DNSC 4280 Machine Learning Class Notes
8/29: Introduction
8/31: Review - Data Mining
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Supervised learning: explain relationship between predictor and target
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Predictor/explanatory variable/covariates = same
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Model Fitting
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training/validation
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Build model that optimizes performance of training data setoverfittink=n
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Try to have best fit of training data
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Prevent under/overfitting
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Use validation to check which model performs the best, then deploy best
model on test data set
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Use training to train different models
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No overlapping info between training and validation data
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underfitting/overfitting
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Trade off
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Predictive accuracy vs interpretability
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Parsimony vs blackbox
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Assess performance on validation (hold-out) data
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Problem of overfitting
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Fit may look good but it doesn’t perform well on other datasets
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Training - 80, Validation - 20
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Validation: test different models
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Compute MSE for each model to compare performance
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Choose best model
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Test data: summary
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Model Complexity
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Overfitting
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It’s too flexible around the main points of the data
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The points in the data though only represent the training dataset not the
validation or the test datasets
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Improve performance on testing dataset not just training
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Model is too complicated
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Variability of model is large, increase testing MSE but decease training
MSE (focus on testing error)
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Underfitting - not flexible enough to capture relationships
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MSE would be very large for testing/training
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Bias Variance Tradeoff
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Simple model - bias large, variance small
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Testing MSE is summation of bias and variance
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If you use complicated model you will not have bias, prediction will be too
uncertain for future, high variance ○
We want flexibility so that bias and variance are properly controlled
Practice from Assignment 1 (I realized these are available on BB)
Exercise 1: Sequences
x3 = (1, 0, -1, -2)
1:(-2)
x4 = c(“Hellow, “ “, “World”. “!”)
X4 = c(x4, paste(x4, collapse = “”)
X4
X5 = c(TRUE, FALSE, NA, FALSE) ; x6
X6 <- c(rep(1:2), 2), rep (1:2, each = 2)); x6
Exercise 2: Matrix
X <- rbind(1:4, x3, matrix(x2, 2, 4, byrow = TRUE)
X
Lists: List()
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Extract list info - use double bracket, or a $
9/7: HW 1 Overview
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Girl what is going on i have no idea lol. All i know is that Pedro said that the homework is
rough
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Loops <3
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(f, lower, upper, tol = 1e-6) to find the root of univariate function F on the interval
(upper,lower)
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Searching for a root between 1 and 2
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with the precision tolerance <tol defaulted to be a 10^-6 via bisection which
returns a list consisting of root, f.root (f evaluated at root), iter (# of iterations)
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How many times it takes to find the root
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Track whether two points are root or not..?
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Find whether midpoint is a root of function of x .. = 0
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F(x)= x^3 -x -1
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Root between two points that =0
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F(a+b/2)>0 or <0
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Function value of root = F(x) (Lol)
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Root = x
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Discrete Random Sampling
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Stratified sampling: identically separated ○
Each level contains same proportion as the entire data set
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Train a model
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Probability density function
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Optimization problems
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Finding maximum of likelihood typically written in a particular form
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F(x)=X^2-2x-1
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Minimize f(x)
9/12: Clustering
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Clustering is an example of undirected data mining techniques
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It is used to segment the data, or to find islands of similarity within the data
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Find islands of similarity
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Can be useful for marketing segmentation
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Classification of species
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Portfolio management
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You want to know which stocks are similar and which arent
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Clustering techniques
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K means clustering
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Agglomerative clustering
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Decision trees
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Neural nets
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Decide how many clusters we want to have before hand, decide criteria to decide what
clusters are best fitting toward the data
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Calculate variance of clusters, find overall variance within cluster
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Want variance to be small to find evidence of similarity
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Want total variance within clusters to be small
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Find two cluster such that the summation of the two variances are small
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Total variance within clusters are small
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As you increase the number of clusters the total variance decreases (stabilizes)
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Morse and more clusters, you need to explain underlying common pattern in
cluster, hard to explain/interpret
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Hierarchical Methods -
most popular method
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Agglomerative Methods
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Bottom to top method
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Begin with N clusters - total number of observations, keep trying to merch
clusters based on the distance between all clusters
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Therefore reducing number of clusters
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Do this until one cluster is left
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Divisive Method
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Top down method
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Start with all inclusive cluster but then repeatedly divide all datapoints into
smaller clusters, a cluster for each datapoint
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Dendrogram - calculate pairwise distances between clusters
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Y axis is distances between clusters ○
Want to find clusters to merge, based on their distance
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21 and 12, 10 and 13
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Calculate distance between two
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Distance between 12 to 10
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12 to 12
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21 to 10
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21 to 13
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D1 as ameasure to
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Euclidean distance
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Draw points on XY plane
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If all variables are categorical you cannot use euclidean distance to
calculate
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Calculate differences
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A has one difference b has 0 difference, 1+0=1, so distance is 1
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Scaling
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The variables contributions to distance function won’t be based on the
size of the units they are measured in
9/14: Clustering
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Dendrogram: starts out with the number of observations we have then starts to cluster
each observation together based on the distance from each observation
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Cannot have a nice visual representation with a large dataset, it is computationally
expensive (DRAWBACK OF CLUSTERING)
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Interpreting the clusters
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Summarize descriptive statistics of each cluster
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Find column means to know what kind of words to use to describe cluster
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Can use cluster to identify outliers
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Data are from the same population and are independent and normally distributed
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If you have one big cluster you may want to refine it to be able to find more pattern in
detail
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Merge two cloisters based on closest distance - single linkage method
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May end up getting cluster with long shape
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