"Boosting" is a general method for improving the performance of any learning algorithm that consistently generates classifiers which need to perform only slightly better than random guessing. A recently proposed and very promising boosting algorithm is AdaBoost [5]. It has been ap(cid:173) plied with great success to several benchmark machine learning problems using rather simple learning algorithms [4], and decision trees [1, 2, 6]. In this paper we use AdaBoost to improve the performances of neural networks. We compare training methods based on sampling the training set and weighting the cost function. Our system achieves about 1.4% error on a data base of online handwritten digits from more than 200 writers.

Multiple-instance learning is a variation on supervised learning, where the task is to learn a concept given positive and negative bags of instances. Each bag may contain many instances, but a bag is labeled positive even if only one of the instances in it falls within the concept. A bag is labeled negative only if all the instances in it are negative. We describe a new general framework, called Diverse Density, for solving multiple-instance learning problems. We apply this framework to learn a simple description of a person from a series of images (bags) containing that person, to a stock selection problem, and to the drug activity prediction problem.

We have constructed an inexpensive video based motorized tracking system that learns to track a head. It uses real time graphical user inputs or an auxiliary infrared detector as supervisory signals to train a convolutional neural network. The inputs to the neural network consist of normalized luminance and chrominance images and motion information from frame differences. Subsampled images are also used to provide scale invariance. During the online training phases the neural network rapidly adjusts the input weights depending up on the reliability of the different channels in the surrounding environment. This quick adaptation allows the system to robustly track a head even when other objects are moving within a cluttered background.

Online learning is one of the most common forms of neural net(cid:173) work training. We present an analysis of online learning from finite training sets for non-linear networks (namely, soft-committee ma(cid:173) chines), advancing the theory to more realistic learning scenarios. Dynamical equations are derived for an appropriate set of order parameters; these are exact in the limiting case of either linear networks or infinite training sets. Preliminary comparisons with simulations suggest that the theory captures some effects of finite training sets, but may not yet account correctly for the presence of local minima.

O(ws(s log d log(dqh/ s))) and O(ws((h/ s) log q) log(dqh/ s)) are upper bounds for the VC-dimension of a set of neural networks of units with piecewise polynomial activation functions, where s is the depth of the network, h is the number of hidden units, w is the number of adjustable parameters, q is the maximum of the number of polynomial segments of the activation function, and d is the maximum degree of the polynomials; also n(wslog(dqh/s)) is a lower bound for the VC-dimension of such a network set, which are tight for the cases s 8(h) and s is constant. For the special case q 1, the VC-dimension is 8(ws log d).

Partially Observable Markov Decision Processes (pO "MOPs) constitute an important class of reinforcement learning problems which present unique theoretical and computational difficulties. In the absence of the Markov property, popular reinforcement learning algorithms such as Q-Iearning may no longer be effective, and memory-based methods which remove partial observability via state-estimation are notoriously expensive. An alternative approach is to seek a stochastic memoryless policy which for each observation of the environment prescribes a probability distribution over available actions that maximizes the average reward per timestep. A reinforcement learning algorithm which learns a locally optimal stochastic memoryless policy has been proposed by Jaakkola, Singh and Jordan, but not empirically verified. We present a variation of this algorithm, discuss its implementation, and demonstrate its viability using four test problems.

We replace the commonly used Gaussian noise model in nonlinear regression by a more flexible noise model based on the Student-t(cid:173) distribution. The degrees of freedom of the t-distribution can be chosen such that as special cases either the Gaussian distribution or the Cauchy distribution are realized. The latter is commonly used in robust regres(cid:173) sion. Since the t-distribution can be interpreted as being an infinite mix(cid:173) ture of Gaussians, parameters and hyperparameters such as the degrees of freedom of the t-distribution can be learned from the data based on an EM-learning algorithm. We show that modeling using the t-distribution leads to improved predictors on real world data sets.

The project pursued in this paper is to develop from first information-geometric principles a general method for learning the similarity between text documents. Each individual docu(cid:173) ment is modeled as a memoryless information source. Based on a latent class decomposition of the term-document matrix, a low(cid:173) dimensional (curved) multinomial subfamily is learned. From this model a canonical similarity function - known as the Fisher kernel - is derived. Our approach can be applied for unsupervised and supervised learning problems alike.

Stochastic meta-descent (SMD) is a new technique for online adap(cid:173) tation of local learning rates in arbitrary twice-differentiable sys(cid:173) tems. Like matrix momentum it uses full second-order information while retaining O(n) computational complexity by exploiting the efficient computation of Hessian-vector products. Here we apply SMD to independent component analysis, and employ the result(cid:173) ing algorithm for the blind separation of time-varying mixtures. By matching individual learning rates to the rate of change in each source signal's mixture coefficients, our technique is capable of si(cid:173) multaneously tracking sources that move at very different, a priori unknown speeds.

Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a finite sample. While a sim(cid:173) ple variational argument shows that Bayes averaging is generaliza(cid:173) tion optimal given that the prior matches the teacher parameter distribution the situation is less clear if the teacher distribution is unknown. I define a class of averaging procedures, the temperated likelihoods, including both Bayes averaging with a uniform prior and maximum likelihood estimation as special cases. I show that Bayes is generalization optimal in this family for any teacher dis(cid:173) tribution for two learning problems that are analytically tractable: learning the mean of a Gaussian and asymptotics of smooth learn(cid:173) ers.