this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.

We present a method for learning a set of generative models which are suitable for representing variations of selected image-domain features of the scene as a function of changes in the camera viewpoint. Such models are important for robotic tasks, such as probabilistic position estimation (i.e. localization), as well as visualization. Our approach entails the selection of image-domain features, as well as the synthesis of models of their visual behavior. The model we propose is capable of generating maximum likelihood views of automatically selected features, as well as a measure of the likelihood of a particular view from a particular camera position. Training the models involves regularizing observations of the features from known camera locations. The uncertainty of the model is evaluated using cross validation. The features themselves are initially selected automatically as salient points by a measure of visual attention, and are tracked across multiple views. While the motivation for this work is for robot localization, the results have implications for image interpolation, virtual scene reconstruction and object recognition. This paper presents a formulation of the problem and illustrative experimental results.

Abstract — We present a method for learning a set of models of visual features which are invariant to scale and translation in the image domain. The models are constructed by first applying the Scale-Invariant Feature Transform (SIFT) to a set of training images, and matching the extracted features across the images, followed by learning the pose-dependent behavior of the features. The modeling process avoids assumptions with respect to scene and imaging geometry, but rather learns the direct mapping from camera pose to feature observation. Such models are useful for applications to robotic tasks, such as localization, as well as visualization tasks. We present the model learning framework, and experimental results illustrating the success of the method for learning models that are useful for robot localization. I.

This paper brings together methods from two different disciplines: statistics and machine learning. We address the problem of estimating the variance of cross-validation (CV) estimators of the generalization error. In particular, we approach the problem of variance estimation of the CV estimators of generalization error as a problem in approximating the moments of a statistic. The approximation illustrates the role of training and test sets in the performance of the algorithm. It provides a unifying approach to evaluation of various methods used in obtaining training and test sets and it takes into account the variability due to different training and test sets. For the simple problem of predicting the sample mean and in the case of smooth loss functions, we show that the variance of the CV estimator of the generalization error is a function of the moments of the random T variables Y = Card(S j S j ′) and Y ∗ = Card(Sc T j Sc j ′), where S j, S j ′ are two training sets, and Sc j, Sc j ′ are the corresponding test sets. We prove that the distribution of Y and Y * is hypergeometric and we compare our estimator with the one proposed by Nadeau and Bengio (2003). We extend these results in the regression case and the case of absolute error loss, and indicate how the methods can be extended to the classification case. We illustrate the results through simulation.

Abstract:- With the Latent Semantic Analysis (LSA), it is possible to automatically grade essays, i.e., free-text responses to examinations, by comparing them to a corpus of available learning materials. In order to get grades that correspond to those given by human assessors, it is crucial to train the system with essays that have already been graded. Noise reduction refers to a process in which individual words used for comparing essays with learning materials are given weight according to their significance. To find out the optimal parameters for noise reduction, the system is trained with different parameters, and the corresponding grades for essays are predicted by each of these models. Three standard validation methods, holdout, bootstrap, and k-fold cross-validation, were applied for noise reduction. In an experiment that consisted of 283 essays from three examinations, each of a different subject, the holdout validation method turned out to give the best predictions, and hence, reduce most of the noise.

Proc. R. Soc. A doi:10.1098/rspa.2010.0041 Pictish symbols revealed as a written language

Abstract. Recent advances in diffusion weighted MR imaging (dMRI) has made it a tool of choice for investigating white matter abnormalities of the brain and central nervous system. In this work, we design a system that detects abnormal features (biomarkers) of first-episode schizophrenia patients and then classifies them using these features. We use two different models of the dMRI data, namely, spherical harmonics and the two-tensor model. The algorithm works by first computing several diffusion measures from each model. An affine-invariant representation of each subject is then computed, thus avoiding the need for registration. This representation is used within a kernel based feature selection algorithm to determine the biomarkers that are statistically different between the two populations. Confirmation of how well these biomarkers identify each population is obtained by using several classifiers such as, k-nearest neighbors, Parzen window classifier, and support vector machines to separate 21 first-episode patients from 20 age-matched normal controls. Classification results using leave-manyout cross-validation scheme are given for each representation. This algorithm is a first step towards early detection of schizophrenia. 1

We present a method for learning a set of generative models which are suitable for synthesizing views of scene features from arbitrary camera positions. The model is capable of generating maximum likelihood views of selected features, as well as a measure of the likelihood of a particular view from a particular camera position. Training the models involves regularizing observations of the features from known camera locations. The uncertainty of the model is evaluated using cross validation. The features themselves are initially selected automatically as salient points by a measure of visual attention, and are tracked across multiple views. While the motivation for this work is for robot localization and navigation, the results have implications for image interpolation, virtual scene reconstruction and object recognition. This paper presents a formulation of the problem and illustrative experimental results.

An estimator of shrinkage based on information contained in a single sample is presented and the results of a simulation study are reported. The effects of sample size, amount, and severity of nonrepresentative data in the population, inclusion of noninformative predictors, and least (sum of) absolute deviations and least (sum of) squared deviations regression models are examined on the estimator. A single-sample estimator of shrinkage based on drop-one cross-validation is shown to be highly accurate under a wide variety of research conditions. 1.

Over the last two decades, Functional Magnetic Resonance Imaging (fMRI) has revolutionized the study of the brain. This non-invasive technique produces snapshots of brain activity over time, allowing researchers to literally peer into the mind as it performs everyday tasks like reading or viewing images. Gradually the need has emerged for fMRI analysis techniques that model activity occurring at numerous locations throughout the brain simultaneously, and make predictions about what a person is doing or thinking solely from his or her brain activity, or ”mind read. ” Machine learning techniques can accomplish both these goals, and thus have become a popular modeling choice; however, most standard machine learning algorithms were designed for problems in which there are relatively few candidate predictor variables, and the modeling objective is to make accurate predictions. In fMRI data, the number of predictor variables can be very large, while the likely number of relevant predictors may be quite small. Furthermore, machine learning algorithms are increasingly being employed in the natural sciences, and while accurate predictions can serve to validate scientific models, the end goal of such modeling is