Machine Learning Bioinformatics Data Analysis and Tools V B M S U Lecture 6 Machine Learning Bioinformatics Data Analysis and Tools elena@few.vu.nl

? model Supervised Learning property of interest observations System (unknown) supervisor Train dataset ? ML algorithm new observation model prediction Classification

Unsupervised Learning ML for unsupervised learning attempts to discover interesting structure in the available data Data mining, Clustering

What is your question? What are the targets genes for my knock-out gene? Look for genes that have different time profiles between different cell types. Gene discovery, differential expression Is a specified group of genes all up-regulated in a specified conditions? Gene set, differential expression Can I use the expression profile of cancer patients to predict survival? Identification of groups of genes that predictive of a particular class of tumors? Class prediction, classification Are there tumor sub-types not previously identified? Are there groups of co-expressed genes? Class discovery, clustering Detection of gene regulatory mechanisms. Do my genes group into previously undiscovered pathways? Clustering. Often expression data alone is not enough, need to incorporate sequence and other information

Basic principles of discrimination Each object associated with a class label (or response) Y  {1, 2, …, K} and a feature vector (vector of predictor variables) of G measurements: X = (X1, …, XG) Aim: predict Y from X. Predefined Class {1,2,…K} 1 2 K Objects Y = Class Label = 2 X = Feature vector {colour, shape} Classification rule ? X = {red, square} Y = ?

Discrimination and Prediction Learning Set Data with known classes Prediction Classification rule Data with unknown classes Classification Technique Class Assignment Discrimination

Example: A Classification Problem Categorize images of fish—say, “Atlantic salmon” vs. “Pacific salmon” Use features such as length, width, lightness, fin shape & number, mouth position, etc. Steps Preprocessing (e.g., background subtraction) Feature extraction Classification example from Duda & Hart

Classification in Bioinformatics Computational diagnostic: early cancer detection Tumor biomarker discovery Protein folding prediction Protein-protein binding sites prediction Gene function prediction …

Predefine classes Objects Feature vectors Classification rule Learning set Bad prognosis recurrence < 5yrs Good Prognosis recurrence > 5yrs Good Prognosis Matesis > 5 ? Predefine classes Clinical outcome Objects Array Feature vectors Gene expression new array Reference L van’t Veer et al (2002) Gene expression profiling predicts clinical outcome of breast cancer. Nature, Jan. . Classification rule

Classification Techniques K Nearest Neighbor classifier Support Vector Machines …

Instance Based Learning Key idea: just store all training examples <xi,f(xi)> Nearest neighbor: Given query instance xq, first locate nearest training example xn, then estimate f(xq)=f(xn) K-nearest neighbor: Given xq, take vote among its k nearest neighbors (if discrete-valued target function) Take mean of f values of k nearest neighbors (if real-valued) f(xq)=i=1k f(xi)/k

K-Nearest Neighbor A lazy learner … Issues: How many neighbors? What similarity measure? prova

Which similarity or dissimilarity measure? A metric is a measure of the similarity or dissimilarity between two data objects Two main classes of metric: Correlation coefficients (similarity) Compares shape of expression curves Types of correlation: Centered. Un-centered. Rank-correlation Distance metrics (dissimilarity) City Block (Manhattan) distance Euclidean distance

Correlation (a measure between -1 and 1) Pearson Correlation Coefficient (centered correlation) Sx = Standard deviation of x Sy = Standard deviation of y You can use absolute correlation to capture both positive and negative correlation Positive correlation Negative correlation

Potential pitfalls Correlation = 1

Distance metrics City Block (Manhattan) distance: Euclidean distance: Sum of differences across dimensions Less sensitive to outliers Diamond shaped clusters Euclidean distance: Most commonly used distance Sphere shaped cluster Corresponds to the geometric distance into the multidimensional space X Y Condition 1 Condition 2 Y Condition 2 X Condition 1 where gene X = (x1,…,xn) and gene Y=(y1,…,yn)

Euclidean vs Correlation (I) Euclidean distance Correlation

When to Consider Nearest Neighbors Instances map to points in RN Less than 20 attributes per instance Lots of training data Advantages: Training is very fast Learn complex target functions Do not loose information Disadvantages: Slow at query time Easily fooled by irrelevant attributes

Voronoi Diagram query point qf nearest neighbor qi

3-Nearest Neighbors query point qf 3 nearest neighbors 2x,1o

7-Nearest Neighbors query point qf 7 nearest neighbors 3x,4o

Nearest Neighbor (continuous)

Nearest Neighbor (continuous)

Nearest Neighbor (continuous)

Nearest Neighbor Approximate the target function f(x) at the single query point x = xq Locally weighted regression = generalization of IBL

Curse of Dimensionality Imagine instances are described by 20 attributes but only 10 are relevant to target function Curse of dimensionality: nearest neighbor is easily misled when the instance space is high-dimensional One approach: weight the features according to their relevance! Stretch j-th axis by weight zj, where z1,…,zn chosen to minimize prediction error Use cross-validation to automatically choose weights z1,…,zn Note setting zj to zero eliminates this dimension alltogether (feature subset selection)

Practical implementations Weka – IBk Optimized – Timbl

Example: Tumor Classification Reliable and precise classification essential for successful cancer treatment Current methods for classifying human malignancies rely on a variety of morphological, clinical and molecular variables Uncertainties in diagnosis remain; likely that existing classes are heterogeneous Characterize molecular variations among tumors by monitoring gene expression (microarray) Hope: that microarrays will lead to more reliable tumor classification (and therefore more appropriate treatments and better outcomes) 4

Tumor Classification Using Gene Expression Data Three main types of ML problems associated with tumor classification: Identification of new/unknown tumor classes using gene expression profiles (unsupervised learning – clustering) Classification of malignancies into known classes (supervised learning – discrimination) Identification of “marker” genes that characterize the different tumor classes (feature or variable selection). 4 relevant to other types of classification problems, not just tumors

Predefine classes Objects Feature vectors Classification Rule Learning set Predefine classes Tumor type B-ALL T-ALL AML T-ALL ? Objects Array Feature vectors Gene expression new array Reference Golub et al (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286(5439): 531-537. Classification Rule

Nearest neighbor rule

SVM SVMs were originally proposed by Boser, Guyon and Vapnik in 1992 and gained increasing popularity in late 1990s. SVMs are currently among the best performers for a number of classification tasks ranging from text to genomic data. SVM techniques have been extended to a number of tasks such as regression [Vapnik et al. ’97], principal component analysis [Schölkopf et al. ’99], etc. Most popular optimization algorithms for SVMs are SMO [Platt ’99] and SVMlight [Joachims’ 99], both use decomposition to hill-climb over a subset of αi’s at a time. Tuning SVMs remains a black art: selecting a specific kernel and parameters is usually done in a try-and-see manner.

SVM In order to discriminate between two classes, given a training dataset Map the data to a higher dimension space (feature space) Separate the two classes using an optimal linear separator

Feature Space Mapping Map the original data to some higher-dimensional feature space where the training set is linearly separable: Φ: x → φ(x)

The “Kernel Trick” The linear classifier relies on inner product between vectors K(xi,xj)=xiTxj If every datapoint is mapped into high-dimensional space via some transformation Φ: x → φ(x), the inner product becomes: K(xi,xj)= φ(xi) Tφ(xj) A kernel function is some function that corresponds to an inner product in some expanded feature space. Example: 2-dimensional vectors x=[x1 x2]; let K(xi,xj)=(1 + xiTxj)2, Need to show that K(xi,xj)= φ(xi) Tφ(xj): K(xi,xj)=(1 + xiTxj)2,= 1+ xi12xj12 + 2 xi1xj1 xi2xj2+ xi22xj22 + 2xi1xj1 + 2xi2xj2= = [1 xi12 √2 xi1xi2 xi22 √2xi1 √2xi2]T [1 xj12 √2 xj1xj2 xj22 √2xj1 √2xj2] = = φ(xi) Tφ(xj), where φ(x) = [1 x12 √2 x1x2 x22 √2x1 √2x2]

Linear Separators

Optimal hyperplane Support vectors uniquely characterize optimal hyper-plane ρ margin Optimal hyper-plane Support vector

Optimal hyperplane: geometric view

Soft Margin Classification What if the training set is not linearly separable? Slack variables ξi can be added to allow misclassification of difficult or noisy examples. ξj ξk

Weakening the constraints Allow that the objects do not strictly obey the constraints Introduce ‘slack’-variables

Influence of C Erroneous objects can still have a (large) influence on the solution

SVM Advantages: Disadvantages: maximize the margin between two classes in the feature space characterized by a kernel function are robust with respect to high input dimension Disadvantages: difficult to incorporate background knowledge Sensitive to outliers

SVM and outliers outlier

Classifying new examples Given new point x, its class membership is sign[f(x, *, b*)], where Data enters only in the form of dot products! and in general Kernel function

Classification: CV error N samples Training error Empirical error Error on independent test set Test error Cross validation (CV) error Leave-one-out (LOO) N-fold CV splitting 1/n samples for testing N-1/n samples for training Count errors Summarize CV error rate