An Extended Kernel for Generalized Multiple-Instance Learning

The multiple-instance learning (MIL) model has been successful in areas such as drug discovery and content-based image-retrieval. Recently, this model was generalized and a corresponding kernel was introduced to learn generalized MIL concepts with a support vector machine. While this kernel enjoyed empirical success, it has limitations in its representation. We extend this kernel by enriching its representation and empirically evaluate our new kernel on data from content-based image retrieval, biological sequence analysis, and drug discovery. We found that our new kernel generalized noticeably better than the old one in content-based image retrieval and biological sequence analysis and was slightly better or even with the old kernel in the other applications, showing that an SVM using this kernel does not overfit despite its richer representation.

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

SAMPLING OF CORN TO ASSESS BIRD DAMAGE: A Preliminary Review of a Comprehensive Study

"How large a sample is needed to survey the bird damage to corn in a county in Ohio or New Jersey or South Dakota?" Like those in the Bureau of Sport Fisheries and Wildlife and the U.S.D.A. who have been faced with a question of this sort we found only meager information on which to base an answer, whether the problem related to a county in Ohio or to one in New Jersey, or elsewhere. Many sampling methods and rates of sampling did yield reliable estimates but the judgment was often intuitive or based on the reasonableness of the resulting data. Later, when planning the next study or survey, little additional information was available on whether 40 samples of 5 ears each or 5 samples of 200 ears should be examined, i.e., examination of a large number of small samples or a small number of large samples. What information is needed to make a reliable decision? Those of us involved with the Agricultural Experiment Station regional project concerned with the problems of bird damage to crops, known as NE-49, thought we might supply an ans¬wer if we had a corn field in which all the damage was measured. If all the damage were known, we could then sample this field in various ways and see how the estimates from these samplings compared to the actual damage and pin-point the best and most accurate sampling procedure. Eventually the investigators in four states became involved in this work1 and instead of one field we were able to broaden the geographical base by examining all the corn ears in 2 half-acre sections of fields in each state, 8 sections in all. When the corn had matured well past the dough stage, damage on each corn ear was assessed, without removing the ear from the stalk, by visually estimating the percent of the kernel surface which had been destroyed and rating it in one of 5 damage categories. Measurements (by row-centimeters) of the rows of kernels pecked by birds also were made on selected ears representing all categories and all parts of each field section. These measurements provided conversion factors that, when fed into a computer, were applied to the more than 72,000 visually assessed ears. The machine now had in its memory and could supply on demand a map showing each ear, its location and the intensity of the damage.