Hidden Markov models (HMMs) for automatic speech recognition rely on high dimensional feature vectors to summarize the shorttime properties of speech. Correlations between features can arise when the speech signal is non-stationary or corrupted by noise. We investigate how to model these correlations using factor analysis, a statistical method for dimensionality reduction. Factor analysis uses a small number of parameters to model the covariance structure of high dimensional data. These parameters are estimated by an Expectation-Maximization (EM) algorithm that can be embedded in the training procedures for HMMs.

The ability to rely on similarity metrics invariant to image transformations is an important issue for image classification tasks such as face or character recognition. We analyze an invariant metric that has performed well for the latter - the tangent distance - and study its limitations when applied to regular images, showing that the most significant among these (convergence to local minima) can be drastically reduced by computing the distance in a multiresolution setting. This leads to the multi resolution tangent distance, which exhibits significantly higher invariance to image transformations, and can be easily combined with robust estimation procedures.

Further, the greater the similarity between objects, the stronger is the dependence on object appearance, and the more important twodimensional (2D) image information becomes. These findings, however, do not rule out the use of 3D structural information in recognition, and the degree to which 3D information is used in visual memory is an important issue. Liu, Knill, & Kersten (1995) showed that any model that is restricted to rotations in the image plane of independent 2D templates could not account for human performance in discriminating novel object views. We now present results from models of generalized radial basis functions (GRBF), 2D nearest neighbor matching that allows 2D affine transformations, and a Bayesian statistical estimator that integrates over all possible 2D affine transformations. The performance of the human observers relative to each of the models is better for the novel views than for the familiar template views, suggesting that humans generalize better to novel views from template views. The Bayesian estimator yields the optimal performance with 2D affine transformations and independent 2D templates. Therefore, models of 2D affine matching operations with independent 2D templates are unlikely to account for human recognition performance.

"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 applied 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. Adaptive boosting of a multi-layer network achieved 1.5% error on the UCI Letters and 8.1 % error on the UCI satellite data set.

Estimating motion in scenes containing multiple moving objects remains a difficult problem in computer vision. A promising approach to this problem involves using mixture models, where the motion of each object is a component in the mixture. However, existing methods typically require specifying in advance the number of components in the mixture, i.e. the number of objects in the scene.

The idea is to calculate differentials by using a relative increment instead of an absolute increment in the parameter space. This idea has been extended to compute the relative Hessian by (Pham, 1996).

The proof given here shows that for any finite, discrete transfer function used by the units of an RCC network, there are finite-state automata (FSA) that the network cannot model, no matter how many units are used. The proof also applies to continuous transfer functions with a finite number of fixed-points, such as sigmoid and radial-basis functions.

Severe contamination of electroencephalographic (EEG) activity by eye movements, blinks, muscle, heart and line noise is a serious problem for EEG interpretation and analysis. Rejecting contaminated EEG segments results in a considerable loss of information and may be impractical for clinical data. Many methods have been proposed to remove eye movement and blink artifacts from EEG recordings. Often regression in the time or frequency domain is performed on simultaneous EEG and electrooculographic (EOG) recordings to derive parameters characterizing the appearance and spread of EOG artifacts in the EEG channels. However, EOG records also contain brain signals [1, 2], so regressing out EOG activity inevitably involves subtracting a portion of the relevant EEG signal from each recording as well. Regression cannot be used to remove muscle noise or line noise, since these have no reference channels. Here, we propose a new and generally applicable method for removing a wide variety of artifacts from EEG records. The method is based on an extended version of a previous Independent Component Analysis (lCA) algorithm [3, 4] for performing blind source separation on linear mixtures of independent source signals with either sub-Gaussian or super-Gaussian distributions. Our results show that ICA can effectively detect, separate and remove activity in EEG records from a wide variety of artifactual sources, with results comparing favorably to those obtained using regression-based methods.

One frequently estimates density functions for which there is little prior knowledge on the shape of the density and for which one wants a flexible and robust estimator (allowing multimodality if it exists). In this context, the methods of choice tend to be finite mixture models and kernel density estimation methods. For mixture modeling, mixtures of Gaussian components are frequently assumed and model choice reduces to the problem of choosing the number k of Gaussian components in the model (Titterington, Smith and Makov, 1986). For kernel density estimation, kernel shapes are typically chosen from a selection of simple unimodal densities such as Gaussian, triangular, or Cauchy densities, and kernel bandwidths are selected in a data-driven manner (Silverman 1986; Scott 1994). As argued by Draper (1996), model uncertainty can contribute significantly to pre- - Also with the Jet Propulsion Laboratory 525-3660, California Institute of Technology, Pasadena, CA 91109 Stacked Density Estimation 669 dictive error in estimation. While usually considered in the context of supervised learning, model uncertainty is also important in unsupervised learning applications such as density estimation. Even when the model class under consideration contains the true density, if we are only given a finite data set, then there is always a chance of selecting the wrong model. Moreover, even if the correct model is selected, there will typically be estimation error in the parameters of that model.

Our model consists of a classical energy mechanism whose output is divided by nonclassical gain control and texture contrast mechanisms. We apply this model to review movies, a stimulus sequence that replicates the stimulation a cell receives during free viewing of natural images. Data were collected from three cells using five different review movies, and the model was fit separately to the data from each movie. For the energy mechanism alone we find modest but significant correlations (rE 0.41, 0.43, 0.59, 0.35) between model and data. These correlations are improved somewhat when we allow for suppressive surround effects (rE G 0.42, 0.56, 0.60, 0.37). In one case the inclusion of a delayed suppressive surround dramatically improves the fit to the data by modifying the time course of the model's response.