Teaching Dimension versus VC Dimension
نویسندگان
چکیده
In this report, we give a brief survey of various results relating the Teaching Dimension and VC-Dimension. The concept of Teaching Dimension was first introduced by Goldman and Kearns, 1995 and Sinohara and Miyano, 1991. In this model, an algorithm tries to learn the hidden concept c from examples, called the teaching set, which uniquely identifies c from the rest of the concepts in the concept class C. In a seemingly unrelated direction, the notion of sample compression was introduced by Warmuth and Littlestone, where they study if the number of samples needed to learn a concept can somehow be compressed so that the number of training examples needed is minimized. In this survey, we give results from recent literature which makes interesting connections between Teaching Sets and VC Dimension.
منابع مشابه
Open Problem: Recursive Teaching Dimension Versus VC Dimension
The Recursive Teaching Dimension (RTD) of a concept class C is a complexity parameter referring to the worst-case number of labelled examples needed to learn any target concept in C from a teacher following the recursive teaching model. It is the first teaching complexity notion for which interesting relationships to the VC dimension (VCD) have been established. In particular, for finite maximu...
متن کاملRecursive teaching dimension, VC-dimension and sample compression
This paper is concerned with various combinatorial parameters of classes that can be learned from a small set of examples. We show that the recursive teaching dimension, recently introduced by Zilles et al. (2008), is strongly connected to known complexity notions in machine learning, e.g., the self-directed learning complexity and the VC-dimension. To the best of our knowledge these are the fi...
متن کاملSauer's Bound for a Notion of Teaching Complexity
This paper establishes an upper bound on the size of a concept class with given recursive teaching dimension (RTD, a teaching complexity parameter.) The upper bound coincides with Sauer’s well-known bound on classes with a fixed VC-dimension. Our result thus supports the recently emerging conjecture that the combinatorics of VC-dimension and those of teaching complexity are intrinsically interl...
متن کاملRecursive Teaching Dimension, Learning Complexity, and Maximum Classes
This paper is concerned with the combinatorial structure of concept classes that can be learned from a small number of examples. We show that the recently introduced notion of recursive teaching dimension (RTD, reflecting the complexity of teaching a concept class) is a relevant parameter in this context. Comparing the RTD to self-directed learning, we establish new lower bounds on the query co...
متن کاملTeaching and compressing for low VC-dimension
In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. We present relatively efficient constructions of sample compression schemes and teaching sets for classes of low VC-dimension. Let C be a finite boolean concept class of VC-dimension d. Set k = O(d2d log log |C|). We construct sample compression schemes of size k...
متن کامل