The nature of scientific and technological data collection is evolving rapidly: data volumes and rates grow exponentially, with increasing complexity and information content, and there has been a transition from static data sets to data streams that must be analyzed in real time. Interesting or anomalous phenomena must be quickly characterized and followed up with additional measurements via optimal deployment of limited assets. Modern astronomy presents a variety of such phenomena in the form of transient events in digital synoptic sky surveys, including cosmic explosions (supernovae, gamma ray bursts), relativistic phenomena (black hole formation, jets), potentially hazardous asteroids, etc. We have been developing a set of machine learning tools to detect, classify and plan a response to transient events for astronomy applications, using the Catalina Real-time Transient Survey (CRTS) as a scientific and methodological testbed. The ability to respond rapidly to the potentially most interesting events is a key bottleneck that limits the scientific returns from the current and anticipated synoptic sky surveys. Similar challenge arise in other contexts, from environmental monitoring using sensor networks to autonomous spacecraft systems. Given the exponential growth of data rates, and the time-critical response, we need a fully automated and robust approach. We describe the results obtained to date, and the possible future developments.

The amount of collected data in many scientific fields is increasing, all of them requiring a common task: extract knowledge from massive, multi parametric data sets, as rapidly and efficiently possible. This is especially true in astronomy where synoptic sky surveys are enabling new research frontiers in the time domain astronomy and posing several new object classification challenges in multi dimensional spaces; given the high number of parameters available for each object, feature selection is quickly becoming a crucial task in analyzing astronomical data sets. Using data sets extracted from the ongoing Catalina Real-Time Transient Surveys (CRTS) and the Kepler Mission we illustrate a variety of feature selection strategies used to identify the subsets that give the most information and the results achieved applying these techniques to three major astronomical problems.

An automated, rapid classification of transient events detected in the modern synoptic sky surveys is essential for their scientific utility and effective follow-up using scarce resources. This presents some unusual challenges: the data are sparse, heterogeneous and incomplete; evolving in time; and most of the relevant information comes not from the data stream itself, but from a variety of archival data and contextual information (spatial, temporal, and multi-wavelength). We are exploring a variety of novel techniques, mostly Bayesian, to respond to these challenges, using the ongoing CRTS sky survey as a testbed. The current surveys are already overwhelming our ability to effectively follow all of the potentially interesting events, and these challenges will grow by orders of magnitude over the next decade as the more ambitious sky surveys get under way. While we focus on an application in a specific domain (astrophysics), these challenges are more broadly relevant for event or anomaly detection and knowledge discovery in massive data streams.

This paper describes a method for learning the terrain classification of long-range appearance data from short- range, stereo-based geometry, along with a map representation for utilizing this data to improve autonomous off-road navigation. The continuous, online learning method allows the system to constantly adapt to changing terrain and environmental conditions, while the polar-perspective map representation allows the system to effectively plan with stereo data at long ranges. Various evaluations of the long-range classification and improvements in system performance are described, including results from an independent third-party testing team.

We describe and test a software approach to fault detection in common numerical algorithms. Such result checking or algorithm-based fault tolerance (ABFT) methods may be used, for example, to overcome single-event upsets in computational hardware or to detect errors in complex, high-efficiency implementations of the algorithms. Following earlier work, we use checksum methods to validate results returned by a numerical subroutine operating subject to unpredictable errors in data. We consider common matrix and Fourier algorithms which return results satisfying a necessary condition having a linear form; the checksum tests compliance with this condition. We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent in finite-precision floating-point calculations. We concentrate on comprehensively defining and evaluating tests having various accuracy/computational burden tradeoffs, and we emphasize average-case algorithm behavior rather than using worst-case upper, bounds on error.

We describe and test a software approach to overcoming radiation-induced errors in spaceborne applications running on commercial off-the-shelf components. The approach uses checksum methods to validate results returned by a numerical subroutine operating subject to unpredictable errors in data. We can treat subroutines that return results satisfying a necessary condition having a linear form; the checksum tests compliance with this condition. We discuss the theory and practice of setting numerical tolerances to separate errors caused by a fault from those inherent infinite-precision numerical calculations. We test both the general effectiveness of the linear fault tolerant schemes we propose, and the correct behavior of our parallel implementation of them.

The solar chromosphere consists of three classes which contribute differentially to ultraviolet radiation reaching the Earth. We describe a data set of solar images, means of segmenting the images into the constituent classes, and a novel high-level representation for compact objects based on a triangulated spatial 'membership function.' Such representations are fitted in a variable-dimension Markov chain Monte Carlo scheme.

We estimate the number of training samples required to ensure that the performance of a neural network on its training data matches that obtained when fresh data is applied to the network. Existing estimates are higher by orders of magnitude than practice indicates. This work seeks to narrow the gap between theory and practice by transforming the problem into determining the distribution of the supremum of a random field in the space of weight vectors, which in turn is attacked by application of a recent technique called the Poisson clumping heuristic. 1 INTRODUCTION AND KNOWN RESULTS We investigate the tradeofi"s among network complexity, training set size, and sta(cid:173) tistical performance of feedforward neural networks so as to allow a reasoned choice of network architecture in the face of limited training data. Nets are functions 7](x; w), parameterized by their weight vector w E W ~ Rd , which take as input points x E Rk. For classifiers, network output is restricted to {a, 1} while for fore(cid:173) casting it may be any real number. The architecture of all nets under consideration is N, whose complexity may be gauged by its Vapnik-Chervonenkis (VC) dimension v, the size of the largest set of inputs the architecture can classify in any desired way ('shatter'). Nets 7] EN are chosen on the basis of a training set T = {(Xi, YiHr=l. These n samples are i.i.d. according to an unknown probability law P. Performance of a network is measured by the mean-squared error