Statistical inference with anchored Bayesian mixture of regressions models: A case study analysis of allometric data

We present a case study in which we use a mixture of regressions model to improve on an ill-fitting simple linear regression model relating log brain mass to log body mass for 100 placental mammalian species. The slope of this regression model is of particular scientific interest because it corresponds to a constant that governs a hypothesized allometric power law relating brain mass to body mass. A specific line of investigation is to determine whether the regression parameters vary across subgroups of related species. We model these data using an anchored Bayesian mixture of regressions model, which modifies the standard Bayesian Gaussian mixture by pre-assigning small subsets of observations to given mixture components with probability one. These observations (called anchor points) break the relabeling invariance typical of exchangeable model specifications (the so-called label-switching problem). A careful choice of which observations to pre-classify to which mixture components is key to the specification of a well-fitting anchor model. In the article we compare three strategies for the selection of anchor points. The first assumes that the underlying mixture of regressions model holds and assigns anchor points to different components to maximize the information about their labeling. The second makes no assumption about the relationship between x and y and instead identifies anchor points using a bivariate Gaussian mixture model. The third strategy begins with the assumption that there is only one mixture regression component and identifies anchor points that are representative of a clustering structure based on case-deletion importance sampling weights. We compare the performance of the three strategies on the allometric data set and use auxiliary taxonomic information about the species to evaluate the model-based classifications estimated from these models

Pentapods with Mobility 2

In this paper we give a full classification of all pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. Therefore this paper solves the famous Borel-Bricard problem for 2-dimensional motions beside the excluded case of five collinear points with spherical trajectories. But even for this special case we present three new types as a side-result. Based on our study of pentapods, we also give a complete list of all non-architecturally singular hexapods with 2-dimensional self-motions.Comment: 18 pages, 5 figure

Chromatin loop anchors are associated with genome instability in cancer and recombination hotspots in the germline

Abstract Background Chromatin loops form a basic unit of interphase nuclear organization, with chromatin loop anchor points providing contacts between regulatory regions and promoters. However, the mutational landscape at these anchor points remains under-studied. Here, we describe the unusual patterns of somatic mutations and germline variation associated with loop anchor points and explore the underlying features influencing these patterns. Results Analyses of whole genome sequencing datasets reveal that anchor points are strongly depleted for single nucleotide variants (SNVs) in tumours. Despite low SNV rates in their genomic neighbourhood, anchor points emerge as sites of evolutionary innovation, showing enrichment for structural variant (SV) breakpoints and a peak of SNVs at focal CTCF sites within the anchor points. Both CTCF-bound and non-CTCF anchor points harbour an excess of SV breakpoints in multiple tumour types and are prone to double-strand breaks in cell lines. Common fragile sites, which are hotspots for genome instability, also show elevated numbers of intersecting loop anchor points. Recurrently disrupted anchor points are enriched for genes with functions in cell cycle transitions and regions associated with predisposition to cancer. We also discover a novel class of CTCF-bound anchor points which overlap meiotic recombination hotspots and are enriched for the core PRDM9 binding motif, suggesting that the anchor points have been foci for diversity generated during recent human evolution. Conclusions We suggest that the unusual chromatin environment at loop anchor points underlies the elevated rates of variation observed, marking them as sites of regulatory importance but also genomic fragility

No Fuss Distance Metric Learning using Proxies

We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship -- an anchor point $x$ is similar to a set of positive points $Y$, and dissimilar to a set of negative points $Z$, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15% points, while converging three times as fast as other triplet-based losses.Comment: To be presented in ICCV 201