The Informational Complexity of Learning from Examples

This thesis attempts to quantify the amount of information needed to learn certain tasks. The tasks chosen vary from learning functions in a Sobolev space using radial basis function networks to learning grammars in the principles and parameters framework of modern linguistic theory. These problems are analyzed from the perspective of computational learning theory and certain unifying perspectives emerge.

Using Recurrent Networks for Dimensionality Reduction

This report explores how recurrent neural networks can be exploited for learning high-dimensional mappings. Since recurrent networks are as powerful as Turing machines, an interesting question is how recurrent networks can be used to simplify the problem of learning from examples. The main problem with learning high-dimensional functions is the curse of dimensionality which roughly states that the number of examples needed to learn a function increases exponentially with input dimension. This thesis proposes a way of avoiding this problem by using a recurrent network to decompose a high-dimensional function into many lower dimensional functions connected in a feedback loop.

Representation and Detection of Shapes in Images

We present a set of techniques that can be used to represent and detect shapes in images. Our methods revolve around a particular shape representation based on the description of objects using triangulated polygons. This representation is similar to the medial axis transform and has important properties from a computational perspective. The first problem we consider is the detection of non-rigid objects in images using deformable models. We present an efficient algorithm to solve this problem in a wide range of situations, and show examples in both natural and medical images. We also consider the problem of learning an accurate non-rigid shape model for a class of objects from examples. We show how to learn good models while constraining them to the form required by the detection algorithm. Finally, we consider the problem of low-level image segmentation and grouping. We describe a stochastic grammar that generates arbitrary triangulated polygons while capturing Gestalt principles of shape regularity. This grammar is used as a prior model over random shapes in a low level algorithm that detects objects in images.

Learning-Based Approach to Real Time Tracking and Analysis of Faces

This paper describes a trainable system capable of tracking faces and facialsfeatures like eyes and nostrils and estimating basic mouth features such as sdegrees of openness and smile in real time. In developing this system, we have addressed the twin issues of image representation and algorithms for learning. We have used the invariance properties of image representations based on Haar wavelets to robustly capture various facial features. Similarly, unlike previous approaches this system is entirely trained using examples and does not rely on a priori (hand-crafted) models of facial features based on optical flow or facial musculature. The system works in several stages that begin with face detection, followed by localization of facial features and estimation of mouth parameters. Each of these stages is formulated as a problem in supervised learning from examples. We apply the new and robust technique of support vector machines (SVM) for classification in the stage of skin segmentation, face detection and eye detection. Estimation of mouth parameters is modeled as a regression from a sparse subset of coefficients (basis functions) of an overcomplete dictionary of Haar wavelets.

Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Sigmoid type belief networks, a class of probabilistic neural networks, provide a natural framework for compactly representing probabilistic information in a variety of unsupervised and supervised learning problems. Often the parameters used in these networks need to be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EM-algorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. We introduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well.

Example Based Learning for View-Based Human Face Detection

We present an example-based learning approach for locating vertical frontal views of human faces in complex scenes. The technique models the distribution of human face patterns by means of a few view-based "face'' and "non-face'' prototype clusters. At each image location, the local pattern is matched against the distribution-based model, and a trained classifier determines, based on the local difference measurements, whether or not a human face exists at the current image location. We provide an analysis that helps identify the critical components of our system.

Sequential Optimal Recovery: A Paradigm for Active Learning

In most classical frameworks for learning from examples, it is assumed that examples are randomly drawn and presented to the learner. In this paper, we consider the possibility of a more active learner who is allowed to choose his/her own examples. Our investigations are carried out in a function approximation setting. In particular, using arguments from optimal recovery (Micchelli and Rivlin, 1976), we develop an adaptive sampling strategy (equivalent to adaptive approximation) for arbitrary approximation schemes. We provide a general formulation of the problem and show how it can be regarded as sequential optimal recovery. We demonstrate the application of this general formulation to two special cases of functions on the real line 1) monotonically increasing functions and 2) functions with bounded derivative. An extensive investigation of the sample complexity of approximating these functions is conducted yielding both theoretical and empirical results on test functions. Our theoretical results (stated insPAC-style), along with the simulations demonstrate the superiority of our active scheme over both passive learning as well as classical optimal recovery. The analysis of active function approximation is conducted in a worst-case setting, in contrast with other Bayesian paradigms obtained from optimal design (Mackay, 1992).

Observations on Cortical Mechanisms for Object Recognition andsLearning

This paper sketches a hypothetical cortical architecture for visual 3D object recognition based on a recent computational model. The view-centered scheme relies on modules for learning from examples, such as Hyperbf-like networks. Such models capture a class of explanations we call Memory-Based Models (MBM) that contains sparse population coding, memory-based recognition, and codebooks of prototypes. Unlike the sigmoidal units of some artificial neural networks, the units of MBMs are consistent with the description of cortical neurons. We describe how an example of MBM may be realized in terms of cortical circuitry and biophysical mechanisms, consistent with psychophysical and physiological data.

People Recognition in Image Sequences by Supervised Learning

We describe a system that learns from examples to recognize people in images taken indoors. Images of people are represented by color-based and shape-based features. Recognition is carried out through combinations of Support Vector Machine classifiers (SVMs). Different types of multiclass strategies based on SVMs are explored and compared to k-Nearest Neighbors classifiers (kNNs). The system works in real time and shows high performance rates for people recognition throughout one day.

A Unified Framework for Regularization Networks and Support Vector Machines

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples -- in particular the regression problem of approximating a multivariate function from sparse data. We present both formulations in a unified framework, namely in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics.

Natural Object Categorization

This thesis addresses the problem of categorizing natural objects. To provide a criteria for categorization we propose that the purpose of a categorization is to support the inference of unobserved properties of objects from the observed properties. Because no such set of categories can be constructed in an arbitrary world, we present the Principle of Natural Modes as a claim about the structure of the world. We first define an evaluation function that measures how well a set of categories supports the inference goals of the observer. Entropy measures for property uncertainty and category uncertainty are combined through a free parameter that reflects the goals of the observer. Natural categorizations are shown to be those that are stable with respect to this free parameter. The evaluation function is tested in the domain of leaves and is found to be sensitive to the structure of the natural categories corresponding to the different species. We next develop a categorization paradigm that utilizes the categorization evaluation function in recovering natural categories. A statistical hypothesis generation algorithm is presented that is shown to be an effective categorization procedure. Examples drawn from several natural domains are presented, including data known to be a difficult test case for numerical categorization techniques. We next extend the categorization paradigm such that multiple levels of natural categories are recovered; by means of recursively invoking the categorization procedure both the genera and species are recovered in a population of anaerobic bacteria. Finally, a method is presented for evaluating the utility of features in recovering natural categories. This method also provides a mechanism for determining which features are constrained by the different processes present in a multiple modal world.

Maygen: A Symbolic Debugger Generation System

With the development of high-level languages for new computer architectures comes the need for appropriate debugging tools as well. One method for meeting this need would be to develop, from scratch, a symbolic debugger with the introduction of each new language implementation for any given architecture. This, however, seems to require unnecessary duplication of effort among developers. This paper describes Maygen, a "debugger generation system," designed to efficiently provide the desired language-dependent and architecture-dependent debuggers. A prototype of the Maygen system has been implemented and is able to handle the semantically different languages of C and OPAL.

Learning from Ambiguity

There are many learning problems for which the examples given by the teacher are ambiguously labeled. In this thesis, we will examine one framework of learning from ambiguous examples known as Multiple-Instance learning. Each example is a bag, consisting of any number of instances. A bag is labeled negative if all instances in it are negative. A bag is labeled positive if at least one instance in it is positive. Because the instances themselves are not labeled, each positive bag is an ambiguous example. We would like to learn a concept which will correctly classify unseen bags. We have developed a measure called Diverse Density and algorithms for learning from multiple-instance examples. We have applied these techniques to problems in drug design, stock prediction, and image database retrieval. These serve as examples of how to translate the ambiguity in the application domain into bags, as well as successful examples of applying Diverse Density techniques.

From First Contact to Close Encounters: A Developmentally Deep Perceptual System for a Humanoid Robot

This thesis presents a perceptual system for a humanoid robot that integrates abilities such as object localization and recognition with the deeper developmental machinery required to forge those competences out of raw physical experiences. It shows that a robotic platform can build up and maintain a system for object localization, segmentation, and recognition, starting from very little. What the robot starts with is a direct solution to achieving figure/ground separation: it simply 'pokes around' in a region of visual ambiguity and watches what happens. If the arm passes through an area, that area is recognized as free space. If the arm collides with an object, causing it to move, the robot can use that motion to segment the object from the background. Once the robot can acquire reliable segmented views of objects, it learns from them, and from then on recognizes and segments those objects without further contact. Both low-level and high-level visual features can also be learned in this way, and examples are presented for both: orientation detection and affordance recognition, respectively. The motivation for this work is simple. Training on large corpora of annotated real-world data has proven crucial for creating robust solutions to perceptual problems such as speech recognition and face detection. But the powerful tools used during training of such systems are typically stripped away at deployment. Ideally they should remain, particularly for unstable tasks such as object detection, where the set of objects needed in a task tomorrow might be different from the set of objects needed today. The key limiting factor is access to training data, but as this thesis shows, that need not be a problem on a robotic platform that can actively probe its environment, and carry out experiments to resolve ambiguity. This work is an instance of a general approach to learning a new perceptual judgment: find special situations in which the perceptual judgment is easy and study these situations to find correlated features that can be observed more generally.