42,667 research outputs found
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Slingshot: cell lineage and pseudotime inference for single-cell transcriptomics.
BackgroundSingle-cell transcriptomics allows researchers to investigate complex communities of heterogeneous cells. It can be applied to stem cells and their descendants in order to chart the progression from multipotent progenitors to fully differentiated cells. While a variety of statistical and computational methods have been proposed for inferring cell lineages, the problem of accurately characterizing multiple branching lineages remains difficult to solve.ResultsWe introduce Slingshot, a novel method for inferring cell lineages and pseudotimes from single-cell gene expression data. In previously published datasets, Slingshot correctly identifies the biological signal for one to three branching trajectories. Additionally, our simulation study shows that Slingshot infers more accurate pseudotimes than other leading methods.ConclusionsSlingshot is a uniquely robust and flexible tool which combines the highly stable techniques necessary for noisy single-cell data with the ability to identify multiple trajectories. Accurate lineage inference is a critical step in the identification of dynamic temporal gene expression
Gains in Power from Structured Two-Sample Tests of Means on Graphs
We consider multivariate two-sample tests of means, where the location shift
between the two populations is expected to be related to a known graph
structure. An important application of such tests is the detection of
differentially expressed genes between two patient populations, as shifts in
expression levels are expected to be coherent with the structure of graphs
reflecting gene properties such as biological process, molecular function,
regulation, or metabolism. For a fixed graph of interest, we demonstrate that
accounting for graph structure can yield more powerful tests under the
assumption of smooth distribution shift on the graph. We also investigate the
identification of non-homogeneous subgraphs of a given large graph, which poses
both computational and multiple testing problems. The relevance and benefits of
the proposed approach are illustrated on synthetic data and on breast cancer
gene expression data analyzed in context of KEGG pathways
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