1 Introduction to Predictive Learning Electrical and Computer Engineering LECTURE SET 1 INTRODUCTION and OVERVIEW

2 OUTLINE of Set Overview: what is this course about: - subject matter - philosophical connections - prerequisites and HW1 - expected outcome of this course 1.2 Historical Perspective 1.3 Motivation for Empirical Knowledge 1.4 General Experimental Procedure for Estimating Models from Data

Subject Matter Uncertainty and Learning Decision making under uncertainty Biological learning (adaptation) (examples and discussion) Induction, Statistics and Philosophy Ex. 1: Many old men are bald Ex. 2: Sun rises on the East every day

4 (cont’d) Many old men are bald Psychological Induction: - inductive statement based on experience - also has certain predictive aspect - no scientific explanation Statistical View: - the lack of hair = random variable - estimate its distribution (depending on age) from past observations (training sample) Philosophy of Science Approach: - find scientific theory to explain the lack of hair - explanation itself is not sufficient - true theory needs to make non-trivial predictions

5 Conceptual Issues Any theory (or model) has two aspects: 1. explanation of past data (observations) 2. prediction of future (unobserved) data Achieving both goals perfectly not possible Important issues to be addressed: - quality of explanation and prediction - is good prediction possible at all ? - if two models explain past data equally well, which one is better? - how to distinguish between true scientific and pseudo- scientific theories?

6 Beliefs vs True Theories Men have lower life expectancy than women Because they choose to do so Because they make more money (on average) and experience higher stress managing it Because they engage in risky activities Because ….. Demarcation problem in philosophy

Philosophical Connections Oxford English dictionary: Induction is the process of inferring a general law or principle from the observations of particular instances. Clearly related to Predictive Learning. All science and (most of) human knowledge involves induction How to form ‘good’ inductive theories?

8 Challenge of Predictive Learning Explain the past and predict the future

9 Background: philosophy William of Ockham: entities should not be multiplied beyond necessity Epicurus of Samos: If more than one theory is consistent with the observations, keep all theories

10 Background: philosophy Thomas Bayes: How to update/ revise beliefs in light of new evidence Karl Popper: Every true (inductive) theory prohibits certain events or occurences, i.e. it should be falsifiable

11 Background: philosophy George W. Bush: I am The Decider

12 Background: philosophy Bill Clinton: I told the Truth

Prerequisites and Hwk1 Math: working knowledge of basic Probability + Linear Algebra Statistical software (of your choice): - MATLAB, also R-project, Mathematica etc. Note: you will be using s/w implementations of learning algorithm (not writing programs) Writing: no special requirements Philosophy: no special requirements

14 Homework 1 Purpose: testing background on probability and computer skills Goal: estimate pdf of a random variable X Real Data: X=daily price changes of SP500 i.e.where Z(t) = closing price Typical + Useful Statistics - Histogram (empirical pdf) - mean, standard deviation

15 (cont’d) Homework 1 Histogram = estimated pdf (from data) Example: histograms of 5 and 30 bins to model N(0,1) also mean and standard deviation (estimated from data)

16 (cont’d) Homework 1 NOTE: histogram ~ empirical pdf, i.e. scale of y-axis scale is in % (frequency). See histogram of SP500 daily price changes in 1981:

17 Homework 1 (background) Is the stock market truly random? - model daily price changes of SP500 as a random coin toss process - measure average trend duration, i.e. UP, DOWN,UP, DOWN,…~ +1,-1,+1,-1,… here average trend duration =1 day and the process is not random Calculate average trend duration for random coin toss process, compare it with the stock market, and draw conclusions

Expected Outcome (of this course) Scientific: Learning = generalization, concepts and issues Math theory: Statistical Learning Theory aka VC-theory Implications for Philosophy and Applications Philosophical: Nature of human knowledge and intelligence Demarcation principle Psychology of learning Practical: Financial engineering Security Genomics Predicting successful marriage, climate modeling etc., etc. What is this course NOT about

19 OUTLINE of Set Overview: what is this course about 1.2 Historical Perspective Handling uncertainty and risk: - probabilistic vs - risk minimization 1.3 Motivation for Empirical Knowledge 1.4 General Experimental Procedure for Estimating Models from Data

Handling Uncertainty and Risk Ancient times Probability for quantifying uncertainty - degree-of-belief - frequentist (Cardano-1525, Pascale, Fermat) Newton and causal determinism Probability theory and statistics (20 th century) Modern science (A. Einstein)  Goal of science: estimating a true model or system identification

21 Handling Uncertainty and Risk(2) Making decisions under uncertainty = risk management Probabilistic approach: - estimate probabilities (of future events) - assign costs and minimize expected risk Risk minimization approach: - apply decisions to known past events - select one minimizing expected risk Common in all living things: learning, generalization

22 Human Generalization All men by nature desire knowledge - Aristotle Example 1: continue given sequence 6, 10, 14, 18,…. Example 2: Sceitnitss osbevred: it is nt inptrant how lteters are msspled isnide the word. It is ipmoratnt that the fisrt and lsat letetrs do not chngae, tehn the txet is itneprted corrcetly

23 Human Generalization Example 3: Emily CherkasskyThe Dictator

24 Scientific Example: Planetary Motions How planets move among the stars? - Ptolemaic system (geocentric) - Copernican system (heliocentric) Tycho Brahe (16 century) - measure positions of the planets in the sky - use experimental data to support one’s view Johannes Kepler: - used volumes of Tycho’s data to discover three remarkably simple laws

25 First Kepler’s Law Sun lies in the plane of orbit, so we can represent positions as (x,y) pairs An orbit is an ellipse, with the sun at a focus

26 Second Kepler’s Law The radius vector from the sun to the planet sweeps out equal areas in the same time intervals

27 Third Kepler’s Law PDP2P2 D3D3 Mercury Venus Earth1.00 Mars Jupiter Saturn P = orbit period D = orbit size (half-diameter) For any two planets: P 2 ~ D 3

28 Empirical Scientific Theory Kepler’s Laws can - explain experimental data - predict new data (i.e., other planets) - BUT do not explain why planets move. Popular explanation - planets move because there are invisible angels beating the wings behind them First principle scientific explanation Galileo, Newton discovered laws of motion and gravity that explain Kepler’s laws.

29 OUTLINE of Set Overview: what is this course about 1.2 Historical Perspective 1.3 Motivation for Empirical Knowledge - human (scientific) knowledge - growth of empirical knowledge - the nature of human knowledge 1.4 General Experimental Procedure for Estimating Models from Data

Human scientific knowledge Knowledge is relationship between facts and ideas (mental constructs) Two types of scientific knowledge: - First-principles vs empirical Classical (first principles) knowledge: - rich in ideas - relatively few facts (amount of data) - simple relationships Examples/ discussion

Growth of empirical knowledge Huge growth of the amount of data in 20 th century (computers and sensors) Complex systems (engineering, life sciences and social) Classical first-principles science is inadequate for empirical knowledge Need for Data-Analytic Modeling: How to estimate good predictive models from noisy data

Nature of human knowledge Three types of knowledge - scientific (first-principles, deterministic) - empirical - metaphysical (beliefs) Boundaries are poorly understood

33 More on Empirical Knowledge Demarcation: Empirical Knowledge vs Beliefs Examples Empirical vs First Principle Knowledge Examples

34 Example: Empirical Knowledge vs Beliefs From WSJ, January 13, 2007; Page B5, By Isabelle Lindemayer Dollar Ends Three-Day Advance But Could Be Poised for Gains "The dollar saw an after-the-fact selloff following better-than- expected retail-sales numbers for December," Naomi Fink, currency strategist at BNP Paribas, said. "More likely than not, investors felt as though the dollar's three- day rally preceding the release had compensated adequately for the upside surprise," she said

35 Empirical vs First Principle Knowledge Compare: First Principle Knowledge Example: Newton’s Law of Gravity Empirical Knowledge Example: my wife’s successful betting Question for Discussion: What is the difference btwn the two approaches to knowledge discovery?

36 Summary First-principles knowledge (taught at school): deterministic relationships between a few concepts (variables) Importance of empirical knowledge: - statistical in nature - (possibly) many variables Goal of modeling: to act/perform well, rather than system identification

General Experimental Procedure 1. Statement of the Problem 2. Hypothesis Formulation (Learning Problem Statement) 3. Data Generation/ Experiment Design 4. Data Collection and Preprocessing 5. Model Estimation (learning) 6. Model Interpretion, Model Assessment and Drawing Conclusions Note: - each step is complex and usually involves several iterations - estimated model depends on all previous steps

38 Honest Disclosure of Results Recall Tycho Brahe (16 th century) Modern drug studies Review of studies submitted to FDA Of 74 studies reviewed, 38 were judged to be positive by the FDA. All but one were published. Most of the studies found to have negative or questionable results were not published, researchers found. Source: The New England Journal of Medicine, WSJ Jan 17, 2008) Publication bias: widespread in modern research