Catálogo de publicaciones - libros

Philosophers have pondered the phenomenon of learning for millennia; scientists and psychologists have studied learning for more than a century. But the analysis of learning as a and phenomenon is much more recent, going back only a few decades. Learning theory is now an active research area that incorporates ideas, problems, and techniques from a wide range of disciplines including statistics, artificial intelligence, information theory, pattern recognition, and theoretical computer science. Learning theory has many robust connections with more applied research in machine learning and has made significant contributions to the development of applied systems and to fields such as electronic commerce and computational biology.

Kernel methods have proven to be powerful tools in machine learning. They perform well in many applications, and there is also a well-developed theory of sufficient conditions for a kernel to be useful for a given learning problem. However, while a kernel can be thought of as just a pairwise similarity function that satisfies additional mathematical properties, this theory requires viewing kernels as implicit (and often difficult to characterize) maps into high-dimensional spaces. In this talk I will describe work on developing a theory that applies to more general similarity functions (not just legal kernels) and furthermore describes the usefulness of a given similarity function in terms of more intuitive, direct properties, without need to refer to any implicit spaces.

An interesting feature of the proposed framework is that it can also be applied to learning from purely unlabeled data, i.e., clustering. In particular, one can ask how much stronger the properties of a similarity function should be (in terms of its relation to the unknown desired clustering) so that it can be used to well: to learn well without any label information at all. We find that if we are willing to relax the objective a bit (for example, allow the algorithm to produce a hierarchical clustering that we will call successful if some pruning is close to the correct answer), then this question leads to a number of interesting graph-theoretic and game-theoretic properties that are sufficient to cluster well. This work can be viewed as an approach to defining a PAC model for clustering.

This talk is based on work joint with Maria-Florina Balcan and Santosh Vempala.

The emerging field of Ecosystem Informatics applies methods from computer science and mathematics to address fundamental and applied problems in the ecosystem sciences. The ecosystem sciences are in the midst of a revolution driven by a combination of emerging technologies for improved sensing and the critical need for better science to help manage global climate change. This paper describes several initiatives at Oregon State University in ecosystem informatics.

We describe a technique for comparing distributions without the need for density estimation as an intermediate step. Our approach relies on mapping the distributions into a reproducing kernel Hilbert space. Applications of this technique can be found in two-sample tests, which are used for determining whether two sets of observations arise from the same distribution, covariate shift correction, local learning, measures of independence, and density estimation.

We study the parameterized complexity of learning -juntas and some variations of juntas. We show the hardness of learning -juntas and subclasses of -juntas in the PAC model by reductions from a W[2]-complete problem. On the other hand, as a consequence of a more general result we show that -juntas are exactly learnable with improper equivalence queries and access to a W[P] oracle.

We investigate two of the language classes intensively studied by the algorithmic learning theory community in the context of learning with correction queries. More precisely, we show that any pattern language can be inferred in polynomial time in length of the pattern by asking just a linear number of correction queries, and that -reversible languages are efficiently learnable within this setting. Note that although the class of all pattern languages is learnable with membership queries, this cannot be done in polynomial time. Moreover, the class of -reversible languages is not learnable at all using membership queries only.

We study the class of hypothesis composed of linear functionals superimposed with smooth feature maps. We show that for “typical” smooth feature map, the pointwise convergence of hypothesis implies the convergence of some standard metrics such as error rate or area under ROC curve with probability 1 in selection of the test sample from a (Lebesgue measurable) probability density. Proofs use transversality theory. The crux is to show that for every “typical”, sufficiently smooth feature map into a finite dimensional vector space, the counter-image of every affine hyperplane has Lebesgue measure 0.

The results extend to every real analytic, in particular polynomial, feature map if its domain is connected and the limit hypothesis is non-constant. In the process we give an elementary proof of the fundamental lemma that locus of zeros of a real analytic function on a connected domain either fills the whole space or forms a subset of measure 0.