Normalization and variance stabilization of single-cell RNA-seq data using regularized negative binomial regression

Christoph Hafemeister, Rahul Satija · Genome biology · 2019 · biology · 10.1186/s13059-019-1874-1 · record hafemeister2019-normalization-and-variance-stabili
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Other fields define these differently the same word, defined another way in another discipline
overfitting 6 fields · generalized linear model 2 fields · negative binomial 2 fields · normalization 2 fields · sequencing depth 2 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 12 concept tags on this paper, all 12 are grounded in a quoted sentence. All carry the tagger's gloss of what the term means in this paper, which is not something the article can license.
normalization size factor Pearson residuals overfitting regularization Chromium control dataset kernel bandwidth zero-inflated negative binomial Poisson sequencing depth PPBP regularized NB abundance-dependent depth effect defeating a single scaling factor overfitting absorbing biological signal pooling across genes as a constraint low RNA content masquerading as a depth relation negative binomial generalized linear model system-or-tool-building
Method, as described: negative binomial GLM per gene with sequencing depth as covariate, kernel regression to regularize the parameters across genes of similar abundance, and a second constrained fit whose Pearson residuals are the output

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claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
concept edgeconcept_edgesan asserted relation between two concepts, with the sentence asserting it
conceptconceptsan idea the paper works with, quoted where the paper uses it
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
contributioncontributionwhat the paper claims to add
controlcontrolsan experiment run to eliminate a rival explanation
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
object of studyobject_of_studywhat the paper is about — the thing it investigates
phenomenonphenomenonthe effect or regularity under study
research questionresearch_questionthe question the paper sets itself
sensesensesa distinct use of a term, quoted where the paper fixes it
transfertransfersa method or concept carried in from another field

The paper

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Every tag on this page

claim_relations 4 · claim_type 1 · concept_edges 2 · concepts 12 · content_tags 14 · contribution 1 · controls 6 · limitations 4 · mechanisms 4 · method 1 · object_of_study 1 · phenomenon 1 · research_question 1 · senses 4 · transfers 2

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facettagfieldconf.whose words
object_of_studynormalisation of single-cell RNA-seq counts - how to remove the effect of sequencing depth without removing the biology along with it
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object_of_studythe paper's words
research_questionwhether any single per-cell scaling factor can normalise genes of different abundance, and if not, what error model should replace it
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research_questionthe paper's words
contributionregularized negative binomial regression - fit a GLM per gene with depth as covariate, pool parameters across genes of similar abundance, and take the Pearson residuals as normalised values
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contributionthe paper's words
claim_typemethod
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claim_typethe paper's words
phenomenona preprocessing choice that decides what counts as biological signal - the same data yielding heterogeneity or not depending on how the error model is constrained
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phenomenonthe paper's words
methodsystem-or-tool-building
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methodthe paper's words
mechanismscounts of low- and high-abundance genes respond differently to sequencing depth, so one factor per cell cannot correct both; dividing by depth leaves the high-abundance tiers still confounded and the variance contribution of the other tiers dampened
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mechanisms[0]0.95the tagger's words
mechanismsan unconstrained per-gene model has enough freedom to explain real cell-type differences as technical effects of depth, so the residuals it produces have had the biology subtracted along with the noise - even cell-type markers come out with low residual variance
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mechanisms[1]0.95the tagger's words
mechanismsestimating each gene's parameters independently makes them a function of that gene's sampling noise; smoothing them against mean abundance replaces the noise with the population trend, and the estimates become reproducible across bootstraps
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mechanisms[2]0.95the tagger's words
mechanismsmegakaryocytes carry little RNA, so they appear at low sequencing depth for reasons of biology rather than sampling; an unconstrained fit reads that as a negative slope between depth and the marker's count, which cannot be true of any single cell type
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mechanisms[3]0.95the tagger's words
limitationsthe regularisation assumes the majority of genes do not vary biologically, which the authors say may be overly simplistic on a highly heterogeneous sample
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limitations[0]0.95the tagger's words
limitationsthe kernel bandwidth is a user-adjustable parameter; robust over an order of magnitude and producing over- or under-smoothing at the extremes
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limitations[1]0.95the tagger's words
limitationsthe batch extension requires all cell types to share a similar batch effect, which is an assumption about the experiment rather than a property of the model
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limitations[2]0.95the tagger's words
limitationsPearson residuals are an intermediate rather than a model - an alternative would fit the count distribution directly, as GLM-PCA does, instead of passing residuals to methods that assume normal errors
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limitations[3]0.85the tagger's words
transfersparameter regularisation by pooling across similar features, carried from bulk RNA-seq differential-expression error models into single-cell normalisation
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transfers[0]0.95the tagger's words
transfersgeneralized linear models and Pearson residuals, carried from regression theory to serve as the normalised data values themselves rather than as a diagnostic
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transfers[1]0.95the tagger's words
controlsa dataset with NO biological variation by construction - droplets that are technical replicates of one bulk RNA sample - run through the unregularised model to see whether the parameter heterogeneity persists when biology cannot explain it
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eliminates: true biological variation as the explanation of the parameter heterogeneity across genes - in a sample where every droplet is a technical replicate of one bulk RNA extract there is no biology left that could produce it · outcome: failed
controls[0]0.95the tagger's words
controlsthe same control dataset run through the FINISHED method, where a correct model must find no high-variance genes at all
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eliminates: residual technical variation as the source of the high-variance genes the finished method selects - run on a sample containing no biology, a correct model must find none, and does · outcome: held
controls[1]0.95the tagger's words
controlsbootstrapping the fit over randomised subsets of cells, to separate real between-gene differences from sampling variation in the estimates
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eliminates: real between-gene differences as the explanation of the parameter spread - estimates that move when the cells are resampled are measuring the sample and not the gene · outcome: failed
controls[2]0.95the tagger's words
controlssubstituting a Poisson and an unconstrained NB error model into the same pipeline, so the regularisation step is tested rather than assumed
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eliminates: the generalised linear model framework itself as the source of the result - swapping only the error model shows the work is done by the regularisation, not by using a GLM · outcome: held
controls[3]0.95the tagger's words
controlschecking what the high-residual-variance genes actually are, rather than reporting that some exist
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eliminates: residual technical noise as the explanation of the surviving high-variance genes - noise does not produce a list that is exclusively markers of known immune cell subsets · outcome: held
controls[4]0.95the tagger's words
controlsrepeating the whole analysis on five UMI datasets from plate- and droplet-based protocols rather than on the one dataset the method was developed against
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eliminates: the single development dataset, and the droplet protocol it came from, as the source of the result · outcome: held
controls[5]0.95the tagger's words
conceptsnormalization
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also in: normalization
concepts[0]0.95the paper's words
conceptssize factor
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also in: size factor
concepts[1]0.95the paper's words
conceptsPearson residuals
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concepts[2]0.95the paper's words
conceptsoverfitting
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also in: overfitting
concepts[3]0.95the paper's words
conceptsregularization
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concepts[4]0.95the paper's words
conceptsChromium control dataset
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concepts[5]0.95the paper's words
conceptskernel bandwidth
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concepts[6]0.95the paper's words
conceptszero-inflated negative binomial
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concepts[7]0.95the paper's words
conceptsPoisson
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also in: Poisson
concepts[8]0.95the paper's words
conceptssequencing depth
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concepts[9]0.95the paper's words
conceptsPPBP
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also in: PPBP
concepts[10]0.95the paper's words
conceptsregularized NB
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concepts[11]0.95the paper's words
sensesparameter heterogeneity across genes - READING 1: true biological variation in the distribution of single-cell gene expression
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senses[0]0.95the tagger's words
sensesparameter heterogeneity across genes - READING 2: irreproducible variation driven by overfitting. Resolved in favour of this one by a control dataset with no biological variation in it, where the heterogeneity persisted
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senses[1]0.95the tagger's words
senses"effectively normalized" - UNDER LOG-NORMALIZATION: true only of the bottom three abundance tiers; high-abundance genes remain confounded with sequencing depth
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senses[2]0.95the tagger's words
senses"effectively normalized" - UNDER PEARSON RESIDUALS: level and variance independent of sequencing depth across the full range of expression
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senses[3]0.95the tagger's words
claim_relationscritiques → size-factor normalisation for single-cell data - including recent methods that compute the factor more cleverly, since the problem is the single factor and not its estimation
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claim_relations[0]0.95the tagger's words
claim_relationscritiques → unconstrained negative binomial and zero-inflated negative binomial error models as used in current statistical and deep-learning methods for scRNA-seq
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claim_relations[1]0.95the tagger's words
claim_relationsbuilds-on → regularisation of error-model parameters across genes of similar abundance, standard in bulk RNA-seq differential expression and not previously used for single-cell normalisation
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claim_relations[2]0.95the tagger's words
claim_relationsqualifies → SCnorm's conclusion that gene groups need separate treatment - reached for non-UMI data by a method that ignores the zero values which dominate droplet-based assays
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claim_relations[3]0.95the tagger's words
concept_edgessize factor —distinct-from→ normalization
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differs in: whether one constant per cell can serve genes across the whole range of abundance · the relation itself is separately evidenced · strength of the relation: 0.95 · differs in (stated by the tagger, no quotation): whether one constant per cell can serve genes across the whole range of abundance · the relation stated: a single per-cell scaling factor introduces different effects on genes of different average abundance, so it is not normalization for all of them Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says a single size factor has distinct effects; distinct-from is loose.
concept_edges[0]0.95the tagger's words
concept_edgesPoisson —distinct-from→ regularized NB
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differs in: whether the error model can represent overdispersion without absorbing the biology · the relation itself is separately evidenced · strength of the relation: 0.95 · differs in (stated by the tagger, no quotation): whether the error model can represent overdispersion without absorbing the biology · the relation stated: the single-parameter Poisson cannot represent overdispersion and leaves residual variance above one for highly expressed genes; the unconstrained NB overfits in the other direction and flattens the markers
concept_edges[3]0.95the tagger's words
content_tagsa single per-cell scaling factor cannot normalise genes of different abundance, whatever method computes the factor
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content_tags.findings[0]0.95the tagger's words
content_tagslog-normalisation effectively normalises only the bottom three abundance tiers; high-abundance genes stay confounded with depth
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content_tags.findings[1]0.95the tagger's words
content_tagsan unconstrained negative binomial model overfits and removes biological variation along with technical variation
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content_tags.findings[2]0.95the tagger's words
content_tagsthe parameter heterogeneity persists in a dataset containing no biological variation, which is what identifies it as overfitting
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content_tags.findings[3]0.95the tagger's words
content_tagsafter normalisation the genes with high residual variance are exclusively markers of known immune cell subsets
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content_tags.findings[4]0.95the tagger's words
content_tagsboth non-regularised models fit a negative depth-count slope for a megakaryocyte marker, which cannot be true of a single cell type
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content_tags.findings[5]0.95the tagger's words
content_tagsremoving the influence of technical effects in the underlying molecular counts while preserving true biological variation
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also in: normalization
content_tags.definitions[0]0.95the tagger's words
content_tagsresponse residuals divided by the expected standard deviation, effectively a variance-stabilizing transformation putting lowly and highly expressed genes on a common scale
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content_tags.definitions[1]0.95the tagger's words
content_tagsdroplets each representing a technical replicate of a bulk RNA sample - no biological variation in it by construction
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content_tags.definitions[2]0.95the tagger's words
content_tagsthe unit residual variance expected for a gene with no biological heterogeneity
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content_tags.quantities[0]0.85the tagger's words
content_tagsnegative binomial
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content_tags.statistics[0]0.95the tagger's words
content_tagskernel bandwidth
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content_tags.statistics[1]0.95the tagger's words
content_tagsgeneralized linear model
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content_tags.statistics[2]0.85the tagger's words
content_tagssequencing depth
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content_tags.variables[0]0.95the tagger's words

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