Abstract: We study the problem of deterministically predicting boolean values by combining the boolean predictions of several experts. Previous on-line algorithms for this problem predict with the weighted majority of the experts'' predictions. These algorithms give each expert an exponential weight beta^m where beta is a constant in [0,1) and m is the number of mistakes made by the expert in the past. We show that it is better to use sums of binomials as weights. In particular, we present a deterministic algorithm using binomial weights that has a better worst case mistake bound than the best deterministic algorithm using exponential weights. The binomial weights naturally arise from a version space argument. We also show how both exponential and binomial weighting schemes can be used to make prediction algorithms robust against noise.

Abstract: This dissertation addresses the problem of unsupervised learning for pattern classification or category learning. A model that is based on gross cortical anatomy and implements biologically plausible computations is developed and shown to have classification power approaching that of a supervised discriminant algorithm. .pp The advantage of supervised learning is that the final error metric is available during training. Unfortunately, when modeling human category learning, or in constructing classifiers for autonomous robots, one must deal with not having an omniscient entity labeling all incoming sensory patterns. We show that we can substitute for the labels by making use of structure between the pattern distributions to different sensory modalities. For example the co-occurrence of a visual image of a cow with a ``moo'''' sound can be used to simultaneously develop appropriate visual features for distinguishing the cow image and appropriate auditory features for recognizing the moo. .pp We model human category learning as a process of minimizing the disagreement between outputs of sensory modalities processing temporally coincident patterns. We relate this mathematically to the optimal goal of minimizing the number of misclassifications in each modality and apply the idea to derive an algorithm for piecewise linear classifiers in which each network uses the output of the other networks as a supervisory signal. .pp Using the Peterson-Barney vowel dataset we show that the algorithm finds appropriate placement for the classification boundaries. The algorithm is then demonstrated on the task of learning to recognize acoustic and visual speech from images of lips and their emanating sounds Performance on these tasks is within 1-7\% of the related supervised algorithm (LVQ2.1). .pp Finally we compare the algorithm to Becker''s IMAX algorithm and give suggestions as to how the algorithm may be implemented in the brain using physiological results concerning the relationship between two types of neural plasticity, LTP and LTD, observed in visual cortical cells. We also show how the algorithm can be used as an efficient method for dealing with learning from data with missing values.

Abstract: We present a membership query (i.e. black box interpolation) algorithm for exactly identifying the class of read-once formulas over the basis of Boolean threshold functions. We also present a catalogue of generic transformations that can be used to convert an algorithm in one learning model into an algorithm in a different model.

Abstract: We study the worst-case behavior of a family of learning algorithms based on Sutton's [7] method of temporal differences. In our on-line learning framework, learning takes place in a sequence of trials, and the goal of the learning algorithm is to estimate a discounted sum of all the reinforcements that will be received in the future. In this setting, we are able to prove general upper bounds on the performance of a slightly modified version of Sutton's so-called TD(A) algorithm. These bounds are stated in terms of the performance of the best linear predictor on the given training sequence, and are proved without making any statistical assumptions of any kind about the process producing the learner's observed training sequence. We also prove lower bounds on the performance of any algorithm for this learning problem, and give a similar analysis of the closely related problem of learning to predict in a model in which the learner must produce predictions for a whole batch of observations before receiving reinforcement.

Abstract: This paper proposes a new adaptive competitive learning algorithm called "the probabilistic winner-take-all." The algorithm is based on a learning scheme developed by Agrawala within the statistical pattern recognition literature (Agrawala 1970). Its name stems from the fact that for a given input pattern once each competitor computes the probability of being the one that generated this pattern, the computed probabilities are utilized to probabilistically choose a winner. Then, only this winner is permitted to learn. The learning rule of the algorithm is derived for three different cases. Its properties are discussed and compared to those of two other competitive learning algorithms, namely the standard winner-take-all and the maximum-likelihood soft competition. Experimental comparison is also given. When all three algorithms are used to train the hidden layer of radial-basis-function classifiers, experiments indicate that classifiers trained with the probabilistic winner-take-all outperform those trained with the other two algorithms.

Abstract: Achieving a higher prediction accuracy rate is crucial for all learning algorithms, particularly for real application purposes. This paper presents the factors which could prevent a learning algorithm from achieving a higher prediction accuracy rate, and indicates that overfitting on low-quality data and being misled by this are two important factors. It also presents strategies for dealing with this problem. A new approach, called field learning, is described, by which the learnt rules can overcome this problem and achieve a higher prediction accuracy on new unseen cases. Our experiments show that this approach can achieve a higher prediction accuracy rate on new unseen cases, but it achieved a lower accuracy rate on some of the training data sets. >

Abstract: This paper deals with the implementation of a fast algorithm for two-dimensional weighted median filtering. Because of the vast amount of data that must be handled, the development of fast algorithms is very important. A fast running algorithm for weighted median filtering, which is based on using a histogram and updating it, is proposed. Experimental results prove the superiority of the proposed algorithm over that of finding the weighted median either by sorting with the Quick Sort or by selecting the r-th order statistic.

Abstract: We describe and compare two paradigms of on-line learning, which we call Bayesian and Popperian. In this paper the Bayesian paradigm is represented by Littlestone and Warmuth's Weighted Majority Algorithm, and the Popperian paradigm is represented by Rivest and Schapire's reset-free algorithm for exact learning of finite automata with membership and equivalence queries. Both algorithms are applied to the problem of optimal control of a finite-state plant in a finite-state environment. The advantage of the control strategy based on the Weighted Majority Algorithm is its robustness and better performance (actually, its performance is nearly optimal in the class of deterministic control strategies), and the advantage of the control strategy based on Rivest and Schapire's algorithm is its computational efficiency.

Abstract: In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e. it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.

Abstract: A simple learning algorithm for Hidden Markov Models (HMMs) is presented together with a number of variations. Unlike other classical algorithms such as the Baum-Welch algorithm, the algorithms described are smooth and can be used on-line (after each example presentation) or in batch mode, with or without the usual Viterbi most likely path approximation. The algorithms have simple expressions that result from using a normalized-exponential representation for the HMM parameters. All the algorithms presented are proved to be exact or approximate gradient optimization algorithms with respect to likelihood, log-likelihood, or cross-entropy functions, and as such are usually convergent. These algorithms can also be casted in the more general EM (Expectation-Maximization) framework where they can be viewed as exact or approximate GEM (Generalized Expectation-Maximization) algorithms. The mathematical properties of the algorithms are derived in the appendix.

Abstract: I show that the linear threshold functions are polynomially learnable in the presence of classification noise, i.e., polynomial in n, 1/e, 1/δ, and 1/s, where n is the number of Boolean attributes, e and δ are the usual accuracy and confidence parameters, and s indicates the minimum distance of any example from the target hyperplane, which is assumed to be lower than the average distance of the examples from any hyperplane. This result is achieved by modifying the Perceptron algorithm—for each update, a weighted average of a sample of misclassified examples and a correction vector is added to the current weight vector. Similar modifications are shown for the Weighted Majority algorithm. The correction vector is simply the mean of the normalized examples. In the special case of Boolean threshold functions, the modified Perceptron algorithm performs O (n2e−2 ) iterations over O(n4e −2ln(n/(δe))) examples. This improves on the previous classification-noise result of Angluin and Laird to a much larger concept class with a similar number of examples, but with multiple iterations over the examples.