Is there such a thing as a ‘good statistical learner’?
Authors: Louisa Bogaerts, Noam Siegelman, Morten H. Christiansen, Ram Frost
Journal: Trends in Cognitive Sciences (2021)

Statistical learning (SL) has become an important building block of virtually all current theories of information processing.Substantial interindividual variance is a pervasive feature of learning and individual differences in SL have become a focus of interest as predictors of many cognitive functions.Current individual differences approaches treat SL as a general ability, similar to general capacities such as intelligence or working memory. This approach assumes that there is something shared between the computation of regularities across cognitive domains.The statistical structure characterizing different real-world sensory environments (e.g., print, visual scenes) is still poorly understood, but likely displays many idiosyncrasies. Hence, what it takes to be a good statistical learner may be quite different in the context of different cognitive domains. A growing body of research investigates individual differences in the learning of statistical structure, tying them to variability in cognitive (dis)abilities. This approach views statistical learning (SL) as a general individual ability that underlies performance across a range of cognitive domains. But is there a general SL capacity that can sort individuals from 'bad' to 'good' statistical learners? Explicating the suppositions underlying this approach, we suggest that current evidence supporting it is meager. We outline an alternative perspective that considers the variability of statistical environments within different cognitive domains. Once we focus on learning that is tuned to the statistics of real-world sensory inputs, an alternative view of SL computations emerges with a radically different outlook for SL research. A growing body of research investigates individual differences in the learning of statistical structure, tying them to variability in cognitive (dis)abilities. This approach views statistical learning (SL) as a general individual ability that underlies performance across a range of cognitive domains. But is there a general SL capacity that can sort individuals from 'bad' to 'good' statistical learners? Explicating the suppositions underlying this approach, we suggest that current evidence supporting it is meager. We outline an alternative perspective that considers the variability of statistical environments within different cognitive domains. Once we focus on learning that is tuned to the statistics of real-world sensory inputs, an alternative view of SL computations emerges with a radically different outlook for SL research. Recent years have seen a growing body of research tying variation in a range of cognitive capacities to success or failure in assimilating the statistical structure of the input. This reflects an increased appreciation that our environment, be it perceptual, cognitive, or social, is saturated with statistical regularities (see Glossary) that are the target of learning and processing. The neurocognitive mechanism for detecting and assimilating the range of regularities in the input has been labelled 'statistical learning' (SL) [1.Saffran J.R. et al.Statistical learning by 8-month-old infants.Science. 1996; 274: 1926-1928Crossref PubMed Scopus (3015) Google Scholar, 2.Kirkham N.Z. et al.Visual statistical learning in infancy: evidence for a domain general learning mechanism.Cognition. 2002; 83: B35-B42Crossref PubMed Scopus (638) Google Scholar, 3.Gebhart A.L. et al.Statistical learning of adjacent and nonadjacent dependencies among nonlinguistic sounds.Psychon. Bull. Rev. 2009; 16: 486-490Crossref PubMed Scopus (102) Google Scholar, 4.Sherman B.E. et al.The prevalence and importance of statistical learning in human cognition and behavior.Curr. Opin. Behav. Sci. 2020; 32: 15-20Crossref PubMed Scopus (14) Google Scholar]. Although the impact of statistical regularities on cognitive processing had been previously recognized, interest in SL surged after the seminal paper by Saffran and colleagues on speech segmentation [1.Saffran J.R. et al.Statistical learning by 8-month-old infants.Science. 1996; 274: 1926-1928Crossref PubMed Scopus (3015) Google Scholar]. The concept of SL has subsequently permeated many other cognitive domains (e.g., visual perception, music, social cognition, attention, etc.; see [5.Frost R. et al.Statistical learning research: a critical review and possible new directions.Psychol. Bull. 2019; 145: 1128-1153Crossref PubMed Scopus (59) Google Scholar] for review), because they all involve statistical structure. With this new perspective on cognition came a novel prediction: that individual differences in these various domains are fundamentally linked to SL capability. As a result, the last decade has seen a growing body of work targeting SL as a general individual ability for perceiving and assimilating regularities in the input. The main premise of this research is that individuals range from 'good' to 'bad' statistical learners and that 'good' statistical learners are expected to have better skills across the wide range of cognitive functions that require the assimilation of statistical structure (e.g., reading [6.Arciuli J. Reading as statistical learning.Lang. Speech. Hear. Serv. Sch. 2018; 49: 634-643Crossref PubMed Scopus (26) Google Scholar, 7.Frost R. et al.What predicts successful literacy acquisition in a second language?.Psychol. Sci. 2013; 24: 1243-1252Crossref PubMed Scopus (110) Google Scholar, 8.Chetail F. Reconsidering the role of orthographic redundancy in visual word recognition.Front. 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Learn. 2012; 62: 302-331Crossref Scopus (153) Google Scholar,18.Pavlidou E. Bogaerts L. Implicit statistical learning across modalities and its relationship with reading in childhood.Front. Psychol. 2019; 10: 1834Crossref PubMed Scopus (0) Google Scholar], have consequently assessed correlations between performance in laboratory SL tasks and cognitive abilities in a variety of domains, in normal and special populations. A few studies, in particular those investigating language and literacy acquisition, have tested more narrow and nuanced predictions about the predictive power of individual differences in SL, for example, by linking the sensitivity to orthography-to-phonology regularities to early reading skills [19.Siegelman N. et al.Individual differences in learning the regularities between orthography, phonology and semantics predict early reading skills.J. Mem. Lang. 2020; 114104145Crossref PubMed Scopus (12) Google Scholar], or by establishing a relation between infants' knowledge of their native language's sound structure and their vocabulary size [20.Graf Estes K. et al.Finding patterns and learning words: infant phonotactic knowledge is associated with vocabulary size.J. Exp. Child Psychol. 2016; 146: 34-49Crossref PubMed Scopus (16) Google Scholar]. However, most studies have selected a given SL task, assuming that performance on the chosen task is sufficiently representative of one's general SL capacity to be predictive of the targeted cognitive ability (or disability), be it reading, musicality, or social skills, to name a few. Although results have not been unequivocal [18.Pavlidou E. Bogaerts L. Implicit statistical learning across modalities and its relationship with reading in childhood.Front. Psychol. 2019; 10: 1834Crossref PubMed Scopus (0) Google Scholar,21.Schmalz X. et al.Is statistical learning ability related to reading ability, and if so, why?.Sci. Stud. Read. 2019; 23: 64-76Crossref Scopus (24) Google Scholar, 22.West G. et al.The procedural learning deficit hypothesis of language learning disorders: we see some problems.Dev. Sci. 2018; 21e12552Crossref PubMed Scopus (66) Google Scholar, 23.van Witteloostuijn M. et al.The contribution of individual differences in statistical learning to reading and spelling performance in children with and without dyslexia.Dyslexia. 2021; 27: 168-186Crossref PubMed Scopus (2) Google Scholar], and although effect sizes are often small, most published work has reported significant positive correlations between SL performance and performance in multiple cognitive functions (Table 1). Typically, null effects within this research line have been discussed in terms of insufficient variability in performance [24.Kidd E. Arciuli J. Individual differences in statistical learning predict children's comprehension of syntax.Child Dev. 2015; 87: 184-193Crossref PubMed Scopus (81) Google Scholar] and poor task reliability more generally [18.Pavlidou E. Bogaerts L. Implicit statistical learning across modalities and its relationship with reading in childhood.Front. Psychol. 2019; 10: 1834Crossref PubMed Scopus (0) Google Scholar,23.van Witteloostuijn M. et al.The contribution of individual differences in statistical learning to reading and spelling performance in children with and without dyslexia.Dyslexia. 2021; 27: 168-186Crossref PubMed Scopus (2) Google Scholar]. Importantly, underlying this experimental approach is the (typically implicit) supposition that an individual has a general, unitary ability for discovering regularities, which assists the learning of any type of statistical structure. In some studies this supposition is formulated explicitly, as can be seen in the following quotes. Parks et al. [25.Parks K.M.A. et al.Statistical learning and social competency: the mediating role of language.Sci. Rep. 2020; 10: 1-15Crossref PubMed Scopus (4) Google Scholar] state:We are interested in how the ability to learn patterns overall is related to language and social competency skills […]. It is therefore expected that auditory and visual statistical learning will contribute similarly […] given that both tasks assess the ability to learn statistical patterns in general. (p. 3)Table 1Examples of studies tying individual differences in the learning of statistical structure to variance in cognitive abilitiesPredicted cognitive abilityCognitive measureStatistical learning task, learning measure(s)Stimuli of statistical learning taskSample (age)Main findingsRefsLiteracySentence readingWord and nonword readingAuditory triplet learning, acceleration of target detection times during familiarization, and two-alternative forced choice (2-AFC) familiarity testPure tonesAdults (18–34 years)Children (8–16 years)Full sample: positive correlation between 2-AFC measure and sentence reading, null findings with acceleration measureChildren: positive correlations between the acceleration measure and word and nonword reading, null findings with 2-AFC[27.Qi Z. et al.Hearing matters more than seeing: a cross-modality study of statistical learning and reading ability.Sci. Stud. Read. 2019; 23: 101-115Crossref Scopus (22) Google Scholar]Visual triplet learning, acceleration of target detection times during familiarization, and2-AFC familiarity testAlien figuresFull sample: positive correlation between 2-AFC measure and sentence reading, null findings with acceleration measureChildren: null findingsWord and nonword readingMorphological primingVisual triplet learning,2-AFC familiarity testAbstract shapesAdults (18–34 years), native English speakers learning HebrewPositive correlation with all reading measures[7.Frost R. et al.What predicts successful literacy acquisition in a second language?.Psychol. Sci. 2013; 24: 1243-1252Crossref PubMed Scopus (110) Google Scholar]Word readingVisual triplet learning,2-AFC familiarity testAlien figuresAdults (18–34 years)Children (6.4-12.5 years)Adults: positive correlationChildren: positive correlation[28.Arciuli J. Simpson I.C. Statistical learning is related to reading ability in children and adults.Cogn. Sci. 2012; 36: 286-304Crossref PubMed Scopus (147) Google Scholar]Word and nonword readingSpelling testVisual triplet learning, self-paced measure during familiarization, pattern completion test, and 2-AFC familiarity testAlien figuresChildren (8.3–11.2 years) with and without a dyslexia diagnosisNull findings: no evidence of a relationship between any of the SL measures and reading or spelling skills above and beyond participant-level variables[23.van Witteloostuijn M. et al.The contribution of individual differences in statistical learning to reading and spelling performance in children with and without dyslexia.Dyslexia. 2021; 27: 168-186Crossref PubMed Scopus (2) Google Scholar]Serial reaction time taskFour locationsOral language processingLexical-processing efficiencyVocabulary sizeAuditory pair learning,2-AFC familiarity test with head-turn preference measureSyllablesInfants (15–16 months)Positive correlations with lexical- processing efficiency, null findings for vocabulary size[9.Lany J. et al.Infant statistical-learning ability is related to real-time language processing.J. Child Lang. 2018; 45: 368-391Crossref PubMed Scopus (15) Google Scholar]WordsVocabulary size and growthAuditory non‐adjacent dependency learning,2-AFC familiarity test with head turn preference measureSyllablesInfants (15.5–17.5 months, tested at multiple time points until the age of 30 months)Positive correlation with vocabulary size (at multiple time points), null findings for vocabulary growth[10.Frost R.L.A. et al.Non-adjacent dependency learning in infancy, and its link to language development.Cogn. Psychol. 2020; 120101291Crossref PubMed Scopus (5) Google Scholar]Syntax comprehensionVocabularyVisual triplet learning,2-AFC familiarity testAlien figuresChildren (6.1–8.1 years)SL independently predicts comprehension of passives and object relative clauses, null findings for other grammatical structures and vocabulary[24.Kidd E. Arciuli J. Individual differences in statistical learning predict children's comprehension of syntax.Child Dev. 2015; 87: 184-193Crossref PubMed Scopus (81) Google Scholar]Music skillsMelody discrimination and rhythm discrimination (combined in a general music score)Auditory triplet learning,2-AFC familiarity testPure tonesChildren (mean = 10.3 years) with and without musical trainingPositive correlation with general music score[29.Mandikal Vasuki P.R. et al.Statistical learning and auditory processing in children with music training: an ERP study.Clin. Neurophysiol. 2017; 128: 1270-1281Crossref PubMed Scopus (11) Google Scholar]Visual triplet learning,2-AFC familiarity testAlien figuresPositive correlation with general music scoreSocial competencySocial competency questionnaireAutistic traits questionnaireReceptive and expressive language abilitiesVisual triplet learning,psychometrically optimized familiarity testAbstract shapesYoung adults (16–21 years)Positive correlation with receptive language and social competency abilities, null finding for relation with autism symptomatology[25.Parks K.M.A. et al.Statistical learning and social competency: the mediating role of language.Sci. Rep. 2020; 10: 1-15Crossref PubMed Scopus (4) Google Scholar]Auditory triplet learning,2-AFC familiarity testSyllablesNull findings for receptive language and social competency abilities, positive correlation to autism symptomatologyFeature-comparison skillsVisual comparison performanceVisual distributional statistical learning, psychometrically optimized familiarity test and frequency estimatesAbstract shapesYoung adults (17–26 years), trained forensic examiners, and novices (informed, uninformed, and misinformed)Informed novices: positive correlation between familiarity measure and visual comparison performance, null findings for frequency estimates measureNull findings for all other groups[30.Growns B. Martire K.A. Forensic feature-comparison expertise: statistical learning facilitates visual comparison performance.J. Exp. Psychol. Appl. 2020; 26: 493-506Crossref PubMed Scopus (1) Google Scholar] Open table in a new tab Kirkham, Slemmer, and Johnson [26.Jeste S.S. et al.Electrophysiological evidence of heterogeneity in visual statistical learning in young children with ASD.Dev. Sci. 2015; 18: 90-105Crossref PubMed Scopus (33) Google Scholar] write: These results are consistent with the existence of a domain general statistical learning device that is available to even very young infants […]. (p. 40) From a historical perspective, this approach to individual differences in SL resonates with research into other general cognitive capacities, such as the study of human intelligence, with its G-factor, or memory, with its general working memory factor (Box 1). It assumes that a general SL capacity determines individual performance in regularity learning across domains, resulting in something akin to a 'general SL factor'. As the qualification 'general' has also been used in the context of discussing domain-specificity versus -generality (see [31.Bogaerts L. et al.Integrating statistical learning into cognitive science.J. Mem. Lang. 2020; 115104167Crossref Scopus (4) Google Scholar] for discussion), we should clarify that a 'general SL capacity', as used here, implies that SL is a domain-general ability, whereas domain-generality does not require the existence of a unitary SL capacity. Rather, 'domain-generality' in the context of SL research reflects the recognition that sensitivity to regularities is found across all cognitive domains and extends beyond the original finding of sensitivity to trisyllabic patterns in a continuous speech stream [1.Saffran J.R. et al.Statistical learning by 8-month-old infants.Science. 1996; 274: 1926-1928Crossref PubMed Scopus (3015) Google Scholar] (see [5.Frost R. et al.Statistical learning research: a critical review and possible new directions.Psychol. Bull. 2019; 145: 1128-1153Crossref PubMed Scopus (59) Google Scholar] for discussion). The idea of a general SL capacity is a more specific claim. It presupposes that individuals differ in their general ability for learning regularities, whatever those regularities are, and that this general capacity contributes to their learning in any domain. As such, sensitivity to statistical regularities is taken to be a major cognitive construct, subserving basic and higher-order cognitive functions, thus impacting human performance across the board. Importantly, this unitary view assumes that there is something common to the computation of statistical regularities across modalities and domains, leading to some shared variance in individuals' performance in assimilating regularities across cognition.Box 1A short history of salient general factors in cognitive scienceHigher-order latent variables have been proposed across a wide range of cognitive abilities. Here, we outline two examples of impactful general factors.IntelligenceMore than a century ago, Charles Spearman demonstrated that different measures of intelligence tend to correlate with each other to various degrees, known as the positive manifold. He proposed the two-factor theory of intelligence, stating that intellectual abilities are comprised of two kinds of factors: (i) a general ability, labeled the G-factor; and (ii) a number of specific abilities (S-factors), all having some load on the general factor [40.Spearman C. "General intelligence," objectively determined and measured.Am. J. Psychol. 1904; 15: 201Crossref Google Scholar]. Whereas conceptualizations of intelligence have since further evolved, the G-factor is still omnipresent and has been validated cross-culturally [99.Warne R.T. Burningham C. Spearman's g found in 31 non-Western nations: strong evidence that g is a universal phenomenon.Psychol. Bull. 2019; 145: 237-272Crossref PubMed Scopus (26) Google Scholar]. The current version of the Wechsler Adult Intelligence Scale (WAIS-IV [100.Wechsler D. Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Pearson, 2010Google Scholar]) still provides a broad IQ-score to summarize general intellectual ability, which results from aggregating performance across a range of specific tasks and is taken to predict a wide range of cognitive functions.Working memoryTogether with intelligence, working memory has been one of the most frequently studied constructs in cognitive science. Working memory has been suggested to modulate a range of cognitive abilities (e.g., reading, mathematics [101.Gathercole S.E. et al.How common are WM deficits in children with difficulties in reading and mathematics?.J. Appl. Res. Mem. Cogn. 2016; 5: 384-394Crossref PubMed Scopus (32) Google Scholar]). Some work using confirmatory factor analyses has supported the concept of a general, higher-order working memory capacity factor and hence the view that a broad set of tasks that use different working memory contents (e.g., verbal, visuospatial) and tap different processing demands (e.g., maintenance, updating) all purportedly engage a higher-level capacity [102.Oswald F.L. et al.The development of a short domain-general measure of working memory capacity.Behav. Res. Methods. 2014; 47: 1343-1355Crossref Scopus (81) Google Scholar, 103.Wilhelm O. et al.What is working memory capacity, and how can we measure it?.Front. Psychol. 2013; 4: 433Crossref PubMed Scopus (214) Google Scholar, 104.Waris O. et al.A latent factor analysis of working memory measures using large-scale data.Front. Psychol. 2017; 8: 1062Crossref PubMed Scopus (17) Google Scholar]. Higher-order latent variables have been proposed across a wide range of cognitive abilities. Here, we outline two examples of impactful general factors. Intelligence More than a century ago, Charles Spearman demonstrated that different measures of intelligence tend to correlate with each other to various degrees, known as the positive manifold. He proposed the two-factor theory of intelligence, stating that intellectual abilities are comprised of two kinds of factors: (i) a general ability, labeled the G-factor; and (ii) a number of specific abilities (S-factors), all having some load on the general factor [40.Spearman C. "General intelligence," objectively determined and measured.Am. J. Psychol. 1904; 15: 201Crossref Google Scholar]. Whereas conceptualizations of intelligence have since further evolved, the G-factor is still omnipresent and has been validated cross-culturally [99.Warne R.T. Burningham C. Spearman's g found in 31 non-Western nations: strong evidence that g is a universal phenomenon.Psychol. Bull. 2019; 145: 237-272Crossref PubMed Scopus (26) Google Scholar]. The current version of the Wechsler Adult Intelligence Scale (WAIS-IV [100.Wechsler D. Wechsler Adult Intelligence Scale-Fourth Edition (WAIS-IV). Pearson, 2010Google Scholar]) still provides a broad IQ-score to summarize general intellectual ability, which results from aggregating performance across a range of specific tasks and is taken to predict a wide range of cognitive functions. Working memory Together with intelligence, working memory has been one of the most frequently studied constructs in cognitive science. Working memory has been suggested to modulate a range of cognitive abilities (e.g., reading, mathematics [101.Gathercole S.E. et al.How common are WM deficits in children with difficulties in reading and mathematics?.J. Appl. Res. Mem. Cogn. 2016; 5: 384-394Crossref PubMed Scopus (32) Google Scholar]). Some work using confirmatory factor analyses has supported the concept of a general, higher-order working memory capacity factor and hence the view that a broad set of tasks that use different working memory contents (e.g., verbal, visuospatial) and tap different processing demands (e.g., maintenance, updating) all purportedly engage a higher-level capacity [102.Oswald F.L. et al.The development of a short domain-general measure of working memory capacity.Behav. Res. Methods. 2014; 47: 1343-1355Crossref Scopus (81) Google Scholar, 103.Wilhelm O. et al.What is working memory capacity, and how can we measure it?.Front. Psychol. 2013; 4: 433Crossref PubMed Scopus (214) Google Scholar, 104.Waris O. et al.A latent factor analysis of working memory measures using large-scale data.Front. Psychol. 2017; 8: 1062Crossref PubMed Scopus (17) Google Scholar]. The possibility of a general SL factor, common to learning regularities across domains, has far-reaching theoretical and practical implications. It suggests that a general computational device assimilates the wide range of regularities in the environment and that individuals differ in its efficiency. Even more importantly, since performance in multiple SL tasks was found to be independent of intelligence, working memory, and executive functions [32.Siegelman N. Frost R. Statistical learning as an individual ability: theoretical perspectives and empirical evidence.J. Mem. Lang. 2015; 81: 105-120Crossref PubMed Scopus (118) Google Scholar,33.Kaufman S.B. et al.Implicit learning as an ability.Cognition. 2010; 116: 321-340Crossref PubMed Scopus (256) Google Scholar], a general SL factor has the promise to account for a substantial portion of unexplained variance in cognitive performance. If a general SL factor could be comprehensively assessed through a validated and normed test battery, similar to the G-factor, a general SL score could provide a reliable estimate of an individual's SL capacity relative to the population distribution. Then, this single general SL score could predict, at least to some extent, an individual's performance in a given cognitive function over and above intelligence or memory. Because SL is an important building block of virtually all current theories of cognitive processing, this could revolutionize research on individual differences in cognitive science. In this paper, we evaluate this intriguing prospect and outline some of the challenges it might face. We start by discussing what a general SL factor would imply as a theoretical construct, before considering evidence for the notion of a 'good statistical learner'. Next, we outline a broader ecological perspective on the variety of statistics that need to be accommodated and consider existing challenges for the notion of good statistical learners. We then outline an alternative view of SL computations and discuss its implications for future research. Theoretical constructs should be well-defined so that they can be empirically validated. We thus start by outlining three implicit suppositions that underlie the concepts of good statistical learners and a general SL factor. First, and foremost, there is the supposition of nesting and sharing. A general SL factor implies that all modality- and domain-specific SL abilities (e.g., detecting word-boundaries, learning spatial contingencies, etc.) are nested within it, just as vocabulary, comprehension, and visual-spatial abilities are nested within intelligence. Nesting could be hierarchical or not [34.Carroll J.B. Human Cognitive Abilities. Cambridge University Press, 1993Crossref Google Scholar], but it necessarily entails a relation of whole and parts between the general factor and its components. Nesting leads inevitably to sharing. Given that statistical regularities vary in sensory modality, material, type of contingencies, etc., recent studies have argued that SL is a componential ability spanning an array of dimensions [35.Siegelman N. et al.Towards a theory of individual differences in statistical learning.Philos. Trans. R. Soc. B Biol. Sci. 2017; 37220160059Crossref PubMed Scopus (90) Google Scholar, 36.Raviv L. Arnon I. The developmental trajectory of children's auditory and visual statistical learning abilities: modality-based differences in the effect of age.Dev. Sci. 2018; 21e12593Crossref PubMed Scopus (47) Google Scholar, 37.Emberson L.L. et al.Comparing statistical learning across perceptual modalities in infancy: an investigation of underlying learning mechanism(s).Dev. 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