Transcript Lecture 9
CSC 599: Computational Scientific Discovery Lecture 9: Introduction to the Scienceomatic Architecture Outline Motivation CSD thus far Scienceomatic Architecture First Trend in CSD 1. Data structures that are more predictive Single simple equations BACON, late 1980s List of mechanisms MECHEM, mid 1990s Differential equations Lagramge, mid 1990s Process network IPM, mid 2000's Second Trend in CSD 2. Better application of domain knowledge “Better” in the sense that 1. Provides more efficiency for limiting search 2. Provides In scientist-friendly format Examples: Ad hoc BACON, late 1980s Grammar Lagramge, mid 1990s Domain constraints of acceptable solutions MECHEM, mid 1990s Abstract processes IPM, mid 2000's Emphases of CSD Predictive data structures: 1. More structurally complex 2. More embedded in knowledge scientists already have Use domain knowledge More “understandable” 3. Integrates simulation and exhaustive search 2 strengths of computers But what do scientists do? Give reasons why! (explanations) Templates for solving problems: Philosophy of science Artificial Intelligence Kuhn's exemplars Explanation Based Learning Explanations need: 1. Assertions 2. Reasoning method(s) to tie them together About Explanations Assertions come in (at least) two flavors What Prolog would call “facts” What Prolog would call “rules” Measurements (thermometer1 read 20.6 C at time t0) Fundamental properties (c = 299,792,458 m/s) F = ma Modern philosophers of science don't like this Thinks it smells too much like logical empiricism Reasoning comes in several flavors Deduction: A; A->B; therefore B Abduction: B; A->B; therefore A Analogy: f(A); g(a); relates(A,a); f(B); g(b); therefore relates(B,b) Maybe Induction: f(1); f(2); f(3); therefore "n: f(n) Explanation-based Learning Deductive learning from one training example Requires: 1. The training example World provides proof of one legal configuration 2. A Goal Concept High level description of what to learn 3. An Operationality Criteria Tells which concepts are usable 4. A Domain Theory Tells relationship between rules & action in domain EBL generalizes example to describe goal concept and satisfy operationality criteria 1. Explanation: remove unimportant details from training example with respect to goal concept 2. Generalization: generalize as much as can while still describing goal concept EBL Applied to Scientific Reasoning We have Newton's Law of gravity: F = GMm/r2 (domain know.) (Example): Mass of an apple Force on apple due to gravity (ie. Its weight) mass[earth] >> mass[apple]; r = radius[earth] Force of weight (Goal concept to learn) Data struct outlining how (Operationality criterion) weight[apple]=(GM/radius[earth]) *mass[apple] Generalize data struct to anything fitting criteria: mass[earth] >> mass[X], r=radius[earth] weight[X]=GM*mass[X]/radius[earth] But what else do scientists do? Remember what has been tried, and why! Historical trajectory of scientific effort Reason where to put effort Human science Artificial Intelligence Funding agency Reinforcement learning Issues: 1. Strategy vs. tactics 2. Tried-and-true vs. brand new Science under limited resources Ranking (priority queue) of operators to try Funding agencies Limited resource = money (and time) Reinforcement learning Limited resource = CPU time (and memory) What is Reinforcement Learning? Is type of learning Not particular algorithm! Agent always acting in environment Gets reward at end, or as goes along Can be delay j between action and its payoff Goal: maximize the payoff Strategy vs. Tactics (Military) (Definitions from Compact Oxford English Dictionary) Strategy: “a plan designed to achieve a particular long-term aim” Examples: “Destroy enemy's forces” “Destroy enemy's economy/industrial base” “Destroy enemy's morale” Tactics: “the art of disposing armed forces in order of battle and of organizing operations.” Examples: Frontal assault Siege Pincer Hit and run Strategy (Scientific Discovery) Strategy: “What should the long-term process of science be?” Topic in contemporary philosophy of science: Examples: Lakatos Minimize number unpredicted phenomena Cumulatively build upon research programmes' hardcore Laudan Maximize number of predicted attributes, Research traditions less structured, not necessarily cumulative Tactics (Scientific Discovery) Tactics: “What should this scientist be doing right now?” Related to inductive bias in machine learning Examples: Information gain Minimize cross-validation error Maximize conditional independence Strategy vs. Tactics: related issues Tried-and-true vs. Brand new When does the strategy switch from conventional tactics to unconventional ones? Philosophy of science: Kuhn: Normal science vs. revolution Lakatos: Progressive vs. degenerate research programmes Artificial Intelligence Exploration vs. exploitation Exploration (revolution: look for the brand new) Exploitation (normal science: get what can from known structure) Issue studied in reinforcement learning community Can Implement each object separately Assertion data structure Directly uses assertions Explanation data structure Gives explanations Historical data structure Gives historical context to justify what to do next Assertion Usage Object Sample of important methods: Retrieve assertion a1 Predict object o1's attribute attr1 Show assertion Edit assertion Plot these values Compare predicted and recorded values Justify (e.g. logical resolution) assertion a1 Explanation Usage Object Sample of important methods: Predict o1's attribute attr1 Satisfy with assertion usage obj Satisfy with solved problem library Philosophy of science justification Kuhnian exemplar: what scientists do Artificial Intelligence justification: EBL: cheaper than de novo reasoning Give trace why object o1's attribute attr1 is value v1. Give trace how assertion a1 is justified (e.g. derived) Refine reasoning method “I like traces like this over traces like that because . . .” Historical Trajectory Object Sample of important methods: Predict o1's attribute attr1 Show vs. edit (assertion object) De novo vs. exemplar (explanation) Why this trace? Previous traces? Change strategy Lakatos, Laudan or other? Change tactics Change operator library Add/delete/modify operators Examine history Which inductive bias When to use operator op1 How well do ops work, and when? Selectively erase history Change priority queue Reorder operator instances Three objects under Manual or Autonomous Control Ontology Is-a hierarchy Single inheritance (except for processes) Instance-of leaves Each instance only belongs to one class Inherited properties from classes Override-able at instance or derived class level Assertion Usage Object Types of assertions “Assertions of state” “Facts” (in the Prolog sense) “Rules” (in the Prolog sense) Relations (e.g. equations) Numeric computation Decision trees Symbolic computation “Assertions of motion” Process classes Process instances analogous to “facts” Rules Numeric relations for processes Decision trees for processes About assertions Assertions have: Name List of entities (things they interrelate) Conditions (when they hold) Expression <entity,attribute> pair that they define (optional) Authorship Who is responsible for putting them in kb When placed in? Where they came from (Operator? User edit?) List of assertions that they depend on (if created by operator) Numeric Relation example Numeric relation: Ideal gas law Name: ideal_gas_law List of entities (things they interrelate) [gas_ent, container_ent, molecule_ent] gas_ent is the gas sample being described container_ent is the container holding the gas sample molecule_ent is the Conditions (when they hold), ex: “Gas phase molecules are not attractive or repulsive” Expression PV = nRT <entity,attribute> pair that they define (optional) Gas's thermal energy = PV = nRT (?) Numeric Relation Example (2) Authorship Of discovery Who discovered it person(some_scientist) operator(bacon3) When it was discovered date(century19) date(1990) On inclusion Who included it person(joseph_perry_phillips) When it was included date(2008,may,27) Processes Describe changes over time Process classes Langley et al call them “abstract processes” Whole class of similar events Arranged hierarchically Have assertions associated with them Process instances Instance of process class Single event May be decomposed into finer process instances Processes example Motion Very abstract 1-D motion Specifies that motion along one dimension only abstract means “fnc to be given in derived class” 1-D uniform acceleration Specifies uniform accel. abstract_const means “constant to be given in derived class” 1-D gravitational accel. Gives conditions Process assertion example Decision tree to stochastically compute child's genotype form parents Non-leaves are tests Some are random Leaves are answers Explanation Usage Object Returns traces of reasoning Akin to resolution refutation traces Given: A; B; AB -> C (or not(A) not(B)∨C) Prove: C Method: Assume not(C) Show contradiction C must be true! Explanation Usage Object (2) Can look up in library If not found calls assertion usage object Works for: Justifying single values Justifying whole assertions Optionally allow more than deduction History Trajectory Object Does several things: 1. Decides which operator to do next based on: a) How successful they have been (operator id) b) Type of data (data id) c) Tactics d) Strategy 2. Keeps track of what's been tried before a) operator/data b) success/failure c) “by how much” d) who/when/why/etc. 3. Modifiable a) Learns best operators on for given data b) PROGRAMMABLE?!? (Under these conditions create an operator that does this . . .) Next time 1. More detail about kb structure A “culture” for science Value hierarchy States and time Java/C++ simulators 2. Writing programs in Scienceomatic architecture Dynamically configured discovery operators in history trajectory object 3. Scienceomatic in action a) What might “normal science” look like? b) What might “revolution” look like?