Unsupervised learning with generative adversarial networks (GANs) has proven hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LS-GANs) which adopt the least squares loss function for the discriminator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson χ 2 divergence. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stable during the learning process. We evaluate LSGANs on five scene datasets and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by regular GANs. We also conduct two comparison experiments between LSGANs and regular GANs to illustrate the stability of LSGANs. *

We describe the Phase II HapMap, which characterizes over 3.1 million human single nucleotide polymorphisms (SNPs) genotyped in 270 individuals from four geographically diverse populations and includes 25-35% of common SNP variation in the populations surveyed. The map is estimated to capture untyped common variation with an average maximum r2 of between 0.9 and 0.96 depending on population. We demonstrate that the current generation of commercial genome-wide genotyping products captures common Phase II SNPs with an average maximum r2 of up to 0.8 in African and up to 0.95 in non-African populations, and that potential gains in power in association studies can be obtained through imputation. These data also reveal novel aspects of the structure of linkage disequilibrium. We show that 10-30% of pairs of individuals within a population share at least one region of extended genetic identity arising from recent ancestry and that up to 1% of all common variants are untaggable, primarily because they lie within recombination hotspots. We show that recombination rates vary systematically around genes and between genes of different function. Finally, we demonstrate increased differentiation at non-synonymous, compared to synonymous, SNPs, resulting from systematic differences in the strength or efficacy of natural selection between populations.

With the advent of dense maps of human genetic variation, it is now possible to detect positive natural selection across the human genome. Here we report an analysis of over 3 million polymorphisms from the International HapMap Project Phase 2 (HapMap2)1. We used 'longrange haplotype' methods, which were developed to identify alleles segregating in a population that have undergone recent selection2, and we also developed new methods that are based on cross-population comparisons to discover alleles that have swept to near-fixation within a population. The analysis reveals more than 300 strong candidate regions. Focusing on the strongest 22 regions, we develop a heuristic for scrutinizing these regions to identify candidate targets of selection. In a complementary analysis, we identify 26 non-synonymous, coding, single nucleotide polymorphisms showing regional evidence of positive selection. Examination of these candidates highlights three cases in which two genes in a common biological process have apparently undergone positive selection in the same population: LARGE and DMD, both related to infection by the Lassa virus3, in West Africa; SLC24A5 and SLC45A2, both involved in skin pigmentation4,5, in Europe; and EDAR and EDA2R, both involved in development of hair follicles6, in Asia. ©2007 Nature Publishing GroupCorrespondence and requests for materials should be addressed to P.C.S. (pardis@broad.mit.edu).. * These authors contributed equally to this work. † Lists of participants and affiliations appear at the end of the paper. Author Contributions P.C.S., P.V., B.F. and E.S.L. initiated the project. P.V., B.F. and P.C.S. developed key software. P.C.S., P.V., B.F., S.F.S., J.L., E.H., C.C., X.X., E.B., S.A.McC. and R.G. performed analysis. P.C.S., E.B. and E.H. performed experiments. P.C.S., E.S.L., P.V. and S.F.S. wrote the manuscript.Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.Supplementary Information is linked to the online version of the paper at www.nature.com/nature.Reprints and permissions information is available at www.nature.com/reprints. An increasing amount of information about genetic variation, together with new analytical methods, is making it possible to explore the recent evolutionary history of the human population. The first phase of the International Haplotype Map, including ~1 million single nucleotide polymorphisms (SNPs)7, allowed preliminary examination of natural selection in humans. Now, with the publication of the Phase 2 map (HapMap2)1 in a companion paper, over 3 million SNPs have been genotyped in 420 chromosomes from three continents (120 European (CEU), 120 African (YRI) and 180 Asian from Japan and China (JPT + CHB)). Europe PMC Funders GroupIn our analysis of HapMap2, we first implemented two widely used tests that detect recent positive selection by finding common alleles carried on unusually long haplotypes2. The two, the Long-Range Haplotype (LRH)8 and the integrated Haplotype Score (iHS)9 tests...

A haplotype map of the human genomeThe International HapMap Consortium* Inherited genetic variation has a critical but as yet largely uncharacterized role in human disease. Here we report a public database of common variation in the human genome: more than one million single nucleotide polymorphisms (SNPs) for which accurate and complete genotypes have been obtained in 269 DNA samples from four populations, including ten 500-kilobase regions in which essentially all information about common DNA variation has been extracted. These data document the generality of recombination hotspots, a block-like structure of linkage disequilibrium and low haplotype diversity, leading to substantial correlations of SNPs with many of their neighbours. We show how the HapMap resource can guide the design and analysis of genetic association studies, shed light on structural variation and recombination, and identify loci that may have been subject to natural selection during human evolution.

The vast majority of coding variants are rare, and assessment of the contribution of rare variants to complex traits is hampered by low statistical power and limited functional data. Improved methods for predicting the pathogenicity of rare coding variants are needed to facilitate the discovery of disease variants from exome sequencing studies. We developed REVEL (rare exome variant ensemble learner), an ensemble method for predicting the pathogenicity of missense variants on the basis of individual tools: MutPred, FATHMM, VEST, PolyPhen, SIFT, PROVEAN, MutationAssessor, MutationTaster, LRT, GERP, SiPhy, phyloP, and phastCons. REVEL was trained with recently discovered pathogenic and rare neutral missense variants, excluding those previously used to train its constituent tools. When applied to two independent test sets, REVEL had the best overall performance (p < 10) as compared to any individual tool and seven ensemble methods: MetaSVM, MetaLR, KGGSeq, Condel, CADD, DANN, and Eigen. Importantly, REVEL also had the best performance for distinguishing pathogenic from rare neutral variants with allele frequencies <0.5%. The area under the receiver operating characteristic curve (AUC) for REVEL was 0.046-0.182 higher in an independent test set of 935 recent SwissVar disease variants and 123,935 putatively neutral exome sequencing variants and 0.027-0.143 higher in an independent test set of 1,953 pathogenic and 2,406 benign variants recently reported in ClinVar than the AUCs for other ensemble methods. We provide pre-computed REVEL scores for all possible human missense variants to facilitate the identification of pathogenic variants in the sea of rare variants discovered as sequencing studies expand in scale.