Machine Learning

accuracy

(TP + TN)/ (TP + TN + FP + FN)

Major DM prep tasks

- Data cleaning : Fill in missing values, smooth noisy data, identify or remove outliers, and resolve inconsistencies - Data integration : Integration of multiple databases, data cubes, or files - Data transformation : Normalisation and aggregation - Data reduction : Obtains reduced representation in volume but produces the same or similar analytical results - Data discretization : Part of data reduction but with particular importance, especially for numerical data

A Bernoulli trial

- It is a trial with a binary outcome, for which the probability that the outcome is 1 equals p (think of a coin toss of an old warped coin with the probability of throwing heads being p). - A Bernoulli experiment is a number of Bernoulli trials performed after each other. These trials are i.i.d. by definition.

Joint Probability

- Joint probability is the probability of encountering a particular class while simultaneously observing the value of one or more other random variables - Can be generalized for the state of any combination of random variables

Latent variables

- Latent variables are variables that are 'hidden' in the data. They are not directly observed, but must be inferred. - Clustering is one way of finding discrete latent variables in data.

Clustering Applications

- Market segmentation - Social Network Analysis - Vector quantization - Facial Point detection

Regularization

- Maximum likelihood generalization error (i.e. cross-validation) - Regularized error (penalize large weights) - Early stopping

Prior Probability

- Probability of encountering a class without observing any evidence - Can be generalized for the state of any random variable - Easily obtained from training data (i.e. counting)

All probability theory can be expressed in terms of two rules

- Product rule - Sum rule

Data Mining

- Quest to extract knowledge and/ or unknown interesting patterns from apparently unstructured data. aka Knowledge Discovery from Data (KDD) • Data mining bit of a misnomer - information/ knowledge is mined, not data.

Random Initialization

- Randomly Initialize K-Means clusters using actual instances as cluster centers - Run K-Means and store centers and final Cost function - Pick clusters of iteration with lowest Cost function as optimal solution - Most useful if K < 10

Normal distribution

- The Normal distribution has many useful properties. It is fully described by it's mean and variance and is easy to use in calculations. - The good thing: given enough experiments, a Binomial distribution converges to a Normal distribution.

Maximum margin classifiers

- This turns out to be a solution where decision boundary is determined by nearest points only - Minimal set of points spanning decision boundary sought - These points are called Support Vectors

One-class SVM

- Unsupervised learning problem - Similar to probability density estimation - Instead of a pdf, goal is to find smooth boundary enclosing a region of high density of a class

Hypothesis Quality

- We want to know how well a machine learner, which learned the hypothesis as the approximation of the target function , performs in terms of correctly classifying novel, unseen examples - We want to assess the confidence that we can have in this classification measure

Tests for comparing distributions

- t-test compares two distributions - ANOVA compares multiple distributions - If NULL-hypothesis is refuted, there are at least two distributions with significantly different means Does NOT tell you which they are!

K-Means Algorithm

1. Assign each xi to its closest mean. 2. Update the means based on assignment 3. Repeat until convergence

Techniques for canceling out noise

1. Binning - First sort data, then distribute over local bins 2. Regression - Fit a parametric function to the data (e.g. linear or quadratic function) 3. Clustering

Knowledge Discovery Process

1. Data cleaning - remove noise and inconsistencies 2. Data integration - combine data sources 3. Data selection - retrieve relevant data from db 4. Data transformation - aggregation etc. (cf. feature extraction) 5. Data mining - machine learning 6. Pattern Evaluation - identify truly interesting patterns 7. Knowledge representation - visualize and transfer new knowledge

There are three reasons to reduce the dimensionality of a feature set

1. Remove features that have no correlation with the target distribution 2. Remove/combine features that have redundant correlation with target distribution 3. Extract new features with a more direct correlation with target distribution.

Backward Elimination

1. Start with complete SF set (contains all original features) 2. Find feature that, when removed, reduces the filter score least 3. Remove feature from SF set 4. Repeat steps 2-3 until convergence

Forward Selection

1. Start with empty SF set and candidate set being all original features 2. Find feature with highest filter score 3. Remove feature from candidate set 4. Add feature to SF set 5. Repeat steps 2-4 until convergence

Evaluating RuleSets

A complete rule set should be good at classifying all the training examples Complexity: Favour rule sets with the minimal number of rules.

Overfitting

A hypothesis is said to be overfit if its prediction performance on the training data is overoptimistic compared to that on unseen data. It presents itself in complicated decision boundaries that depend strongly on individual training examples.

Predicates

A logic statement, generally as boolean logic

K-medoids clustering

Addresses issue with quadratic error function (L2-norm, Euclidean norm) Replace L2 norm with any other dissimilarity measure (V...)

PGNs are generative models

Allow us to sample from the probability distribution it defines

Apriori algorithm

Apriori algorithm is a fast way of finding frequent itemsets

Backprop is for:

Arbitrary feed-forward topology Differentiable nonlinear activation functions Broad class of error function

Support and Confidence

Are measures of pattern interestingness

t-test

Assesses whether the means of two distributions are statistically different from each other

ARFF

Attribute-Relation File Format

z-score normalisation

Better terminology is zero-mean normalization • min-max normalization cannot cope with outliers, z-score normalization can. • Transforms all attributes to have zero mean and unit standard deviation. • Outliers are in the heavy-tail of the Gaussian. • Still a linear transformation of all data.

Sampling Theory Basics

Binomial and Normal Distributions Mean and Variance

Normal Density

By far the most (ab)used density function is the Normal or Gaussian density

Noisy data - Clustering

Canceling noise by clustering - Cluster data into N groups - Replace original values by means of clusters OR: - Use to detect outliers

Noisy data - Regression

Canceling noise by regression: 1. Fit a parametric function to the data using minimization of e.g. least squares error 2. Replace original values by the parametric function value

Noisy data - Binning

Cancelling noise by binning: - Sort data - Create local groups of data - Replace original values by: ______ The bin mean ______ The closest min/max value of the bin

CART

Classification And Regression Trees

Maximum margin classifier

Classifier which is able to give an associated distance from the decision boundary for each example.

Simpler Method for complex itemset

Closed frequent itemset: X is closed if there exists no super-set Y such that Y has the same support count as X Maximal frequent itemset: X is frequent, and there exist no supersets Y of X that are also frequent

Hidden Unit Activation

Common functions for are unit step, sigmoid or logistic and tanh

DM Functionalities

Concept/Class description • Characterization • Discrimination • Frequent patterns/ Associations/ Correlations • Classification and Regression (Prediction) • Cluster analysis • Outlier analysis • Evolution analysis

K-Means Issues

Convergence is guaranteed but not necessarily optimal - local minima likely to occur • Depends largely on initial values of uk. • Hard to define optimal number K. • K-means algorithm is expensive: requires Euclidean distance computations per iteration. • Each instance is discretely assigned to one cluster. • Euclidian distance is sensitive to outliers.

DM task primitives

DM task primitives forms the basis for DM queries. DM primitives specify: • Set of task-relevant data to be mined • Kind of knowledge to be mined • Background knowledge to be used • Interestingness measures and thresholds for pattern evaluation • Representation for visualizing discovered patterns.

Data Transformation

Data transformation alters original data to make it more suitable for data mining. • Smoothing (noise cancellation) • Aggregation • Generalisation • Normalisation • Attribute/feature construction

Basic Decision Tree

Decision trees apply a series of linear decisions, that often depend on only a single variable at a time. Such trees partition the input space into cuboid regions, gradually refining the level of detail of a decision until a leaf node has been reached, which provides the final predicted label.

What is Deep Learning?

Definition: • Hierarchical organization with more than one (non-linear) hidden layer in-between the input and the output variables • Output of one layer is the input of the next layer

Three ways of constructing new kernels

Direct from feature space mappings Proposing kernels directly Combination of existing (valid) kernels • multiplication by a constant • exponential of a kernel • sum of two kernels • product of two kernels • left/right multiplication by any function of x/x'

Cost function - Euclidean distance

Distance measure between a pair of samples p and q in an n-dimensional feature space

Confusion Matrix

Easy to see if the system is commonly mislabelling one class as another

Directed PGN

Edges have direction (Bayesian Network)

Choosing K

Elbow method • Visual inspection • 'Downstream' Analysis

Rule based learning

Equivalent in expression power to traditional (mono-thetic) decision trees, but with more flexibility • They produce rule sets as solutions, in the form of a set of IF... THEN rules

Bootstrapping

Estimating the sampling distribution of an estimator by resampling with replacement from the original sample.

Some variables are observed, others are hidden/latent

Example observed: Labels of a training set Example hidden: Learned weights of a model

False Positive Rate

FP/actual negative = FP/TN + FP

Feature Selection

Feature Selection returns a subset of original feature set. It does not extract new features. Benefits: • Features retain original meaning • After determining selected features, selection process is fast Disadvantages: • Cannot extract new features which have stronger correlation with target variable

Attribute subset selection

Feature selection Feature selection is a form of dimensionality reduction in ML, hence the DM term 'dimensionality reduction' for manifold projection is problematic. Approaches: • Exact solution infeasible • Greedy forward selection • Backward elimination • Forward-backward • Decision tree induction

The goal of data mining is to

Find interesting patterns!. An interesting pattern is: 1. Easily understood. 2. Valid on new data with some degree of certainty. 3. Potentially useful. 4. Novel.

Forward-backward algorithm

First applies Forward selection and then filters redundant elements using backward elimination

Training algorithm

Given a model h with Solution Space S and a training set {X,Y}, a learning algorithm finds the solution that minimizes the cost function J(S)

Eigenvalue

Given an invertible matrix , an eigenvalue equation can be found in terms of a set of orthogonal vectors , and scalars such that: M

Mutual Information

Gives a measure of how 'close' two components of a joint distribution are to being independent

Minimum Error Rate

Goal is to minimise error rate

Data Discretization

Grouping a possibly infinite space to a discrete set of possible values For categorical data: ________ Super-categories For real numbers: ________ Binning ________ Histogram analysis ________ Clustering

Discrete latent variables

Hidden variables that can take only a limited number of discrete values (e.g. gender or basic emotion).

Importance of cleaning data

If you have good data, the rest will follow

Binomial distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.

SAMPLE ERROR

In statistics, sampling error is incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population.

i.i.d.

Independent and identically distributed random variables

K-Means Clustering

Informally, goal is to find groups of points that are close to each other but far from points in other groups • Each cluster is defined entirely and only by its centre, or mean value µk

Kernel methods

Kernel methods map a non-linearly separable input space to another space which hopefully is linearly separable • This space is usually higher dimensional, possibly infinitely • Even the 'non-linear' kernel methods essentially solve a linear optimization problem!!!!

Machine Learning

Learning from experience. It's also called supervised learning, were experience E is the supervision.

Learning Rulesets

Learning rules sequentially, one at a time • Also known as separate-and-conquer Learning all rules together • Direct rule learning • Deriving rules from decision trees

Kernel methods

Map a non-linearly separable input space to another space which hopefully is linearly separable • This space is usually higher-dimensional, possibly infinitely • The key element is that they do not actually map features to this space, instead they return the distance between elements in this space • This implicit mapping is called the (Definition) Trick

Misclassification Impurity

Minimum probability that training example will be misclassified at node N

Relevance Vector Machines

Model the typical points of a data set, rather than atypical( a la density estimation) while remaining a (very) sparse (like heat map) representation Returns a true posterior Naturally extends to multi-classification Fewer parameters to tune

Data quality measures

Multi-Dimensional Measure of Data Quality • A well-accepted multidimensional view: • Accuracy • Completeness • Consistency • Timeliness • Believability • Value added • Interpretability • Accessibility • Broad categories: • Intrinsic, contextual, representational, and accessibility

Undirected PGN

No edge direction (Markov Random Field)

Noisy data

Noise is a random error or variance in a measured variable

Degrees of freedom of variability

Number of ways data can change/ number of separate transformations possible

How is deep neural network optimized?

Optimized through gradient descent! (Forward-Backward algorithm) - Penalize complex solutions to avoid overfitting

Small set of SVs means that

Our solution is now sparse

Perceptron Algorithm

Perceptron is modeled after neurons in the brain. It has m input values (which correspond with the m features of the examples in the training set) and one output value. Each input value x_i is multiplied by a weight-factor w_i. If the sum of the products between the feature value and weight-factor is larger than zero, the perceptron is activated and 'fires' a signal (+1). Otherwise it is not activated. The weighted sum between the input-values and the weight-values, can mathematically be determined with the scalar-product <w, x>. To produce the behaviour of 'firing' a signal (+1) we can use the signum function sgn(); it maps the output to +1 if the input is positive, and it maps the output to -1 if the input is negative. Thus, this Perceptron can mathematically be modeled by the function y = sgn(b+ <w, x>). Here b is the bias, i.e. the default value when all feature values are zero.

The Principle of Plurality

Plurality should not be posited without necessity.

Emission Probabilities

Probabilities of observed variables

The true error of hypothesis h

Probability that it will misclassify a randomly drawn example from distribution : D However, we cannot measure the true error. We can only estimate it by observing the sample error eS

Stopping Criteria

Reaching a node with a pure sample is always possible but usually not desirable as it usually causes over-fitting.

ROC Curve

Receiver Operator Characteristic (ROC) curves plot TP vs FP rates

RELU

Rectified Linear Unit New trend, responsible for great deal of Deep Learning success. Advantages: • No 'vanishing gradient' problem • Can model any positive real value • Can stimulate sparseness

Instance Reduction

Reduces the number of instances rather than attributes. Much more dangerous, as it risks changing the data distribution properties • Duplicate removal • Random sampling • Cluster sample • Stratified sampling

Numerosity Reduction

Reduces the number of instances rather than attributes. Much more dangerous, as it risks changing the data distribution properties. • Parametrization • Discretization • Sampling

Association Rules

Reflect items that are frequently found (purchased) together, i.e. they are frequent itemsets • Information that customers who buy beer also buy crisps is e.g. encoded as: beer ) crisps[support = 2%, confidence = 75%]

NN Error Functions

Regression: - Binary classification - Multiple independent binary Classification: - Multi-class classification (mutually exclusive):

Regularization

Regularization is a technique used in an attempt to solve the overfitting problem in statistical models.

Abstract Essence of ML

Representation + Evaluation + Optimisation

1st order Markov models

Restricted to encoding sequential correlation on previous element only

Tree components

Root node, branch, node, leaf node.

Multiclass SVM

SVM is an inherently binary classifier. Two strategies to use SVMs for multiclass classification: - One-vs-all - One-vs-one Problems: - Ambiguities (both strategies) - Imbalanced training sets (one-vs-all)

Estimating hypothesis accuracy

Sample Error vs. True Error Confidence Intervals

Linearly-separable SVM

Satisfying solution (e.g. perceptron algorithm): finds a solution, not necessarily the 'best' Best is that solution that promises maximum generalizability

Sequence Data

Sequence data is data that comes in a particular order Opposite of independent, identical distributed (i.i.d.) Strong correlation between subsequent elements - DNA - Time series - Facial Expressions - Speech Recognition - Weather Prediction - Action planning

Kernel

Shortcut that helps us do certain calculation faster which otherwise would involve computations in higher dimensional space.

Data reduction

Should remove what's unnecessary, yet otherwise maintain the distribution and properties of the original data • Data cube aggregation • Attribute subset selection (feature selection) • Dimensionality reduction (manifold projection) • Numerosity reduction • Discretization

Significance level

Significance level α%: α times out of 100 you would find a statistically significant difference between the distributions even if there was none. It essentially defines our tolerance level. If the calculated t value is above the threshold chosen for statistical significance then the null hypothesis that the two groups do not differ is rejected in favor of the alternative hypothesis: the groups do differ.

Mixture of Gaussians

Simple formulation: density model with richer representation than single Gaussian

Slack variable

Slack variables introduced to solve optimization problem by allowing some training data to be misclassified Slack variables en >= 0 give a linear penalty to examples lying on the wrong side of the d.b.: point on correct side of db |tn ! y(xn)|, otherwise

Cross-validation criterion

Split training data in a number of folds. For each fold, train on all other folds and make predictions on the held-out test fold. Combine all predictions and calculate error. If error has gone down, continue splitting nodes, otherwise, stop

Validation set Criterian

Split training data in a training set and a validation set (e.g. 66% training data and 34% validation data). Keep splitting nodes, using only the training data to learn decisions, until the error on the validation set stops going down.

Cost Function

Squared error cost function. J(S)

Gradient points in the direction of

Steepest Ascent

DM Subjective Interest

Subjective measures require a human with domain knowledge to provide measures: • Unexpected results contradicting apriori beliefs • Actionable • Expected results confirming hypothesis

Intrinsic dimensionality

Subspace of data space that captures degrees of variability only, and is thus the most compact possible representation

DM Objective Interest

Support: P(X U Y ) Percentage of transactions that a rule satisfies Confidence: P(Y | X) Degree of certainty of a detected association, i.e. the probability that a transaction containing X also contains Y

TPR - True Positive Rate - Recall

TP/actual Positive = TP/TP + FN

SVMs seek a decision boundary

That maximizes the margin

Complex Itemsets

The general rule procedure for finding frequent item sets would be: 1. Find all frequent itemsets 2. Generate strong association rules However, this is terribly costly, with the total number of item sets to be checked for 100 items being

Kernel trick

The key element of kernel methods is that they do not actually map features to this space, instead they return the distance between elements in this space This implicit mapping is called the (definition)

SVM Margin is defined as

The minimum distance between decision boundary and any sample of a class

Local minima

The smallest value of the function. But it might not be the only one.

How to make trees compact?

To do so, we will seek to minimise impurity of data reaching descendent nodes

Training a network

Training a NN involves finding the parameters that minimize some error function Choice of activation function depends on the output variables: - Unity for regression - Logistic sigmoid for (multiple independent) binary classification - Softmax for exclusive (1-of-K) multiclass classification

Non-linearly Separable Problem

Usually problems aren't linearly separable (not even in feature space) 'Perfect' separation of training data classes would cause poor generalization due to massive overfitting

Soft Margin

We have effectively replaced the hard margin with a soft margin New optimization goal is maximizing the margin while penalizing points on the wrong side of d.b.

What trees are preferable?

We prefer simple, compact trees, following Occam's Razor

Blocking Paths

When a path is blocked, no information can flow through it This means that observing C, if it blocks a path A-C-B, it means there is no added value in observing A, and B is fully determined by C

Acquiring emissions

Wide range of options to model ****** probabilities: - Discrete tables - Gaussians - Mixture of Gaussians - Neural Networks/RVMs etc to mode

Directed Acyclic Graphs (DAGs)

are Bayesian Networks. Meaning there are no cyclic paths from any node back to itself

Rule confidence

confidence(A -> B) = P (B|A)

Dirty data

incomplete noisy inconsistent

Ancestral sampling

is a simple sampling method well suited to PGNs

Conditional independence in PGN

is the PGN mechanism to show information in terms of interesting aspects of probability distributions

Probability Theory Recap

p(x) = marginal distribution p(x,y) = joint distribution p(x|y) = conditional distribution

Bayes' Theorem

posterior = (likelihood x prior)/evidence

Itemsets

simply a set of items (cf set theory)

A Latice/Trellis diagram visualizes

state transitions over time Also good tool to to visualize optimal path through states (Viterbi Algorithm)

Rule support

support(A -> B) = P(A u B)

Comparing Hypotheses

t-test Analysis of Variance (ANOVA) test

Causes of incomplete data

• "Not applicable" data value when collected • Different considerations between the time when the data was collected and when it is analyzed. • Human/ hardware/ software problems

Evaluating Rules

• A good rule should not make mistakes and should cover as many examples as possible Complexity: Favour rules with simple predicates (Occam's Razor)

The simplest ANNs consist of

• A layer of D input nodes • A layer of hidden nodes • A layer of output nodes • Fully connected between layers

Frequent Itemset

• Absolute support of an itemset is its frequency count • Relative support is the frequency count of the itemset divided by the total size of the dataset

ANN feature selection

• Artificial Neural Networks can implicitly perform feature selection • A multi-layer neural network where the first hidden layer has fewer units (nodes) than the input layer • Called 'Auto-associative' networks

Filter Scores

• Correlation • Mutual information Entropy • Classification rate • Regression score

CFS

• Correlation based feature selection (CFS) selects features in a forward-selection manner. • Looks at each step at both correlation with target variable and already selected features.

DM query languages

• DM query language incorporates primitives • Allows flexible interaction with DM systems • Provides foundation for building user-friendly GUIs • Example: DMQL

Model Combination View

• Decision Trees combine a set of models (the nodes) • In any given point in space, only one model (node) is responsible for making predictions • Process of selecting which model to apply can be described as a sequential decision making process corresponding to the traversal of a binary tree

Causes of inconsistent data

• Different data sources • Functional dependency violation (e.g., modify linked data)

Min-max normalization

• Enables cost-function minimization techniques to function properly, taking all attributes into equal account • Transforms all attributes to lie on the range [0, 1] or [-1, 1] • Linear transformation of all data

Data Integration

• Entity identification problem • Redundancy detection • Correlation analysis • Detection and resolution of data value conflicts • e.g. weight units, in/exclusion of taxes

Search Methods

• Exhaustive • Greedy forward selection • Greedy backward elimination • Forward-backward approach

Causes of noisy data (incorrect values)

• Faulty data collection instruments • Human or computer error at data entry • Errors in data transmission

Artificial Neural Nets

• Feed-forward neural network/Multilayer Perceptron one of many ANNs • We focus on the Multilayer Perceptron • Really multiple layers of logistic regression models

DM systems can be divided into types based on a number of variables

• Kinds of databases • Kinds of knowledge • Kinds of techniques • Target applications

Commonly used kernels

• Linear kernel • Polynomial kernel • Gaussian kernel (Gaussian kernel is probably the most frequently used kernel out there - Gaussian kernel maps to infinite feature space)

PCA

• Manifold projection • Assumes Gaussian latent variables and Gaussian observed variable distribution • Linear-Gaussian dependence of the observed variables on the latent variables • Also known as Karhunen-Loève transform

Parametric methods

• Many methods learn parameters of prediction function (e.g. linear regression, ANNs) • After training, training set is discarded. • Prediction purely based on learned parameters and new data.

PCA requires calculation of

• Mean of observed variables • Covariance of observed variables • Eigenvalue/eigenvector Computation of covariance matrix

HDF5

• Much more complex file format designed for scientific data handling • It can store heterogeneous and hierarchical organized data. • It has been designed for efficiency.

Sparse Kernel Methods

• Must be evaluated on all training examples during testing • Must be evaluated on all pairs of patterns during training - Training takes a long time - Testing too - Memory intensive (both disk/ RAM) Solution: sparse methods

Sparse kernel methods

• Must be evaluated on all training examples during testing • Must be evaluated on all pairs of patterns during training • Training takes a long time • Testing too • Memory intensive (both disk/RAM) Solution: sparse methods

DM integration with DBS/ Data Warehouses

• No coupling - DMS will not utilize any DB/DW system functionality • Loose coupling - Uses some DB/DW functionality, in particular data fetching/storing • Semi-tight coupling - In addition to loose coupling use sorting, indexing, aggregation, histogram analysis, multiway join, and statistics primitives available in DB/DW systems • Tight coupling

Mining frequent patterns

• One approach to data mining is to find sets of items that appear together frequently: frequent itemsets • To be frequent some minimum threshold of occurrence must be exceeded • Other frequent patterns of interest: ____ frequent sequential patterns ____ frequent structured patterns

DM Types of data

• Relational databases • Data warehouses • Transactional databases • Object-relational databases • Temporal/sequence/time-series databases • Spatial and Spatio-temporal databases • Text & Multimedia databases • Heterogeneous & Legacy databases • Data streams

Output layer can be

• Single node for binary classification • Single node for regression • n nodes for multi-class classification

Rulesets

• Single rules are not the solution of the problem, they are members of rule sets • Rules in a rule set cooperate to solve the problem. Together they should cover the whole search space

EM Algorithm issues

• Takes a long time • Often initialised using k-Means

Memory-based methods

• Uses all training data in every prediction (e.g. kNN) • Becomes a kernel method if using a non-linear example comparison/ metric

ROBBINS-MONRO

•Addresses the slow update speed of the M-step in K-means •Uses linear regression (see lecture 1)

Deep learning methods

(Deep) Neural Networks • Convolutional Neural Networks • Restricted Boltzmann Machines/Deep Belief Networks • Recurrent Neural Networks

Deep Learning

- Basically a Neural Network with Many hidden layers - Can be used for unsupervised learning and dimensionality reduction

Simple data splits

- Fixed train, development and test sets - Bootstrapping - Cross-validation

Evaluation procedure for single split or cross validation

- For large datasets, a single split is usually sufficient. - For smaller datasets, rely on cross validation

Hidden layer(s) can

- Have arbitrary number of nodes/units - Have arbitrary number of links from input nodes and to output nodes (or to next hidden layer) - There can be multiple hidden layers

Overfitting can occur when

- Learning is performed for too long (e.g. in Neural Networks) - The examples in the training set are not representative of all possible situations (is usually the case!) - Model parameters are adjusted to uninformative features in the training set that have no causal relation to the true underlying target function.

LDA

- Linear Discriminant Analysis - Most commonly used as dimensionality reduction technique in the pre-processing step for pattern-classification and machine learning applications. - The goal is to project a dataset onto a lower-dimensional space with good class-separability in order avoid overfitting

Unsupervised Learning Tasks

- Outlier detection: Is this a 'normal' xi ? - Data visualization: What does the high-dimensional X look like? - Association rules: Which xij occur together? - Latent-factors: What 'parts' are the xi made from? - Ranking: Which are the most important xi ? - Clustering: What types of xi are there?

Cross-validation

- Randomly split data into n folds and iteratively use one as test set - All data used to test, and almost all to train - Good for small sets

Fixed train, development and test sets

- Randomly split data into training, development, and test sets. - Does not make use of all data to train or test - Good for large datasets

C4.5

- Successor of ID3. - Multiway splits are used. - Statistical significant split pruning.

Bayes' Error

- The Bayes Error rate is the theoretical lowest possible error rate for a given classifier and a given problem (dataset). - For real data, it is not possible to calculate the Bayes Error rate, although upper bounds can be given when certain assumptions on the data are made. - The Bayes Error functions mostly as a theoretical device in Machine Learning and Pattern Recognition research.

Regression Trees

- Trained in a very similar way - Leaf nodes are now continuous values - the value at a leaf node is that assigned to a test example if it reaches it - Leaf node label assignment is e.g. mean value of its data sample Problem: nodes make hard decisions, which is particularly undesired in a regression problem, where a smooth function is sought.

Orthogonality

- Two vectors and are orthogonal if they're perpendicular - If their inner product is 0: a · b = 0

Backpropagation

- Used to calculate derivatives of error function efficiently - Errors propagate backwards layer by layer

Three common ways to decide when to stop splitting decision tree

- Validation set - Cross-validation - Hypothesis testing (chi-squared statistic)

Batch Gradient descent

- Vanilla gradient descent, aka batch gradient descent - Make small change in weights that most rapidly improves task performance Gradient descent computes the gradient of the cost function w.r.t. to the parameters θ for the entire training dataset - Can be very slow - Intractable for datasets that don't fit in memory - Doesn't allow us to update our model online, i.e. with new examples on-the-fly. - guaranteed to converge to the global minimum for convex error surfaces and to a local minimum for non-convex surfaces.

Unsupervised Learing

- We only have xi values, but no explicit target labels. - You want to do 'something' with them.

accuracy may not be useful measure in cases where

1- There is a large class skew 2- There are differential misclassification costs - say, getting a positive wrong costs more than getting a negative wrong. 3- We are interested in a subset of high confidence predictions

Error Backpropagation

1. Apply input vector to network and propagate forward 2. Evaluate d(k) for all output units 3. Backpropagate d's to obtain d(j) for all hidden units 4. Evaluate error derivatives as:

Six general questions to decide on decision tree algorithm:

1. How many splits per node (properties binary or multi valued)? 2. Which property to test at each node? 3. When to declare a node to be leaf? 4. How to prune a tree that has become too large (and when is a tree too large)? 5. If a leaf node is impure, how to assign a category label? 6. How to deal with missing data?

Random forests

1. Very good performance (speed, accuracy) when abundant data is available. 2. Use bootstrapping/bagging to initialize each tree with different data. 3. Use only a subset of variables at each node. 4. Use a random optimization criterion at each node. 5. Project features on a random different manifold at each node.

Well-posed Learning Problem

A computer program is said to learn from (E)xperience E with respect to some (T)ask T and some (P)erformance measure P, if its performance on T, as measured by P, improves with experience E.

Dropout

A very different approach to avoiding over-fitting is to use an approach called dropout. Here, the output of a randomly chosen subset of the neurons are temporarily set to zero during the training of a given mini-batch. This makes it so that the neurons cannot overly adapt to the output from prior layers as these are not always present. It has enjoyed wide-spread adoption and massive empirical evidence as to its usefulness.

Occam's Razor

All things being equal - the simplest explanation is the best

How to train ANN

An error function on the training set must be minimized. This is done by adjusting: - Weights connecting nodes. - Parameters of non-linear functions h(a).

Branching Factor

Branching factor of node at level L is equal to the number of branches it has to nodes at level L + 1

Cost function - Manhattan or City block distance

Calculate the distance between real vectors using the sum of their absolute difference. Also called City Block Distance

Measures of classification accuracy

Classification Error Rate Cross Validation Recall, Precision, Confusion Matrix Receiver Operator Curves, two-alternative forced choice

Classification measures - Error Rate

Common performance measure for classification problems 1. Success: Instance's class is predicted correctly (True Positives (TP) / Negatives (TN)). 2. Error: Instance's class is predicted incorrectly (False Positives (FP) / Negatives (FN)). 3. False positives - Type I error. False Negative - Type II error. 4. Classification error rate: Proportion of instances misclassified over the whole set of instances.

F-measure

Comparing different approaches is difficult when using multiple evaluation measures (e.g. Recall and Precision) F-measure combines recall and precision into a single measure

Machine Learning

Field of study that gives computers the ability to learn without being explicitly programmed.

Machine Learning broad definition

Field of study that gives computers the ability to learn without being explicitly programmed.

Training LDA objective:

Find (i.e. learn) that minimizes some error function on the training set. Significant approaches: • Least squares • Fisher • Perceptron

Pattern Recognition

Finding patterns without experience. It's also called unsupervised learning.

Pruning

First fully train a tree, without stopping criterion After training, prune tree by eliminating pairs of leaf nodes for which the impurity penalty is small

Generalisation

Generalization is the desired property of a classifier to be able to predict the labels of unseen examples correctly. A hypothesis generalizes well if it can predict an example coming from the same distribution as the training examples well.

Gradient

Gradient shows you in multidimensional functions the direction of the biggest value change (which is based on the directional derivatives) . So given a function i.e. g(x,y) = -x+y^2 you know, that it is better to minimize the value of x, while strongly maximize the value of y. This is a base of gradient based methods, like steepest descent technique.

General classification problem

If classes are disjoint, i.e. each pattern belongs to one and only one class then input space is divided into decision regions separated by decision boundaries or surfaces

EXTREME Dimensionality Case

In an extreme, degenerate case, if D > n, each example can be uniquely described by a set of feature values.

Cross-validation

In k-fold cross-validation, a dataset is split into k roughly equally sized partitions, such that each example is assigned to one and only one fold. At each iteration a hypothesis is learned using k-1 folds as the training set and predictions are made on the k'th fold. This is repeated until a prediction is made for all k folds, and an error rate for the entire dataset is obtained. Cross-validation maximises the amount of data available to train and test on, at cost of increased time to perform the evaluation. • Training Data segments between different folds should never overlap • Training and test data in the same fold should never ovelap Error estimation can either be done per fold separately, or delayed by collating all predictions per fold.

Cost function - ℓ2 norm

In order to avoid over-fitting, one common approach is to add a penalty term to the cost function. Common choices are the ℓ2-norm, given as: Where C0 is the unregularized cost

Multivariate Trees

Instead of monothetic decisions at each node, we can learn polythetic decisions. This can be done using many linear classifiers, but keep it simple!

ID3

Interactive dichotomizer version 3 Used for nominal, unordered, input data only. Every split has branching factor , where is the number of values a variable can take (e.g. bins of discretized variable) has as many levels as input variables

Missing Attributes

It is common to have examples in your dataset with missing attributes/variables. One way of training a tree in the presence of missing attributes is removing all data points with any missing attributes. A better method is to only remove data points that miss a required attribute when considering the test for a given node for a given attribute. This is a great benefit of trees (and in general of combined models,)

The Principle of Parsimony

It is pointless to do with more what is done with less.

Linear Separability

Linearly separable data: • Datasets whose classes can be separated by linear decision surfaces • Implies no class-overlap • Classes can be divided by e.g. lines for 2D data or planes in 3D data

Classification

ML task where T has a discrete set of outcomes. Often classification is binary. Examples: • face detection • smile detection • spam classification • hot/cold

Regression

ML task where T has a real-valued outcome on some continuous sub-space Examples: • Age estimation • Stock value prediction • Temperature prediction • Energy consumption prediction

Features/Attributes

Measurable values of variables that correlate with the label y Examples: • Sender domain in spam detection • Mouth corner location in smile detection • Temperature in forest fire prediction • Pixel value in face detection

Derivative

Measure of how fast function value changes withe the change of the argument. So if you have the function f(x)=x^2 you can compute its derivative and obtain a knowledge how fast f(x+t) changes with small enough t. This gives you knowledge about basic dynamics of the function

On-line Gradient Descent

On-line (or Schotastic) gradient descent also known as incremental gradient descent updates parameter one data point at a time. - Handles redundancy better. (Batch GD has redundancy) - Usually much faster than Batch GD. - SGD performs frequent updates with a high variance that cause the objective function to fluctuate heavily - Can deal with new data better. - Good chance of escaping local minima. However, when we slowly decrease the learning rate, SGD shows the same convergence behaviour as batch gradient descent

Curse of Dimensionality

The curse of dimensionality refers to how certain learning algorithms may perform poorly in high-dimensional data. First, it's very easy to overfit the the training data, since we can have a lot of assumptions that describe the target label (in case of supervised learning). In other words we can easily express the target using the dimensions that we have. Second,we may need to increase the number of training data exponentially, to overcome the curse of dimensionality and that may not be feasible. Third, in ML learning algorithms that depends on the distance, like k-means for clustering or k nearest neighbors, everything can become far from each others and it's difficult to interpret the distance between the data points.

Tree variaties

Trees are called monothetic if one property/variable is considered at each node, polythetic otherwise

Convolutional Neural Networks

Type of feed-forward artificial neural network in which the connectivity pattern between its neurons is inspired by the organization of the animal visual cortex, whose individual neurons are arranged in such a way that they respond to overlapping regions tiling the visual field.

Labels

Values that h aims to predict Example: • Facial expressions of pain • Impact of diet on astronauts in space • Predictions of house prices

Network Topology

Variations include: • Arbitrary number of layers • Fewer hidden units than input units (causes in effect dimensionality reduction, equivalent to PCA) • Skip-layer connections • Fully/sparsely interconnected networks

Evaluation Procedures

• For large datasets, a single split is usually sufficient. • For smaller datasets, rely on cross validation

Decision surfaces are

• Linear functions of x • Defined by (D-1) dimensional hyperplanes in the D dimensional input space.