Analogies and Case-Based Reasoning

Analogy Analogy is either the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from a particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general. -- Wikipedia An analogy is a relationship between two or more entities which are similar in one or more respects. An analogy is present whenever [one or more of] the following descriptions are present: resemblance, similarity, correspondence, likeness, comparison, counterpart, resemblance of relations, and mapping. -- philosophy.lander.edu

Analogy Analogy plays a significant role in many cognitive tasks, including Problem solving & decision making Perception Memory Creativity Emotion Analogy is particularly important in ordinary language and common sense E.g., the use of proverbs, idioms, metaphors It lies behind basic tasks such as the identification of places, objects and people E.g., face perception and facial recognition systems. Hofstadter: Analogy is "the core of cognition" [Gentner et al. 2001 ]

Non-Argumentative Use of Analogy Literary uses Metaphor: a word or phrase literally denoting one kind of object or idea is used in place of another to suggest a likeness or analogy between them E.g., the ship plows the sea. E.g., his fist was a knotty hammer Similié: a figure of speech comparing two unlike things often introduced by the words, "like" or "as." E.g., cheeks like roses E.g., "And ice mast high came floating by as green as emerald" Use in explanation The atom is (like) a miniature solar system A tree is (like) a factory

Analogical Inference An analogical inference is drawn from a resemblance of relations. J. S. Mill's example of a country which has sent out colonies is termed "the mother country." The colonies stand in the same relation to her as parents do to their children Reasoning by analogy, then, obedience or affection is due by the colonies to the mother country. parents → children mother country → colonies

Analogical Inference The general form of an analogical argument is as follows a, b, c, d stand for entities P, Q, R stand for properties Note that this essentially reduces analogy to a form of induction. a, b, c, d all have the properties P and Q. a, b, c all have the further property R _________________________________ therefore, d probably has the property R

Structured Mapping (Gentner) Analogy depends on the mapping or alignment of the elements of source and target The mapping takes place not only between objects, but also between relations of objects and between relations of relations The whole mapping yields the assignment of a predicate or a relation to the target When used in a computational framework, analogy would require the computation of similarities between the source and the target

High-Level Perception Douglas Hofstadter challenged the shared structure theory and mostly its applications in computer science Argued that there is no line between perception, including high-level perception, and analogical thought. Analogy occurs not only after, but also before and at the same time as high-level perception In high-level perception, humans make representations selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers (a student of Hofstadter) concluded that analogy is high-level perception. Other claims Analogy is only a metaphor (Forbus, 1998). Hofstadter and Gentner do not defend opposite views, but are instead dealing with different aspects of analogy (Morrison and Dietrich 1995)

Case-Based Reasoning The computational view of analogy has led to an approach called Case-based reasoning (CBR) with many applications in Computer Science and Artificial Intelligence CBR is the process of solving new problems based on the solutions of similar past problems E.g., an auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms E.g., a judge who makes a ruling in a trial based on legal precedents An example of computations CBR: Collaborative Filtering Recommender Systems.

Case-Based Reasoning To solve a current problem The problem is matched against the cases in the case base Similar cases are retrieved The retrieved cases are used to suggest a solution which is tested for success If necessary, the solution is then revised Finally the current problem and the final solution are retained as part of a new case.

Case-Based Reasoning All case-based reasoning methods have in common the following process: retrieve the most similar case (or cases) comparing the case to the library of past cases; reuse the retrieved case to try to solve the current problem; revise and adapt the proposed solution if necessary; retain the final solution as part of a new case. Retrieving a case starts with a (possibly partial) problem description and ends when a best matching case has been found. The subtasks involve: identifying a set of relevant problem descriptors; matching the case and returning a set of sufficiently similar cases (given a similarity threshold of some kind); and selecting the best case from the set of cases returned.

Collaborative Filtering Applies the basic CBR process to user profile data to predict a new user’s preferences Predictions are computed based the other users’ with similar interests scores on items in the new user’s profile i.e. users with similar tastes (aka “nearest neighbors”) requires computing correlations between user u and other users according to interest scores or ratings

Basic Collaborative Filtering Process Current User Record <user, item1, item2, …> Neighborhood Formation Nearest Neighbors Recommendation Engine Combination Function Historical User Records user item rating Recommendations Neighborhood Formation Phase Recommendation Phase Both of the Neighborhood formation and the recommendation phases are real-time components

Collaborative Filtering: Measuring Similarities Pearson Correlation weight by degree of correlation between user U and user J 1 means very similar, 0 means no correlation, -1 means dissimilar Works well in case of user ratings (where there is at least a range of 1-5) Not always possible (in some situations we may only have implicit binary values, e.g., whether a user did or did not select an item) Average rating of user J on all items.

Example Collaborative System Item1 Item 2 Item 3 Item 4 Item 5 Item 6 Correlation with Alice Alice 5 2 3 ? User 1 4 1 -1.00 User 2 0.33 User 3 .90 User 4 0.19 User 5 User 6 0.65 User 7 Prediction  Best match Using k-nearest neighbor with k = 1

Item-based Collaborative Filtering Find similarities among the items based on ratings across users Prediction of item i for user a is based on the past ratings of user a on items similar to i. Suppose: Predicted rating for Karen on Indep. Day will be 7, because she rated Star Wars 7 (using only the most similar item) sim(Star Wars, Indep. Day) > sim(Jur. Park, Indep. Day) > sim(Termin., Indep. Day)

Item-Based Collaborative Filtering Prediction  Item1 Item 2 Item 3 Item 4 Item 5 Item 6 Alice 5 2 3 ? User 1 4 1 User 2 User 3 User 4 User 5 User 6 User 7 Item similarity 0.76 0.79 0.60 0.71 0.75 Best match

Problem with Collaborative Filtering Can be attacked using profile injection attacks consist of a number of "attack profiles" added to the system by providing ratings for various items engineered to bias the system's recommendations Two basic types: “Push attack” (“Shilling”): designed to promote an item “Nuke attack”: designed to demote a item

A Successful Push Attack Item1 Item 2 Item 3 Item 4 Item 5 Item 6 Correlation with Alice Alice 5 2 3 ? User 1 4 1 -1.00 User 2 0.33 User 3 .90 User 4 0.19 User 5 User 6 0.65 User 7 Attack 1 Attack 2 0.76 Attack 3 0.93 Prediction  Best Match “user-based” algorithm using k-nearest neighbor with k = 1

Movielens Recommender System http://movielens.umn.edu