Far-Field Compression for Fast Kernel Summation Methods in High Dimensions

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix-vector multiplication and scales quadratically with the number of points. Fast kernel summation algorithms reduce this cost to log-linear or linear complexity. Treecodes and Fast Multipole Methods (FMMs) deliver tremendous speedups by constructing approximate representations of interactions of points that are far from each other. In algebraic terms, these representations correspond to low-rank approximations of blocks of the overall interaction matrix. Existing approaches require an excessive number of kernel evaluations with increasing $d$ and number of points in the dataset. To address this issue, we use a randomized algebraic approach in which we first sample the rows of a block and then construct its approximate, low-rank interpolative decomposition. We examine the feasibility of this approach theoretically and experimentally. We provide a new theoretical result showing a tighter bound on the reconstruction error from uniformly sampling rows than the existing state-of-the-art. We demonstrate that our sampling approach is competitive with existing (but prohibitively expensive) methods from the literature. We also construct kernel matrices for the Laplacian, Gaussian, and polynomial kernels -- all commonly used in physics and data analysis. We explore the numerical properties of blocks of these matrices, and show that they are amenable to our approach. Depending on the data set, our randomized algorithm can successfully compute low rank approximations in high dimensions. We report results for data sets with ambient dimensions from four to 1,000.Comment: 43 pages, 21 figure

ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions

We present a fast algorithm for kernel summation problems in high-dimensions. These problems appear in computational physics, numerical approximation, non-parametric statistics, and machine learning. In our context, the sums depend on a kernel function that is a pair potential defined on a dataset of points in a high-dimensional Euclidean space. A direct evaluation of the sum scales quadratically with the number of points. Fast kernel summation methods can reduce this cost to linear complexity, but the constants involved do not scale well with the dimensionality of the dataset. The main algorithmic components of fast kernel summation algorithms are the separation of the kernel sum between near and far field (which is the basis for pruning) and the efficient and accurate approximation of the far field. We introduce novel methods for pruning and approximating the far field. Our far field approximation requires only kernel evaluations and does not use analytic expansions. Pruning is not done using bounding boxes but rather combinatorially using a sparsified nearest-neighbor graph of the input. The time complexity of our algorithm depends linearly on the ambient dimension. The error in the algorithm depends on the low-rank approximability of the far field, which in turn depends on the kernel function and on the intrinsic dimensionality of the distribution of the points. The error of the far field approximation does not depend on the ambient dimension. We present the new algorithm along with experimental results that demonstrate its performance. We report results for Gaussian kernel sums for 100 million points in 64 dimensions, for one million points in 1000 dimensions, and for problems in which the Gaussian kernel has a variable bandwidth. To the best of our knowledge, all of these experiments are impossible or prohibitively expensive with existing fast kernel summation methods.Comment: 22 pages, 6 figure

Tree-Independent Dual-Tree Algorithms

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.Comment: accepted in ICML 201

Selective serotonin reuptake inhibitors in pediatric depression: is the balance between benefits and risks favorable?

Recent controversies surrounding the use of selective serotonin reuptake inhibitors (SSRIs) have highlighted the need to reassess potential benefits, as well as potential risks of this class of medications in the treatment of pediatric depression. The recent availability of data from meta-analyses of published and unpublished antidepressant trials, epidemiological studies, and the Treatment for Adolescents with Depression Study (TADS) has facilitated a reanalysis of this risk/benefit relationship. Despite reviewing similar data, various regulatory agencies have arrived at rather disparate conclusions regarding the data, resulting in continued controversy. Although all groups appear to agree that careful assessment, education regarding risks, and closer monitoring are essential for SSRIs, only the U.S. Food and Drug Administration (FDA) and the U.K. Medicine and Health Care Products Regulatory Agency maintain that an acceptable risk/benefit relationship exists for fluoxetine. The European Medicines Agency concluded that the SSRIs should not be used in the treatment of depression in children and adolescents. The authors of this review have taken into consideration many of these same data and offer a critical discussion of the pros and cons of SSRIs in pediatric depression. The authors have concluded that SSRIs -- in particular, fluoxetine -- do have a role in the treatment of pediatric depression

Barley yield formation under abiotic stress depends on the interplay between flowering time genes and environmental cues

Abstract Since the dawn of agriculture, crop yield has always been impaired through abiotic stresses. In a field trial across five locations worldwide, we tested three abiotic stresses, nitrogen deficiency, drought and salinity, using HEB-YIELD, a selected subset of the wild barley nested association mapping population HEB-25. We show that barley flowering time genes Ppd-H1, Sdw1, Vrn-H1 and Vrn-H3 exert pleiotropic effects on plant development and grain yield. Under field conditions, these effects are strongly influenced by environmental cues like day length and temperature. For example, in Al-Karak, Jordan, the day length-sensitive wild barley allele of Ppd-H1 was associated with an increase of grain yield by up to 30% compared to the insensitive elite barley allele. The observed yield increase is accompanied by pleiotropic effects of Ppd-H1 resulting in shorter life cycle, extended grain filling period and increased grain size. Our study indicates that the adequate timing of plant development is crucial to maximize yield formation under harsh environmental conditions. We provide evidence that wild barley alleles, introgressed into elite barley cultivars, can be utilized to support grain yield formation. The presented knowledge may be transferred to related crop species like wheat and rice securing the rising global food demand for cereals

Peer-Assessed Outcomes in the Multimodal Treatment Study of Children With Attention Deficit Hyperactivity Disorder

Peer-assessed outcomes were examined at the end of treatment (14 months after study entry) for 285 children (226 boys, 59 girls) with attention deficit hyperactivity disorder (ADHD) who were rated by their classmates (2,232 classmates total) using peer sociometric procedures. All children with ADHD were participants in the Multimodal Treatment Study of Children with ADHD (MTA). Treatment groups were compared using the orthogonal treatment contrasts that accounted for the largest amount of variance in prior MTA outcome analyses: Medication Management + Combined Treatment versus Behavior Therapy + Community Care; Medication Management versus Combined Treatment; Behavior Therapy versus Community Care. There was little evidence of superiority of any of the treatments for the peer-assessed outcomes studied, although the limited evidence that emerged favored treatments involving medication management. Post hoc analyses were used to examine whether any of the four treatment groups yielded normalized peer relationships relative to randomly selected- classmates. Results indicated that children from all groups remained significantly impaired in their peer relationships

Mid-Late Quaternary Fluvial Archives near the Margin of the MIS 12 Glaciation in Southern East Anglia, UK: Amalgamation of Multi-Disciplinary and Citizen-Science Data Sources

This paper presents an updated geological reconstruction of the Quaternary evolution of the River Thames at its downstream extremities, close to the North Sea coast, based on new data from multi-disciplinary and citizen-science sources. In this area, the interaction of the Thames with the MIS 12 (Anglian) glaciation is an important part of the Quaternary archive. The Anglian ice sheet, which reached parts of north and east London, was responsible for diverting the Thames southwards into its present course, although the footprint of the maximum ice sheet(s) does not reach the North Sea coast south of Hollesley, Suffolk. Further south, the coastal zone hosts pre-Anglian and early Anglian river-terrace deposits of the pre-diversion Thames system, superimposed upon which are products of later post-Anglian rivers, of both Middle and Late Pleistocene age. On the peninsula between the Stour and Blackwater–Colne estuaries, the lowest and most recent terrace of the pre-diversion Thames includes evidence directly pertaining to the glacial disruption event, for which geochronological data are reported here for the first time. The first post-diversion terrace of the Thames also reaches this peninsula, the river having essentially re-joined its original valley before crossing the alignment of the modern coastline. This terrace passes beneath Clacton-on-Sea, where it includes the type locality of the Clactonian Palaeolithic Industry. The area of interest to this paper, in NE Essex and southern Suffolk, includes a number of interglacial and Palaeolithic sites, the data from which assist in constraining the chronostratigraphy of the sequence. In some cases, there has been uncertainty as to whether these sites represent pre-Anglian environments and hominin occupations, part of the palaeo-Thames sequence, or whether they are the product of later post-Anglian streams, formed after the Thames had migrated southwards. This paper compiles evidence from a wide range of recent sources, including developer-funded archaeological appraisal and citizen-science activities, to explore and update the evidence from sites at Ipswich, Upper Dovercourt and Thorpe-le-Soken, as well as a number of localities associated with the Clacton Channel Deposits (host to the type-Clactonian), amongst others. The resulting new data are placed within the wider context of the Quaternary fluvial archives in southern Britain, with a discussion of how disparate sources of information, including the work of citizen scientists, have contributed

Evaluation Research and Institutional Pressures: Challenges in Public-Nonprofit Contracting

This article examines the connection between program evaluation research and decision-making by public managers. Drawing on neo-institutional theory, a framework is presented for diagnosing the pressures and conditions that lead alternatively toward or away the rational use of evaluation research. Three cases of public-nonprofit contracting for the delivery of major programs are presented to clarify the way coercive, mimetic, and normative pressures interfere with a sound connection being made between research and implementation. The article concludes by considering how public managers can respond to the isomorphic pressures in their environment that make it hard to act on data relating to program performance.This publication is Hauser Center Working Paper No. 23. The Hauser Center Working Paper Series was launched during the summer of 2000. The Series enables the Hauser Center to share with a broad audience important works-in-progress written by Hauser Center scholars and researchers

The Critical Juncture Concept’s Evolving Capacity to Explain Policy Change

This article examines the evolution of our understanding of the critical junctures concept. The concept finds its origins in historical intuitionalism, being employed in the context of path dependence to account for sudden and jarring institutional or policy changes. We argue that the concept and the literature surrounding it—now incorporating ideas, discourse, and agency—have gradually become more comprehensive and nuanced as historical institutionalism was followed by ideational historical institutionalism and constructivist and discursive institutionalism. The prime position of contingency has been supplanted by the role of ideas and agency in explaining critical junctures and other instances of less than transformative change. Consequently, the concept is now capable of providing more comprehensive explanations for policy change