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Role of Analytical and Statistical Modeling in Data Analytics

Ananth Grama

Center for Science of Information, and

Department of Computer Science Purdue University

With lots of help from Shahin Mohammadi, Abram Magner, Mehmet Koyuturk.

July, 2016

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Outline

1 Background

Problem statement Previous work Example

2 Activity Propagation (ActPro)

Standardizing gene expression profiles Computing functional activity of genes Updating global interactome

3 Results

Network statistics Predicting known biology Identifying disease-related pathways

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Basic Concepts

▶ �-Value: the probability of obtaining at least as extreme results given that the null hypothesis is true. Stated otherwise, this is the probability that a random selection (null hypothesis) yields an observation as extreme or more. Example: We have 30 people in this room. All 30 of you are under 40 years of age. The �-value of this observation is the probability that a randomly drawn sample of 30 people from the general population only contains people who are no more than 40 years old. The lower this probability, the more surprising is the observation.

▶ Statistical Signifiance: is attained when a �-value is less than a

prescribed significance level. ▶ Statistical significance is typically used for hypothesis testing.

However, we use this to estimate the “surprisingness” of observations.

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Motivation: Some Examples : Classifiers

Can I predict the Coffee Drinkers – a classification problem?

If I build a classifier with 90% precision and 90% recall, would you be happy?

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Motivation: Some Examples

Can I predict the Coffee Drinkers – a classification problem?

If I build a classifier with 90% precision and 90% recall, would you be happy?

What if I now told you that 90% of all people are coffee drinkers – the Null Hypothesis!!

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Can I predict the Coffee Drinkers – a classification problem?

If I build a classifier with 90% precision and 90% recall, would you be

happy?

What is I now told you that 90% of all people are coffee drinkers – the

Null Hypothesis!!

In the context of the null hypothesis, a classifier with 90% precision and 90% recall has no statistical significance at all.

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Motivation: Some Examples: Associations

How can I infer rules of the kind: P(Bread) -¿ P(Butter)? That is,

people who buy break are also likely to buy butter. The association rule mining algorithm works in two steps – in the first

step, all frequent sets are identified, and in the second step, the conditional probability for these frequent sets is computed to identify association rules.

Frequent sets are themselves computed using downward closure – all subsets of frequent subsets must themselves be frequent.

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▶ In reality, it does not work the way it should – the method mostly

identifies things that are obvious – nothing interesting. ▶ This is because frequency is a poor measure of statistical significance

(if at all). ▶ Even for the simplest priors (all items purchase probabilities are i.i.d),

frequent sets are not “statistically significant sets”.

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Motivation: Some Examples: Clustering

I run a set of uniformly distributed points through a standard clustering algorithm, say, �-means. What happens?

I get a set of completely meaningless clusters! Should I be impressed? How do I find the significance of a given set of clusters under a prior?

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Motivation: Some more questions to ponder.

▶ You run a graph clustering algorithm on facebook and you find a group of 300 people who are (almost) completely connected. Should you be excited?

▶ 70% of your friends on Facebook are male, 60% of your friends are computer scientists, and 80% of your friends are Indian. Do these numbers (and their overlaps) tell you anything?

▶ 75% of evenone’s friends on Facebook live within 50 miles of them. Can I use distance as an indicator of friendship (topology completion)?

▶ Can I trace the flow of a contagion through a network (its lineage), in the form of a directed acyclic graph?

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Motivation: Most probably explanations.

▶ In each of the questions above, I am looking for “surprisingness” of observations. In other words, I am trying to find observations that minimize the �-value.

▶ In yet another class of problems, we can look to maximize the

probability, with respect to a prior:

▶ Given a dynamic network (say the spread of an infection), who

was patient 0? ▶ Who was the first person on facebook?

▶ In each of these questions, we are looking for the explanation most consistent with our understanding of driving processes (priors). These maximize probability w.r.t. the prior.

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Motivation

Global human interactome is a superset of all possible physical interactions that can take places in the cell. It does not provide any information as to which one of these interactions do take place in a given tissue/cell-type context.

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1 Background

Problem statement Previous work Example

2 Activity Propagation (ActPro)

Standardizing gene expression profiles Computing functional activity of genes Updating global interactome

3 Results

Network statistics Predicting known biology Identifying disease-related pathways

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What we have – What we want

Available data sources:

1. A global interactome, which contains the set of possible interacting pairs.

2. A tissue-specific measurement of gene/protein activity within each tissue/cell type.

Problem How can we optimally utilize transcriptional activity of gene products to construct the most informative tissue-specific sub-network?

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1 Background

Problem statement Previous work Example

2 Activity Propagation (ActPro)

Standardizing gene expression profiles Computing functional activity of genes Updating global interactome

3 Results

Network statistics Predicting known biology Identifying disease-related pathways

figures/purdue

Overview

Definition

1. Node Removal (NR): Tissue-specific network is generated by removing from the global network proteins that are not expressed in the relevant tissue.

2. Edge Reweight (ERW): It modify the edge weights to reflect the probability that the corresponding interactions take place in the specific tissue.

�′_{��}= �_{��}∗ α^{�}

where 0 ≤ α ≤ 1 is the re-weighting factor and � ∈ {0, 1, 2} is the number of end-points for the protein-protein interaction that are expressed in the tissue of interest.

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Problems with Previous Methods ▶ Rely on an ad hoc threshold for identifying expressed genes. ▶ Utilize only local topology around each edge, specifically its

end-points, to decide about existence/probability of an interaction.

A. Grama (Purdue)  Analytical Modeling  17 / 36

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1 Background

Problem statement Previous work Example

2 Activity Propagation (ActPro)

Standardizing gene expression profiles Computing functional activity of genes Updating global interactome

3 Results

Network statistics Predicting known biology Identifying disease-related pathways