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Lecture 7: Introduction to Machine Learning
Machine learning: the study and development of algorithms that allow computers to evolve and improve at performing a given task by using past experience.
Examples include recognizing shapes, images, and spoken words; driving a vehicle; classifying new data based on an already existing classification system; game playing.
Learning vs. Understanding and Insight
- Understanding involves the cognitive capacity to formulate knowledge of why certain learning steps proved conducive to reaching a goal, and carries over to similar tasks.
- On the other hand, learning has the less ambitious task of discovering a set of behavioral constraints which are conducive to attaining a goal. Does not require reflection on the significance of the constraints within the context of the problem.
Definition of learning: a program is said to learn form experience E with respect to some class of tasks T and a performance measure P if its performance at tasks in T , as measured by P , improves with experience E.
Learning Example:
- T = shooting free throws
- P measures how close a free throw came to entering the goal
- E represents the collection of previous free throw attempts. Each attempt contains information about trajectory, initial velocity, ball rotation, and is paired with a per- formance measure.
- Method of learning: perform quadratic regression on E. Assume that the func- tion P (E) is a quadratic surface that is concave downward. Then locate the global maximum of the best such surface that fits the data.
Supervised vs. Unsupervised
- Supervised: learning experience is controlled by a teacher; key learning queues are provided by the teacher
- Unsupervised: learning is determined through empirical inquiry and observation
External Learning vs. Internal Learning
- External: task, feedback, and performance measure can be observed by an outside party (but learning mechanisms often remain hidden).
- Internal: task, feedback, and performance measure exist as part of the internal learn- ing mechanism of the machine and is not necessarily observable.
- learning an external task often requires a hierarchy of internal learning tasks.
Alternative definition of learning: The process of evolving a set of internal constraints (based upon the performance results P of past experience E while performing task T ) which will induce a machine to perform task T at optimal performance Popt.
Target function for learning a task: a function f that is similar to a search evaluation function, in that it helps the machine determine its next action for when it gives its next performance. Quite often learning is reduced to evolving a target function until satisfactory performance is met.
- inputs: current state of the system, including all knowledge (feedback) obtained up to that point.
- outputs: next step to be taken by the machine
- must be computationally feasible to be of any use.
- major issue when designing a learning machine: how to choose a representation of the target function f?
Major issues that drive the research in machine learning:
- How to represent a learning target function?
- What learning algorithms exist for evolving a target function based on feedback?
- Which evaluation functions work best for which problems?
- How to prove that a learning algorithms will (efficiently) converge to an acceptable level of performance?
- How much training/experience is needed to effectively evolve a target function?
- How to choose the next training experience?
Concept Learning and General-to-Specific Ordering
Concept Learning: Inferring a Boolean-valued function from the training examples of its input and output.
Concept Learning Example 1: give a Boolean algebraic expression for the function f (W, C, T ) which is true if and only if the piece of fruit with characteristics weight W , color C, and texture T is a watermelon.
Ingredients of a concept learning task:
- attributes and features: used to describe each instance of the domain and to help classify negative and positive instances of the domain.
- Hypothesis space H: consists of a restricted class of Boolean-valued functions h : X → { 0 , 1 }, where X represents the feature space.
- Target concept c : X → { 0 , 1 }: the concept for which the learning algorithm con- verges to.
- Training examples: (x 1 , α 1 ), (x 2 , α 2 ),... , (xm, αm), where each xi ∈ X and αi ∈ { 0 , 1 }, where αi = 1 (respectively, 0) represents a positive (respectively, negative) example.
Inductive-learning hypothesis: any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples.
Algorithms for finding the target concept in the general-to-specific hypothesis space
Find-S Algorithm
- initialize h to the most specific hypothesis in H
- for each positive training example x
- for each attribute constraint ai in h, if the constraint is satisfied by x then do nothing. Otherwise, replace ai in h by the next more general constraint that is satisfied by x.
- output hypothesis h
Theorem 1: assuming there exists a target hypothesis c which correctly classifies all exam- ples from the feature space, Find-S algorithm will converge to c.
Proof:
Find-S Example: use the find-S algorithm to find a target hypothesis for the concept of “apple”, using the following ordered training examples:
- ((medium, red, smooth), yes)
- ((heavy, green, smooth), no)
- ((medium, green, smooth), yes)
Candidate-Elimination Learning Algorithm
Hypothesis h is said to be consistent with respect to a set of training examples D iff h(x) = c(x), f orallx ∈ D, where c(x) represents the classification of x.
Let H be a hypothesis space and D a set of training examples. Then
- the version space VH,D is defined as
VH,D = {h ∈ H|consistent(h, D)}.
- the general boundry is the set of maximally general members of VH,D.
- the specific boundry is the set of maximally specific members of VH,D.
Version Space Theorem:
VH,D = {h ∈ H|(∃s)(∃g)(g ≥ h ≥ s)},
where s is an element from the specific boundry, g is an element from the general boundry, and ≥ represents the general-to-specific ordering.
Proof of Candidate-Elimination Algorithm Correctness:
Candidate-Elimination Example: use the algorithm to find the version space for the concept of “apple”, using the following ordered training examples:
- ((medium, red, smooth), yes)
- ((heavy, brown, rough), no)
- ((medium, green, smooth), yes)
- ((medium, orange, smooth), no)
- ((light, red, rough), no)
Inductive Bias in Learning
Unbiased learner: one that is capable of learning every possible target concept associated with a feature space.
Futility of the unbiased learner: a learner that makes no a priori assumptions regarding the identity of the target concept has no rational basis for classifying new examples.
Inductive Bias in Learning: the assumption that the target concept belongs in a given hypothesis space.
