Check Goodness of fit of model
        (4.1 p28-32)
        
        Adjusted R-squared > 0.7 is a good model fit
        
        Ensure variables are significant
        
        p-value for coefficients < 0.05
        
        Ensure model is better than null model
        
        p-value for model < 0.05
        
        Do residuals analysis
        
        Linearity using Residuals VS Fitted Plot
        (1.1 p61)
        
        Normality
        
        Q-Q Plot
        (1.1 p62)
        
        Shapiro-Wilk Test p-value < 0.05
        
        Equal variance using Scale-Location Plot
        (1.1 p64)
        
        Outliers check using Residuals vs Leverage Plot
        (1.1 p63)
        
        Model testing using test data
        
        Data Exploration
        
        Check distribution of Y
        
        Transform if not normal
        
        Check for outliers
        
        Do scatter plot of Y vs X
        
        Identify and deal with outliers
        
        Check linear relationship between X and Y
        
        If non-linear, can try to perform transformation to become linear
        (1.1 p41)
        
        Check correlation
        (4.1 p9-20)
        
        Pearson correlation coefficient (r) > 0.7 for correlation to be considered strong
        
        Check interaction effects
        (5.1 p21-24)
        
        how the y reacts to different levels or level combinations of predictors (Xs)
        
        interaction is significant
        
        when interaction p-value < 0.05
        
        predictor must stay in the model, even if the individual p-value is not significant
        
        using interaction plots
        
        Build model
        
        Split to train and test dataset
        
        Fit linear regression
        (4.1 p24-27)
      - Algorithms to improve regression accuracy
        
        Variables selection methods
        
        Backward elimination
        (4.2 p24)
        
        Stepwise
        (4.2 p24)
        
        Forward selection
        (4.2 p23)
        
        Cross-Validation
  - - - Steps
        (1.2 p41)
        
        Evaluation
        
        Receiver Operating Characteristic (ROC) curve
        (1.2 p27)
        
        Confusion Matrix
        (1.2 p23-25)
        
        Lift chart
        (1.2 p30-31)
        
        Model fit
        
        AIC / BIC
        
        smaller the value, the better the model fit
        
        Encode Y to 1 or 0
        
        Fit regression model
      - Imbalanced data
        (1.2 p35-37)
        
        Problem
        
        Biased towards the dominating group
        
        Solutions
        
        Over-sample the minority group
        
        Under-sample the majority group
        
        Synthetically generate more minority group
        
        SMOTE
        
        ADASYN
        
        improved version of SMOTE
      - Groups must be mutually exclusive and exhaustive