Rina Dechter Bren school of ICS University of California, Irvine

Rina Dechter Bren school of ICS University of California, Irvine
Artificial Intelligence in UC-Irvine: Automated Reasoning with Graphical models Rina Dechter Bren school of ICS University of California, Irvine The question of this workshop is to assess the success of SAT and to ask what is next. My answer is that the success of SAT is due to understanding of basic principles for improved reasoning and to their implemention them and perfacting and sharing code in the most simplest of frameworks. The next step is to extend this principles to general graphical models and apply the same dedicated effort for code optimization and sharing Research in the Constraint programming field is divided into two primary areas of 1. Algorithms 2. Lanuages. Algorithms for solving the constraint satisfaction problem and solution counting which can be posed over the simple framework of constraint networks. Significant advances have been made in the past 2-3 decades developing both understanding of the fundamental principles of effective csp algorithms such as Exact backtracking search, variable elimination methods and approximation scheme such as constraint propagation and stochastic local search. This research has culminated in the last decade with the emergence of impressively efficient SAT solvers developed in a satellite SAT community, somewhat detached from the constraiint programming one. The primary principles for improved algorithms is in their ability to exploit: 1. Problem decomposition, 2. equivalent sub problems 3. pruning or bounding the problem Solving activity to wherer it has some potential. The remarkable success of SAT solvers can be attributed to that this simpler framework allowed code perfection and specialized data structures that allowed exploiting all these principle In a very cost-effective manner. We are at the point that SAT solvers are used as subroutine for solving harder and more complex queries. The second focus of constraint programming is on languages for modeling real world applications. In fact the area started with emphasis on languages, when logic programming languages were extended and augmented with specialized constraint subsystems such as linear And numerial constraints. These languages used some of the algorithms developed in their compilers. Constraint propagation schemes is the glue that combine both of these directions with the focus of global constraints. Moving to application poses more difficult challenges require addressing mor complex queries such as optimization and likelihood computation posed Over richer knowledge bases such as probabilistic networks, Markov networks, influence diagrams and what we call nowadays graphical models. This term umbrella emphasize the power of graphs as an abstraction that has a unifying power in that it allows extending the same principles to this more difficult queries. One of the most exciting development in the last decade in Computer Science and in AI is in Satisfiability solving. While this is an NP-complete problem, several research communities have joined together to develop effective sat and constraint solvers that are now able to solve orders of magnitude larger satisfiability problems. It reached the point that SAT solvers are now utilized as “efficient” subroutine when we attempt to solve even harder queries over larger domains. This had significant impact on many applications as well as on related fields such as software and hardware verification, planning and learning in AI and general CS . There are two elements behind this development: The scientific research into Understanding of the principles of efficient SAT solving, occuring primarily within the constraint and SAT communities. Code perfection, code engineering and code sharing. Many of the same principles that we have seen in Sat solving can be extended to general graphical models (e.g., optimization and likelihood computation/counting) through the unifying power of graphs which is the underlying abstraction of representing knowledge in all these areas. My plan in this talk is to share with you some of the work we have done towards advance reasoning algorithms for general graphical models while focusing on the graph as a facilitator for understanding and further advances. ICS 90 November 2016

Agenda My work in AI How did I get to AI? ICS-90, 2016

Knowledge representation and Reasoning
Modeling knowledge Knowledge acquisition Machine learning Represent knowledge Reason about the knowledge Answer queries Makes decisions Executes actions ICS-90, 2016

Artificial Intelligence Tasks
Areas: 1. Automated theorem proving 2. Planning and Scheduling 3. Machine Learning 4. Robotics 5. Diagnosis/place recognition 6. Explanation Frameworks: 1. Propositional Logic 2. Constraint Networks 3. Belief Networks 4. Markov Decision Processes Graphical Models

Sample Applications for Graphical Models
Graphical models are everywhere… everywhere in nature and in people’s behavior, But it is also everywhere in science and technology … I will not give too many examples, so this one slide should be enjoyed. What should be clear from this is that in all these examples, we have graph. What we want is to Learn these factored representations, and once we learned them we want to be able to answer queries. To do “reasoning. ICS-90, 2016

Sample Applications for Graphical Models
Learning, Modeling, Representation Graphical models are everywhere… everywhere in nature and in people’s behavior, But it is also everywhere in science and technology … I will not give too many examples, so this one slide should be enjoyed. What should be clear from this is that in all these examples, we have graph. What we want is to Learn these factored representations, and once we learned them we want to be able to answer queries. To do “reasoning. Reasoning ICS-90, 2016

Sudoku – Constraint Satisfaction
Variables: empty slots Domains = {1,2,3,4,5,6,7,8,9} Constraints: 27 all-different Constraint Propagation Inference . 2 Each row, column and major block must be alldifferent “Well posed” if it has unique solution: 27 constraints ICS-90, 2016

Constraint Networks Map coloring Variables: countries (A B C etc.)
Values: colors (red green blue) Constraints: A B red green red yellow green red green yellow yellow green yellow red Constraint graph A B D C G F E C A B D E F G Task: find a solution Count solutions, find a good one ICS-90, 2016

Combinatorial Optimization
Planning & Scheduling Computer Vision Example applications are numerous: Planning and scheduling, 1. Find an optimal schedule for the satellite that maximizes the number of photographs taken, subject to on-board recording capacity In computer vision, Image classification we want to assign a pixel in an image to an object . The model is a structured support vector machine, in which each pixel is a variable, taking states indicating its "class". The factors form a grid structure, where the local (single variable) and pairwise factors are learned from data and depend on the local image features (color, edges, etc.). Both the prediction step on a new image, and the gradient calculation for learning the model parameters, involve finding the most likely configuration (exactly or approximately) of all the pixels' class variables. Find an optimal schedule for the satellite that maximizes the number of photographs taken, subject to on-board recording capacity Image classification: label pixels in an image by their associated object class [He et al. 2004; Winn et al. 2005] ICS-90, 2016

Big Part of Reasoning is Diagnosis
Diagnosis: What has happened here? We want to understand, to make sense from the environment We want to do “plan recognition” Two student carry a book and walk… A student is looking into another student notebook ICS-90, 2016

Application: circuit diagnosis
Problem: Given a circuit and its unexpected output, identify faulty components. The problem can be modeled as a constraint optimization problem and solved…somehow. ICS-90, 2016

Probabilistic Inference
medical diagnosis smoking visit to Asia V S T Lung cancer B C bronchitis tuberculosis abnormality in lungs A X D dyspnoea (shortness of breath) X-ray Query: P(T = yes | S = no, D = yes) = ? ICS-90, 2016

ICS-90, 2016

Monitoring Intensive-Care Patients
The “alarm” network - 37 variables, 509 parameters (instead of 237) PCWP CO HRBP HREKG HRSAT ERRCAUTER HR HISTORY CATECHOL SAO2 EXPCO2 ARTCO2 VENTALV VENTLUNG VENITUBE DISCONNECT MINVOLSET VENTMACH KINKEDTUBE INTUBATION PULMEMBOLUS PAP SHUNT ANAPHYLAXIS MINOVL PVSAT FIO2 PRESS INSUFFANESTH TPR LVFAILURE ERRBLOWOUTPUT STROEVOLUME LVEDVOLUME HYPOVOLEMIA CVP BP ICS-90, 2016

Example: Car Diagnosis
ICS-90, 2016

Example: Printer Troubleshooting
ICS-90, 2016

Linkage Analysis ? ? A a B b A A 4 A | ? B | ? 6 A | a B | b
2 1 ? ? A a B b A A 3 4 A | ? B | ? 5 6 A | a B | b There are many applications to bio-informatics of Bayesian networks. One recent application of graphical models that is quite successful is linkage analysis. Given a family tree, phenotype of individuals in the tree at the studied trait (affected/unaffected/unknown), and partial, unordered genotype information at some marker loci Compute the most probable location of the disease gene. This is done by placing the disease gene on some marker and computing the probability of the data given the assumed location, which is represented by the distance, theta, from a known loci. 6 individuals Haplotype: {2, 3} Genotype: {6} Unknown ICS-90, 2016

Linkage Analysis: 6 People, 3 Markers
L11m L11f L12m L12f X11 X12 S15m S13m L13m L13f L14m L14f X13 X14 Modeling: coming up with the Bayesian network Reasoning: finding the most likely location of a Gene by an Algorithm S15m S15m L15m L15f L16m L16f S15m S16m X15 X16 L21m L21f L22m L22f X21 X22 S25m S23m L23m L23f L24m L24f X23 X24 S25m S25m L25m L25f L26m L26f Here is an example of using Bayesian networks for linkage analysis. It models the genetic inheritance in a family of 6 individuals relative to some genes of interest. The task is to find a disease gene on a chromosome This domain yields very hard probabilistic networks that contain both probabilistic information and deterministic relationship And it drives many of the methods that we currently develop. It is remarkable that the most scalable linkage analysis tool today is Superlink (deceloped in the Technion) which is using general purpose Graphical models algorithms. So, in my talk I would like to focus on the principles that underlie reasoning in graphical models and allow to apply efficient computation Or understand when this is not feasible. . S25m S26m X25 X26 L31m L31f L32m L32f X31 X32 S35m S33m L33m L33f L34m L34f X33 X34 S35m S35m L35m L35f L36m L36f ICS-90, 2016 S35m S36m X35 X36

The Probabilistic Activity Model
dk-1 wk-1 dk wk Time-of-day d Day-of-week w gk-1 gk Modeling = Learning Goal g rk-1 rk Route taken by the person r xk-1 xk x=<location, velocity> GPS reading z Cookie Reading y zk-1 zk Time k-1 Time k Liao et al (2004), Gogate and Dechter (2005) ICS-90, 2016

Example of Route Route Seen Route Predicted Grocery store ICS-90, 2016
Once a probabilistic model is learnt, we can use our system to predict what route the person is more likely to take and what is his current goal. For example, the route on the left was seen in the form of GPS reading by our model and the route on the right was predicted by our model. As we can see our model predicted that the person was likely to go to a grocery store. Grocery store Route Seen Route Predicted ICS-90, 2016

Sample Domains for Graphical Moldels
Web Pages and Link Analysis Linkage analysis Communication Networks (Cell phone Fraud Detection) Natural Language Processing (e.g. Information Extraction and Semantic Parsing Object Recognition and Scene Analysis Battle-space Awareness Epidemiological Studies Citation Networks Geographical Information Systems Intelligence Analysis (Terrorist Networks) Financial Transactions (Money Laundering) Computational Biology … ICS-90, 2016 27 27

Complexity of Automated Reasoning
Constraint satisfaction Counting solutions Combinatorial optimization Belief updating Most probable explanation Decision-theoretic planning Reasoning is computationally hard Complexity is Time and space(memory) ICS-90, 2016

Handling complex tasks
Identifying tractable structures Approximations Using dependency graph structure Structure inherent in relationships. ICS-90, 2016

A Road Map Tasks Methods ICS-90, 2016

Overview What are graphical models
Exact Algorithms: Inference and Search Approximate algorithms: mini-bucket, belief propagation, constraint propagation AND/OR search for combinatorial optimization Current focus: AND/OR search and Compilation Approximation by Sampling and belief propagation So, my plan is to provide a brief overview of principles of reasoning with graphical models developed in the last decade in constraints And probabilistic networks in inference and search andthen focus on a new framework for search algorithms in Graphical models using AND/OR search spaces. Towards the end I will show that and/or search spaces can be used for compilation, Especially how they can extended the notiono f OBDDs ICS-90, 2016 31 31

Distributed Belief Propagation
How many people? 5 5 5 4 3 2 1 5 5 The essence of belief propagation is to make global information be shared locally by every entity 1 2 3 4 The essence of belief propagation is to make global information be shared locally by every entity ICS-90, 2016

Sudoku – Constraint Satisfaction
Variables: empty slots Domains = {1,2,3,4,5,6,7,8,9} Constraints: 27 all-different Constraint Propagation Inference . 2 Each row, column and major block must be alldifferent “Well posed” if it has unique solution: 27 constraints ICS-90, 2016

Constraint Propagation
A < B 1 2 3 A B 1 1 2 2 < 3 3 A B Sound Incomplete Always converges (polynomial) B = C 1 2 3 A < D 1 2 3 < = D D C C 1 < 1 2 D < C 1 2 3 2 3 3 ICS-90, 2016

Distributed Belief Propagation
Causal support The pis are causal support contributed by the parent of X The lambdas denote the current strength of the diagnostic support Diagnostic support ICS-90, 2016

Loopy Belief Propagation
ICS-90, 2016 36

Flattening the Bayesian Network
P(A) 1 .2 2 .5 3 .3 … A 1 2 3 A B P(B|A) 1 2 .3 3 .7 .4 .6 .1 .9 … A B 1 2 3 A C P(C|A) 1 2 3 … A AB AC ABD BCF DFG B 4 5 3 6 2 D F C 1 A AB AC ABD BCF DFG B 4 5 3 6 2 D F C 1 A C 1 2 3 A B D P(D|A,B) 1 2 3 … A B D 1 2 3 B C F P(F|B,C) 1 2 3 … B C F 1 2 3 D F G P(G|D,F) 1 2 3 … D F G 1 2 3 Belief network Flat constraint network ICS-90, 2016

Flat Network - Example 1 3 2 4 5 6 ICS-90, 2016 A AB AC ABD BCF DFG A
P(A) 1 .2 2 .5 3 .3 … A B P(B|A) 1 2 .3 3 .7 .4 .6 .1 .9 … A AB AC ABD BCF DFG B 4 5 3 6 2 D F C 1 A C P(C|A) 1 2 3 … A B D P(D|A,B) 1 2 3 … B C F P(F|B,C) 1 2 3 … D F G P(G|D,F) 1 2 3 … ICS-90, 2016

Agenda My work in AI How did I get to AI?
BSc. in Math and Statistics: (Israel, HUJI 1973) MS. Applied math: (Israel, in Weitzman Institute, 1975 ) I stayed in math because I was afraid of programming PHD. CS, UCLA, 1985 Started in Computer networks… more theory (Kleinrock, the father of the internet) Then was fascinated by the vision of AI … overcame my fear of (some) programming. I was afraid of programming ICS-90, 2016

My Work Constraint networks: Graph-based parameters and algorithms for constraint satisfaction, tree-width and cycle-cutset, summarized in “Constraint Processing”, Morgan Kaufmann, 2003 Probabilistic networks: Transferring these ideas to Probabilistic network, helping unifying the principles. Current work: Mixing probabilistic and deterministic network ICS-90, 2016

Automated Reasoning Group
Thank you Dan Frost Eddie Schwalb Kalev Kask Irina Rish Bozhena Bidyuk Robert Mateescu Radu Marinescu Vibhav Gogate Emma Rollon Lars Otten Natalia Flerova Andrew Gelfand William Lam Junkyu Lee Filjor Broka

Rina Dechter Bren school of ICS University of California, Irvine

Similar presentations

Presentation on theme: "Rina Dechter Bren school of ICS University of California, Irvine"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Rina Dechter Bren school of ICS University of California, Irvine

Similar presentations

Presentation on theme: "Rina Dechter Bren school of ICS University of California, Irvine"— Presentation transcript:

Similar presentations

About project

Feedback