DHQ: Digital Humanities Quarterly
2016
Volume 10 Number 3

# Six Degrees of Francis Bacon: A Statistical Method for Reconstructing Large Historical Social Networks

## Abstract

In this paper we present a statistical method for inferring historical social networks from biographical documents as well as the scholarly aims for doing so. Existing scholarship on historical social networks is scattered across an unmanageable number of disparate books and articles. A researcher interested in how persons were connected to one another in our field of study, early modern Britain (c. 1500-1700), has no global, unified resource to which to turn. Manually building such a network is infeasible, since it would need to represent thousands of nodes and tens of millions of potential edges just to include the relations among the most prominent persons of the period. Our Six Degrees of Francis Bacon project takes up recent statistical techniques and digital tools to reconstruct and visualize the early modern social network.

We describe in this paper the natural language processing tools and statistical graph learning techniques that we used to extract names and infer relations from the Oxford Dictionary of National Biography. We then explain the steps taken to test inferred relations against the knowledge of experts in order to improve the accuracy of the learning techniques. Our argument here is twofold: first, that the results of this process, a global visualization of Britain’s early modern social network, will be useful to scholars and students of the period; second, that the pipeline we have developed can, with local modifications, be reused by other scholars to generate networks for other historical or contemporary societies from biographical documents.

# Introduction

Historians and critics have long studied the ways that early modern writers and thinkers associated with each other and participated in various kinds of formal and informal groups. Although their findings have been published in countless books and articles, there is currently no way to obtain a unified view of the early modern social network. A scholar must start largely from scratch if she seeks to understand complex relations between multiple people, identify potentially important relationships that have yet to be explored, understand the extent of communities of interaction, or visualize the scholarly consensus regarding networks, whether small or large. The creation of a large scale early modern social network gives scholars a visual way to explore scholarly knowledge of relationships and to see what has – or hasn’t – been studied in the extant historiography.
The most desirable outcome of our work would of course be a comprehensive map of the way early modern persons were related. Yet practical challenges abound. The population of Britain rose to over 5.5 million people by the end of the seventeenth century, and little documentary evidence survives on much of that population. Attempting to reconstruct the full network would be unrealistic. Even if we limited ourselves to people alive in 1700 and successfully gathered 5.5 million names, the number of potential relationships in that set exceeds 15 billion. Social relations are exceedingly complex, even in societies considerably smaller than our own. There are thus excellent reasons to proceed more conservatively–focusing only on small, well-documented subsets of the population. Some of the best known digital networks projects, such as Stanford University’s Mapping the Republic of Letters and Oxford University's Cultures of Knowledge, do just that. Adhering to historians’ venerable practice, they proceed incrementally and only include relationships directly attested by documents such as letters. This approach produces relatively small, highly substantiated networks – on the order of, say, 500 nodes [Ahnert and Ahnert 2014] [Basu et al. 2015] – but it also limits these networks to representing an infinitesimal sliver of the rich and varied kinds of relationships between people.
Taking a different approach, we identified biographical data as the most productive starting point for our network reconstruction, which we have named Six Degrees of Francis Bacon (SDFB), after the early modern figure whose life spanned the sixteenth and seventeenth centuries and whose career spanned the domains of politics, science, and letters. We chose biographies because they are a well-established and highly standardized product of modern historical scholarship. Moreover, a central collection of such data was already available to us digitally through the Oxford Dictionary of National Biography (ODNB), which comprises the biographies of people deemed by its editors as significant to British history. Jerome McGann has argued that “the whole of our cultural inheritance has to be recurated and reedited in digital forms and institutional structures”  [McGann 2014, 1]. Most often, in his account, this involves transference of text “from bibliographical to digital machines.” SDFB tackles a related but more difficult problem: the transformation of biographical text, which focuses on a single person but contains rich information about social relations, into a global (non-egocentric) network graph, which requires extracting information about nodes (persons) and edges (relations) while ignoring or discarding other kinds of biographical information.
From the ODNB biographies of persons who lived between 1500-1700 we created an initial dataset of 13,309 actor nodes. Each actor node could potentially be connected to any of the other nodes, leading to over 88 million potential edges to explore. Even within this initial dataset, already limited for manageability, it was not feasible to verify each potential edge. One approach might have been to curate these relationships in an ad-hoc order, as a scholar became interested in a particular relationship or as relationships were explicitly documented in a scholarly source. We would then have collected as many relationships as the time and labor of scholars allowed, but we would have had little to say about the relative importance of collected relationships and nothing at all to say about those relationships yet to be curated. For instance, would the absence of an edge mean that the two nodes shared no association or that the association has yet to be explored in our network? Rather than rebuilding the network by hand, we chose to employ a computational and statistical approach, unifying the dispersed knowledge already extant in the literature into an inferred graph of the network that can then be made available to scholars for correction and curation.
In the following sections, we lay out our statistical method for reconstructing the early modern social network in four broad steps, then examine the significance and limitations of our results from the perspective of humanist scholarship. In section one, we discuss the process of identifying a collection of textual documents to use as input, considering both direct and indirect evidence of historical relationships. In section two, we explain how we used Named-Entity Recognition (NER) to process the unstructured text into structured data – specifically a matrix of documents and named entities – that was amenable to statistical analysis. In section three, we give an overview of how we applied statistical graph-learning methods to our structured data, with more detailed technical information included an appendix. In section four, we discuss methods of validating a sample of proposed relationships using the local expertise of humanist scholars. In section five, we step back to examine the broader significance of this process from the perspective of twenty-first-century researchers in the humanities. We also examine the assumptions underlying our statistical methods and potential areas of modification necessary before redeploying these methods with other historical corpora.
In developing this method, we have demonstrated the feasibility of applying graph learning methods to any large collection of biographical text – early modern or otherwise. This is neither a completely automated process nor a perfect one, but we have also developed a practical mechanism by which expert feedback can improve the network as well as the statistical procedures used to infer it. We have thus created a viable and transferrable approach to inferring large-scale historical social networks, which should be of particular interest to digital humanists, scholars of networks and prosopography, as well as scholars interested in the history of scholarship itself.

# 1. Source Material

The first step of our process was identifying the extent of available texts and determining which texts were potentially the most useful for network inference. Numerous types of primary and secondary sources can provide evidence of historical relationships. Some of these sources provide direct evidence of a link between two actors – for example, society membership rolls, marriage certificates, or archival letters. Other sources may collectively provide indirect evidence: the same two people mentioned together in numerous accounts or biographies is highly suggestive of the possibility that those two people may have come into contact with one another.
In an ideal world we would have made use of all the relevant historical sources and scholarship. In this one, we needed to begin with a collection of texts that was well-defined, accessible, machine readable, and relatively uniform. We also wanted to begin with a collection that included a broad range of potentially relevant figures, according to social, geographic, and temporal standards. We therefore decided to focus on the 58,625 biographical entries that make up the ODNB. Running to sixty volumes in its print format, the ODNB is the labor of 10,000 scholars who have collectively contributed its 62 million words.
On a technical level, the ODNB was praised upon its 2004 release for being “the first to exploit the potential of electronic publication on so vast and imaginative a scale”  [Collini 2005]. We considered the ODNB an appropriate choice for several other reasons as well. Several of the collaborators on this project share a primary interest in the early modern era (c. 1500-1700) in Britain, a period well covered by the ODNB. Both Carnegie Mellon University and Georgetown University have subscriptions to the ODNB, providing us with legal access to the “many possibilities opened up by the online version for accessing and organising the hoard of information”  [Collini 2005]. The ODNB’s dense-in-data documents fit the criteria of machine readability and relative uniformity. Although the biographies vary in length, all have a similar format and the raw text can be extracted in the same manner. Lastly, as biographies, they contain both explicit mentions of relationships – such as “Bacon’s life and career during the 1590s was dominated by his close relationship with Robert Devereux” – as well as numerous implicit indicators of potential relationships. Robert Cecil, for example, is mentioned five times in one section of Bacon’s biography [Peltonen 2004]. The ODNB thus offered opportunities to analyze both direct and indirect relationship data from a single collection.
As we worked with the ODNB data, a further advantage of this particular collection emerged: its ability to shed light on the current state and history of scholarship. Individually, each document in the ODNB is a roughly chronological account of one person’s life, specifically an individual deemed by nineteenth-, twentieth-, or twenty-first-century editors to have “in some way influenced [British] national life”  [Collini 2005]. As a collection, therefore, the ODNB holds significant information about what has and has not risen to the level of scholarly notice since the late Victorian creation of the Dictionary of National Biography, the ODNB’s precursor, in the 1880s. The original DNB primarily emphasized the political, literary, and scientific accomplishments of famous men, dedicating only 5% of its overall entries to women, and only 2% of the entries in the target date range 1500-1700. In the ODNB’s current version, the percentage of women has only increased to 11% overall and 6% in our target date range [Matthew and Harrison 2004].
In our era of text mining and network visualizations, such biases have continued effects. A bias towards men is a known issue in existing historiography; this bias is neither confined to the ODNB nor particularly surprising. However, transforming textual secondary sources into visual representations allows for more purposeful “critical scrutiny of what is known, how, and by whom” – the branch of knowledge increasingly referred to as “metaknowledge”  [Evans 2011]. Our visualizations of the early modern social network demonstrate the need both for more scholarship on women and other marginalized groups and for the integration of this scholarship into broader discussions of earlier modern society and culture; more importantly, it identifies the local areas of the network where the need for such scholarship is most pressing.

# 2. Pre-Processing Source Material

After having identified our collection of source materials, we then had to process the unstructured text – specifically a collection of HTML-formatted documents acquired through the ODNB website – into a format more amenable for analysis. This was done by extracting only the biographical portions of the text from the initial HTML documents – stripping the HTML formatting, bibliographies, and other extraneous text from the documents.[1] We then ran the plaintext documents through two NER tools: one from Stanford’s Natural Language Processing Group, denoted Stanford [Finkel et al. 2005], and another from the LingPipe collection of tools [Alias-i 2008].
These NER tools use probabilistic methods to identify names and to classify those names according to types such as person, location, or organization. For example, the following sentence – “The occasion of ‘Lycidas’ was the death of Edward King, a fellow of Christ's College who had drowned off the coast of Anglesey on 10 August 1637” – might be processed as “The occasion of ‘[PERSON]Lycidas[/PERSON]’ was the death of [PERSON]Edward King[/PERSON], a fellow of [ORGANIZATION]Christ's College[/ORGANIZATION] who had drowned off the coast of [PLACE]Anglesey[/PLACE] on [DATE]10 August 1637[/DATE]”  [Campbell 2004]. This example shows that no classifier is perfect – “Lycidas” in fact is the title of Milton’s great elegy rather than an historical person – and classifiers face particular challenges with multiple-word entities such as “Christ’s College” where the the first word separated from its follower could mistakenly if understandably be classed as a person.
For both Stanford and Lingpipe, we began with the default models trained on news article corpora and ran the tools on ten randomly chosen documents from the ODNB. These documents were then manually tagged to determine the accuracy of the tools’ performance on our target dataset. Two measures of accuracy were used: recall, the fraction of desired results obtained, and precision, or the fraction of obtained results that are correct. For our purposes, high recall was considered necessary, while high precision was desirable but less important. Stanford achieved better recall than LingPipe, at 70.7% and 67.8% respectively, but combining their results led to recall rates of 85.7%. The two tools were combined by taking all of Stanford’s smatches, and then adding in LingPipe’s matches if Stanford did not tag those specific words. In case of overlapping or contradictory tags, we used Stanford’s matches.
 Subset Recall Precision Stanford (ST), Person Tags Only LingPipe (LP), Person Tags Only 63.51%52.44% 91.75%72.11% ST, Person and Organization TagsLP, Person and Organization Tags 70.74%67.83% 74.02%46.19% ST + LP, Person Tags OnlyST + LP, Person and Organization Tags 79.37%85.66% 77.91%51.61%
Table 1.
Recall and Precision for Various Subsets of NER Results
We then implemented two additional procedures to improve recall and precision. First, to improve recall, we ran the documents through NER twice: once to create the initial tags and a second time using the initial tags as a dictionary, which enabled us to search for missed instances of phrases that were tagged during the first pass through the documents. This latter search was particularly successful at capturing partial name co-references, which occur within documents when historical figures are referred to only by their first or last name. With few exceptions, partial names that are part of a longer name found in that document are not actually different people. “Bacon” in a document containing “Francis Bacon” will refer, except in rare cases, to Francis Bacon. If a partial name matched the subject of a biography, it was considered a mention of that subject. Otherwise, partial names were considered mentions of the matching most recent full-name mention.
Second, to improve precision, we implemented manual rules to reduce the number of non-human names detected. This included removing all phrases that contained words beginning with lower-case letters; exceptions were made for the words “of” and “de” which often form part of names during this period, i.e. “Katherine of Aragon.” We also eliminated phrases with non-alphabetic characters – such as \$, *, and numbers – and common non-human proper names supplied by our subject matter experts – such as “Commonwealth,” “Catholic,” “Greek,” and “Roman.”
This resulted in final recall rates of 96.7% and precision rates of 65.5% on the initial test set. Testing on six new randomly-chosen documents led to a similar 95.3% recall rate but a slightly lower 54.0% precision rate. As our priority was a high recall rate, this was deemed acceptable. A later examination of a random 200-entity sample indicated the overall dataset’s precision rates were approximately 59% with +/- 7% margin of error.
From these results, we created a large table of documents and named entities. For each document, we tabulated the named entities and their number of mentions, which led to 494,536 different named entities occurring throughout the collection of 58,625 documents. We then reduced the number of named entities in two ways. First, we ignored named entities that did not occur in an ODNB biography within the period of interest (1500-1700). This made network inference less costly computationally. So too with our second step, in which we omitted names that occurred in fewer than five documents. Since correlations are very difficult to determine with sparse data, inferring relations among low count documents would have increased the number of false positives. While the five mention threshold did unfortunately mean that we had to eliminate many less prominent individuals, or those referred to by different names across the ODNB, the tradeoff was that it helped us achieve better precision at less computational cost. A final stage required further human curation – specifically, searching for names in the ODNB – to disambiguate people who shared the same name and de-duplicate people referenced under multiple names, particularly for names obtained through the NER tools. While recent research in the NLP community has focused on finding a way to automate this final stage, such as the Berkeley Entity Resolution System, we preferred the accuracy of manual curation [Durrett and Klein 2014].
The resulting table of 58,625 rows and 13,309 columns is known mathematically as a matrix. This n×p matrix, Y, has n rows representing documents and p columns representing people, or actors, in the network. The number of times person j is mentioned by name in document i gives us Yij, a non-negative integer for each document/person pair. We used this document-count matrix to infer the social network.

# 3. Statistical Inference

We motivated our statistical model for the previously described document-count matrix by assuming that direct connections between historical figures would be reflected by their being mentioned together in documents. Indeed, prior work has shown it possible to infer a rough graph based on co-mentions alone [Bosch and Camp 2011] [Bosch and Camp 2012]. However, our model requires more than a simple count of co-mentions because co-mentions sometimes result from confounding factors such as mutual acquaintances.
Consider an example such as the one displayed in Figure 2. George Villiers, Duke of Buckingham (1592-1628), knew King Charles I (1600-1649), and Charles I knew Prince Rupert of the Rhine (1619-1682), but Buckingham and Prince Rupert – whose lives only barely overlapped – never met. Because Prince Rupert and Charles I are connected, they will tend to be mentioned together in source documents. How often Prince Rupert is mentioned can therefore be predicted in part from how often Charles I is mentioned. Likewise if Charles I and Buckingham are connected, mentions of Buckingham predict mentions of Charles I. But in the case of no direct tie between Prince Rupert and Buckingham, as here, their names may still correlate due to mentions of Charles I. Despite such correlation, mentions of Buckingham convey no information about mentions of Prince Rupert not already accounted for by mentions of Charles I. We thus reasoned that co-mentions found in our document-count matrix – and correlations between any two given nodes derived from the matrix – might be the result of one or more confounding factors.
Under these assumptions, inferring the existence of network connections is the same problem as inferring the conditional independence structure in a particular statistical model – in this case, our document-count matrix [Glymour et al. 2001]. The method we used to infer the conditional independence structure of the document-count matrix is the Poisson Graphical Lasso, a penalized regression method proposed by Allen and Liu. This method is a generalization of Meinshausen and Bühlmann’s computationally faster approximation to the graphical lasso [Friedman et al. 2008]; it defines the relationships between nodes by a conditional Poisson distribution, instead of a multivariate normal distribution, which allows the penalized regression to be modified by an individual node’s count data [Allen and Liu 2012]. This method allowed us to create a symmetric p×p correlation matrix θ̂, where two nodes j and k are conditionally independent if and only if the coefficient θ̂jk = θ̂kj is zero.
In some applications of graphical models to infer network structure, all non-zero coefficients are of interest. For example, in gene networks, the expression levels of two connected genes may be negatively (conditionally) correlated. In our social network, however, we are primarily concerned with positive coefficients, as a relationship between two people should lead to a positive conditional correlation of their mentions in a document. A small or zero correlation suggests a lack of relationship between two people, while negative correlations might occur for a variety of reasons, including non-overlapping lifespans or two-degree – i.e., friend-of-a-friend – relationships without so-called triadic closure [Simmel 1950].
We therefore used our initial correlation matrix to create an adjacency matrix Y – a symmetric p×p matrix where Yij=Yji=1 when there is a positive correlation and assumed relationship between person i and person j, and 0 otherwise. Because our data and methods provide more information about some edges than others, however, we wanted to be able to attach a confidence estimate to potential edges instead of simply obtaining a yes or no estimate.
Confidence estimates were also better suited to the grey areas of humanistic research often requiring interpretation and even guesswork. In order to create this confidence estimate, we fit the Poisson Graphical Lasso on random subsets of our data 100 times and added the resulting adjacency matrices into a final matrix that we called our confidence matrix, C. This calculation gave us a “confidence level” for the likelihood of a relationship’s existence that ranged between 0 – never inferred – and 100 – always inferred.
Throughout this process, we experimented with tuning parameters and found that our final estimates did not vary significantly for all reasonable tuning parameters, where reasonable is defined as a low enough penalty such that edges are actually added, but high enough penalty that the algorithm converges rapidly. We also conducted penalty parameter training – using expert knowledge to manually confirm the existence of some relationships – but found this produced only very localized changes and had little impact on the overall network structure. The only significant manual intervention in this basic method thus came from our name disambiguation procedures, as we had nearly one thousand non-unique names in our node set. To deal with the the challenge of multiple individuals sharing the same name, we first disallowed positive adjacency estimates between two people with non-overlapping lifespans (with a one-year margin of error for posthumous children). Second, we used probabilities based on biography length to distribute adjacency estimates among people with overlapping lifespans.
A fuller explanation of our application of the Poisson Graphical Lasso can be found in our Appendix, along with a link to our code.

# 4. Expert Validation

Having constructed our confidence matrix of estimated relationships, we then conducted three different types of validation checks: one to ensure that our results showed the homophily that network studies have taught us to expect when semantic context is taken into account; one to confirm that our results were consistent with statistical theory; and one to evaluate the accuracy of our results in comparison with an expert human reading of the ODNB biographies. We first used topic modeling on approximately 90% of our dataset – excluding people with duplicate names whose relationships had to be disambiguated – to evaluate different kinds of actor connectivity in a semantic context. Then, on smaller subsets of our data, we compared our results with alternative statistical methods, and calculated precision and recall rates.
Our first validation step was motivated by the fact that the Poisson Graphical Lasso counts names but ignores semantic context. As a way to test the validity of this approach, we wanted to compare the connectivity of actors who are mentioned in similar contexts to the connectivity of those mentioned in different contexts, since actors who share contexts are more likely to know one another than those who do not [McPherson, Smith-Love and Cook 2001]. Thus for our first validation step, we decided to create and analyze a latent dirichlet allocation (LDA) topic model – an algorithm for extracting semantic clusters from a set of text [Blei et al. 2003] [Weingart 2012]. We hoped to find our network data showed greater connectivity between actors who share a context than between actors in different contexts, as generated through the topic model. If so, we could conclude that our approach produces results compatible with accepted, semantically-sensitive approaches.
To generate our topic model, we created a ‘bag of words’ for each person in our dataset, comprised of all words that appear before and after the person’s name in the ODNB. Specifically, for each person in the network, we located all mentions in the ODNB, and used the previous fifteen words and next twenty-five words – excluding named entities – as their “bag of words”. The choice of these two numbers was motivated by attempting to capture the current sentence and the previous and next sentences. We then removed all named-entity mentions in these biographies and converted the remaining words into lower case. Next we applied the Porter stemmer [Porter 1980], an algorithm that strips away standard English suffixes in a specific order. For example, the Porter stemmer turns the word ‘publisher’ into ‘publish’, and does same to the word ‘published’. We then dropped words that are in a standard stoplist – which includes words like ‘and’, ‘the’, etc. – provided in the text-mining R package tm [Feinerer et al. 2008]. In addition, we dropped all month words, some numbers, and select relationship terms – a complete list can be seen in our topic modeling R code.[2] The remaining words in the ‘bag of words’ for each person thus approximately reflected their profession, accomplishments, or “historical significance” as given by the ODNB.
Using each of these “bags of words” as an individual text, we fit three topic models to our collection of texts.[3] The three topic models were generated with five, ten, and twenty topics, respectively, to ensure the number of topics did not significantly alter our results. The topics were generated automatically and each text – and the person it represents – was assigned to the topic with the highest probability match. The top representative terms in our ten-topic model can be seen in Figure 3. The clustering of historical subjects and people in our topics is encouraging, as many of the topics clearly represent different kinds of historical activities. For example, Topic 3 in our ten-topic model contains the words “bishop,” “church,” “minist” and “preach”, as well as a large number of churchmen such as Richard Bancroft and John Whitgift (see Figure 3). Topic 8 includes the words “publish”, “poem”, and “play,” along with poets like Robert Herrick, John Donne, and John Dryden.
 Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 londonfamilimerchantcolonitradework earllordparliamentsecondkinglondon bishopcollegchurchministpreachlondon armicommandreturnforccaptainship workpublishletterwritepublicbook Topic 6 Topic 7 Topic 8 Topic 9 Topic 10 kingpolitparliamentappointdukelord worklondonpublishbookprintphysician workpublishpoemplaytranslatedit earllondonfamilimarriagsecondwill kingqueenenglishenglandcourtroyal
Table 2.
A table of the top representative terms in the ten-topic model
We then analyzed the frequency of our estimated relationships between people who do and do not share topics. For all three topic models, estimated relationships between people who shared a topic are more frequent than between-topic estimated relationships; the specific results for the ten-topic model can be seen in Figure 4. This coincides with the expectation for homophily (also known as assortativity) and a qualitative, semantics-based reading of the same data: book authors are more likely to be linked to other notable authors as opposed to notable military personnel. While running a topic model with different parameters (i.e. number of topics) changes the specific results, within-topic relationships remain more frequent than between-topic relationships. We therefore concluded that the Poisson Graphical Lasso produces results compatible with other, semantically-sensitive methods.
 Measure Within-Topic Between-Topic Fraction of Edges with Confidence ≥ 90% 0.0001444 0.0000117 Fraction of Edges with Confidence ≥ 75% 0.0004523 0.0000527 Fraction of Edges with Confidence ≥ 50% 0.0016402 0.0003082 Fraction of Edges with Confidence ≥ 30% 0.0033207 0.0007585
Table 3.
A table of relationship confidence estimates in the ten-topic model
Our second validation step was to compare our results with alternative methods of constructing a confidence matrix. Using Spearman correlations, which measure how well the ordering of two ranked lists align, we evaluated how each method performed against expert-generated ranked relationship lists. We had earlier considered using three possible methods for inferring a correlation matrix from the document-count matrix: 1) ranking by simple correlation (high positive correlations are higher ranked relationships); 2) running the Poisson Graphical Lasso and ranking edges by the value of ϱ in which the edge was added to the model (edges added with more penalization are higher ranked relationships); and 3) running the Poisson Graphical Lasso and ranking edges by the value of the regression coefficient (higher positive coefficients are higher ranked relationships). According to statistical theory, both versions of the Poisson Graphical Lasso should perform as well as, if not better than, simple correlation because of their ability to screen off friend-of-a-friend connections, as described in section three above. We hoped to find this reflected in our Spearman correlations, in order to conclude that our approach produces results compatible with statistical theory.
We chose to test this on James Harrington and John Milton by taking the top thirty relationships according to each of these three methods and combining them to create a master list of thirty and eighty relationships, respectively. Faculty and PhD students with backgrounds in the early modern period were given the combined names in random order and asked, first, to rank the relationships according to a question we used to approximate relationship importance, specifically “how unhappy would experts be if this relationship were not included among the main actor’s top relationships?” and, second, to mark the relationships as true/false. Despite only being an approximation to relationship importance, the ranking list still proved far more difficult for the humanists to generate than the true/false list.
We wanted to choose the statistical method that created lists most closely correlated to the humanists’ list, as measured by Spearman correlation. The Spearman correlations of each method were extremely similar in the humanists’ ranked lists and – combined with humanists’ concerns over producing the list in the first place – led us to abandon the effort to optimize our algorithm for the order of ranks. Instead, we attempted to determine which method obtained more correct relationships – that is, relationships humanists marked as true – in the top k estimated connections. For analysis of James Harrington’s thirty connections, all three methods performed similarly; for John Milton’s eighty connections, using simply the correlation coefficient led to worse estimates earlier on, confirming that the Poisson Graphical Lasso can more accurately reproduce sections of the network than correlation alone.
Lastly, for our third validation step, we wanted to evaluate the accuracy of our final inferred network, in comparison to the relational knowledge conveyed by a humanist reading of the ODNB. We therefore chose twelve people from the network and calculated the precision and recall rates for their relationships. The twelve people were not a random sample. Rather, they were chosen to represent a variety of conditions within our dataset, including gender, number of estimated relationships, deduplicated names, and appearance within individual vs. shared ODNB biographies. Some of these conditions are relatively rare within the dataset on the whole. For each person, we checked their inferred edges from 40-100% confidence – qualitatively tagged as our “possible” to “certain” confidence interval – against a list of associations manually compiled from the ODNB documents by reading through each person’s biographical entry and other entries in which their name appears.
Together, these twelve people had twenty-eight relationships in our likely-to-certain (60-100) confidence interval, of which three were incorrect, leading to an 89.29% precision rate (see Figure 5). Expanding our confidence interval to also include possible relationships (40-100) – in other words, sacrificing precision to increase recall – gave us one hundred and seven relationships of which twenty-seven were incorrect, leading to a still-respectable 74.77% precision rate. The majority of these false positives were caused by specific conditions within our data: group biographies, duplicate names, and an abnormally high percentage of co-mentions within related biographies. Removing the four people who satisfied these specific conditions from our sample left us with fifty relationships and a 86.00% precision rate in our 40-100 confidence interval, which suggests that many of the errors in our dataset are associated with people who fulfill these conditions, which impaired our algorithm’s ability to correctly capture their relationships via co-mentions. Because our validation sample had taken care to include some of our most problematic case-types, even though instances of some of those case-types are relatively few, we deemed these measures of precision adequate as a starting point for further curation of the network via crowd-sourcing on our website at www.sixdegreesoffrancisbacon.com.
 Confidence Interval Number of SDFB Inferred Relationships Precision (# correct / # found) Article Recall(# found in article / # in article) SDFB Recall (# found in article also in SDFB / # from article) 80-100 (certain) 5 80.00% 1.98% 3.96% 60-100 (likely) 28 89.29% 8.42% 16.83% 40-100 (possible) 107 74.77% 25.74% 51.49% 10-100(unlikely) 283 ≥28.27%[4] 33.66% 67.33%
Table 4.
Precision and Recall for a Subset of the Inferred Network
Calculating a global recall – the fraction of desired results obtained from the ODNB as a whole – on our dataset would have required us to identify connections across the entire biographical corpus of the ODNB, a prohibitively labor-intensive process when done manually. We therefore calculated two partial measures of recall instead. The first measure is article-level recall – that is, a measure of the ability of our network to capture the same relationships as a human reading a specific biographical article. By this measure, our recall numbers were low, with our 40-100 confidence interval including only 25.74% of the relationships mentioned in the article. Low article recall can be attributed, at least in part, to two factors: first, the decision to impose a five-mentions threshold during the NER stage, which excludes infrequently mentioned names about which the ODNB provides insufficient network data, and, second, the way some names are mentioned in the ODNB, which prevented them from being picked up by NER.
Next, we calculated the measure we call “SDFB” recall – that is, the ability of our computer algorithms to infer relationships for the subset of people mentioned in a specific biographical article who were also included in our overall network. This adjustment – excluding people who did not pass the five-mentions threshold or were not captured by NER – leads to a significantly higher recall numbers, at 51.49%, again for the 40-100 confidence interval. Further expansion of the confidence interval to 10-100 increases the SDFB recall rate to 67.33%, showing that within the subset of names captured by NER and included in our node dataset, high recall rates can be achieved at the lowest confidence intervals. Though higher recall rates would of course be desirable in theory, we deemed it preferable to have a relatively accurate but sparse network rather than a full but error-ridden network, and further increases in recall would require corresponding trade-offs in precision.

# 5. Humanities Significance

Though the map of the early modern social network created by our inference procedures is far from perfect, it provides a sizeable base of persons and relationships that can be gradually corrected and expanded to encompass the interests of a wide range of humanist scholars. This network can also be examined, validated, refined, and expanded by scholars, students, and other end-users through a dynamic wiki front-end with sophisticated network visualization tools. We consider such an approach complementary to several successful approaches that focus on smaller subsets of society [Long and So 2013] [Ahnert and Ahnert 2015] [Basu et al. 2015] [During 2015]. An important possible outcome of the project is the integration, or re-integration, of disparate threads of network scholarship.
The questions humanists care most about often turn on documentary evidence of connections, and immersion in an archive or a published collection of letters yields qualitative knowledge of unparalleled depth and richness. Yet the humanities would need to see massive investments in historical analysis, palaeography, languages, and other humanistic research skills in order to investigate anything close to the number of relationships inferred using our model. Since little in the current funding climate suggests that such investments are immediately forthcoming, the promises of historical network analysis would remain unrealized in the absence of a different approach. Hence our probabilistic network inferences, which create a workable infrastructure for subsequent investigation. Instead of starting the process of mapping the network from scratch, we remediate existing scholarship for further addition, expansion, development, and correction.
The time, moreover, appears to be right. With open access research gaining momentum, and more and more texts entering the public domain, probabilistic text-mining approaches afford wider lenses and present new opportunities [Elson et al. 2010] [Hassan et al. 2012] [Underwood et al. 2013] [Makazhanov et al. 2014] [Riddell 2014] [Smith et al. 2014]. Even as such approaches will always benefit from the depth and precision afforded by more traditional archival analyses, non-commercial repositories like the HathiTrust Research Center and commercial ones (such as Google Books) represent exciting corpora for large scale reconstruction of historical social networks. Treating the high-quality historical scholarship as a source of unstructured data, moreover, helps us avoid some of the pitfalls recently observed in studies based on less scholarly data sources like Wikipedia and Freebase [Gloor et al. 2015] [Schich et al. 2014] [Weingart 2015]. Such studies based on declared links in non-scholarly corpora haven’t yet achieved the plausibility achieved on the smaller scale by old-fashioned archival work and entering attested links by hand.
At the same time, partnerships between traditional small-scale projects and larger-scale projects like Six Degrees of Francis Bacon offer benefits to both sides. For those studying local networks, large, probabilistic global networks offer chances to compare and contextualize findings from smaller groups. For those working at larger scales and with higher cumulative levels of uncertainty and error, small networks can function as ground truths against which to test inferences and from which partners may improve network models.
Our approach isn’t just a new method. It yields substantive insights as well. Applying quantitative network measures like network degree has allowed us to identify interesting figures, such as those who have relatively high degrees but who don’t have ODNB entries of their own. An analysis of high-degree nodes without ODNB entries shows an intriguingly high representation of schoolmasters and publishers. Individuals like Thomas Smelt, an ardent royalist who taught at the Northallerton Free School in Yorkshire, and Edward Sylvester, who ran a grammar school in Oxford, were not deemed significant enough to warrant full biographical entries, but they are nevertheless key nodes connecting those who were [Otis 2014b].
It is also possible from this work to understand more about non-British people who figure prominently the life of the nation. Scholars can learn much about international dimensions by attending to the frequency of non-native names appearing frequently in the ODNB. Our five-mention threshold also helps us see gender differences in a revealing light. The cultural practice of changing one’s surname at marriage means that women face particular obstacles meeting our artificially-imposed five-mention threshold. In several cases, men appear in the dataset simply because they are mentioned in association with important women – wives, sisters, or mothers who for various reasons may not themselves appear in the dataset. The woman referred to in the ODNB as “Audrey, widow of Sir Francis Anderson and eldest daughter of John Boteler, Baron Boteler of Brantfield” does not appear in the dataset whereas John Boteler does [Seccombe and Kelsey 2014]. Similarly, men like Thomas Bellenden and Richard Stubbe aren’t known as historically significant, but they appear in the dataset because their names remain consistent whereas their wives and sisters appear by several names. In other cases, it isn’t a personal ODNB entry that ensures a name gets included but a legal case or a much-cited will [Otis 2014b]. Our analysis has also illustrated how inferred networks differ based on ways of talking about people. James VI of Scotland and James I of England name the same person, yet each name is associated with substantially distinct social networks [Otis 2014a].
Ultimately, our work with the ODNB has shown that processing an entire corpus of documents and running a statistical procedure is computationally feasible with the resources generally available to university scholars. We have also shown that it is possible to implement a statistical approach that infers a validated social network. While not all highest-confidence edges are among the strongest identified by experts – and some expert-identified relationships are not near the top edges found – there is enough overall validation on many classes of relationships to suggest our method is viable for reconstructing historical social networks, within a reasonable margin of error, from large textual corpora.
This process admittedly has several shortcomings, especially from the perspective of humanists for whom “margin of error” is a less than reassuring phrase. Absent further research, there is no surefire way to determine whether a given confidence estimate accurately reflects the current state of scholarship (as represented by the ODNB) or is instead an artifact of the bespoke model we developed. Nor are relationships in the resulting dataset “typed” – friends and enemies remain functionally identical in our results, though the difference of course matters decisively in real life. Proof or other evidence about a given relationship will initially appear elusive: the process yields few clues about where to start researching a relationship – though our crowd-sourcing website does at least provide users links to ODNB and JSTOR articles that mention both people in a relationship. And humanists must be involved at every stage for validation, interpretation, de-duping, and disambiguation. However, the end result of this process is of demonstrable use to experts in early modern Britain and it is likely extensible to other large corpora.
We are the first to acknowledge that our network inference procedure comes freighted with assumptions and technical limitations that may pose obstacles to its transferability to other social networks generated from other data sources. Inferring a network from biographical texts requires assuming that the co-occurrence of names in a document is a reasonable predictor of a relationship between the named persons. Although we believe this is a reasonable and productive assumption for ODNB texts, it is not an equally reasonable assumption for all data sources. Network inference will be only as good as the NER on which it depends. Differences in NER availability and accuracy for different languages (Stanford, for example, has separate modules for Spanish, German, and Chinese), as well as differences in naming conventions across cultures, time periods, discourses, and biographical data may decrease its effectiveness, though NER can be tuned for different datasets. Because the ODNB entries have been carefully edited and checked, they are relatively error free, but projects that aim to mine biographical reference works that exist only in uncorrected Optical Character Recognition documents will begin with a significant level of textual error. Those who seek to employ our procedures on other biographical data sources should perform checks to ensure that it is inferring edges between nodes at level of accuracy that they deem acceptable.

# Conclusion

While our interest has been in reconstructing the social network of a specific time and place – sixteenth- and seventeenth-century Britain – there are few barriers to re-deploying our method in other historical or contemporary societies. We used short biographical entries, but we could with minor changes have used contemporary book prefaces, modern scholarly articles, blogs, or other kinds of texts. All that is needed is machine-readable text in which the co-occurrence of names is a reasonable indicator of connections between persons. Future work on our specific project may thus involve expanding the collection of documents used in our network. Target documents currently include the publishing data in the English Short Title Catalog and the prefatory material in Early English Books Online. We would also aim to incorporate datasets whose strengths would mitigate the data’s current weaknesses, such as collections of letters written by women or urban apprenticeship rolls.
We have also begun to expand our network through the data provided by individual scholars via our website interface at www.sixdegreesoffrancisbacon.com. To encourage mass integration of other datasets, we have incorporated features into our website to allow the tagging of nodes and the visualization of sub-networks by those tags. However, we also have a particular interest in scholars adding citations to confirm our statistically predicted relationships, as well enriching those relationships by providing information about their type and timespan. Our ultimate goal is to create a versatile and extensible network that people interested in all aspects of early modern Britain – including the scholarship on early modern Britain – can use for their research, as well as to pioneer a general technique of creating social networks from texts that other scholars can apply to other periods and societies.

# APPENDIX: The Poisson Graphical Lasso

## Introduction

Our statistical approach follows the model of G.I. Allen and Z. Liu [Allen and Liu 2012]. Inference of the network is based on statistical graph learning techniques. Here we have a graph G=(V,E), where V is the set of p nodes and E is the set of pairwise edges. We relate the graph to a random vector Y=(Y1, ... , Yp) by requiring that for each non-edge (j,k)∉E, the variables Yj and Yk are conditionally independent given all the remaining variables Y∖{j,k}, where ∖{j,k} denotes the complement V∖{j,k}. Commonly, Y=(Y1, ... , Yp) is assumed to follow a multivariate normal distribution Np(µ,∑), in which case pairwise conditional independence holds if and only if ∑jk-1=0 [Lauritzen 1996]. In this case, inferring the graph corresponds to inferring the non-zero elements of ∑-1.
If we have n independent and identically distributed observations of Y, we can employ penalized likelihood methods, where we place a one-norm penalty on elements of the concentration matrix. This penalized likelihood can be maximized efficiently for large p using a graphical lasso [Friedman et al. 2008]. Alternatively, an approximate solution can be obtained through a sequence of penalized regressions of each variable Yj on the remaining variables Y∖j=Y∖{j}. We estimate σjk-1 = 0 if the estimated regression coefficients of variable j on k or k on j are estimated to be 0 [Meinshausen and Bühlmann 2006].

## Poisson Graphical Lasso

For count data like ours the normality assumption may be inappropriate and a modification of the above methods was developed by Allen and Liu for Poisson graphical models, in which the relationships between nodes are defined by a conditional Poisson distribution [Allen and Liu 2012]. For each node: $$p\left( Y_{j} \middle| Y_{\smallsetminus j} = \mathcal{Y}_{\smallsetminus j} \right)\sim\text{Poisson}\left( \exp\left( \theta_{j} + \sum_{k \neq j}^{}{\theta_{\text{jk}}\mathcal{Y}_{k}} \right) \right)$$
The Poisson Markov random field implied by this relationship is not amenable to inferring network structures, as it requires θjk ≤ 0 for all pairs {j,k} [Allen and Liu 2012]. We therefore proceed as they did by estimating the local log-linear models $$\log{\left( \mathbb{E}\left\lbrack Y_{j} \right.\ \middle| \left. \ Y_{\smallsetminus j} = \mathcal{Y}_{\smallsetminus j} \right\rbrack \right) = \theta_{j} + \sum_{k \neq j}^{}{\theta_{\text{jk}}\mathcal{Y}_{k}}}$$ and combine the implied local relationships into a network structure.
We can then view θij as a measure of relationship strength between i and j. In Allen and Liu, the model is fit using the Poisson Graphical Lasso – a penalized regression method similar to the graphical lasso [Friedman et al. 2008], but modified for count data. A penalized Poisson regression is done for each node j’s counts on the rest. That is, for each node we solve the following: $${\widehat{\Theta}}_{\smallsetminus j,j} = \Theta_{\smallsetminus j,j}\frac{1}{n}\sum_{i = 1}^{n}{\left\lbrack Y_{\text{ij}}\left( Y_{i, \smallsetminus j}\Theta_{\smallsetminus j,j} \right) - \exp\left( Y_{i, \smallsetminus j}\Theta_{\smallsetminus j,j} \right) \right\rbrack - \left\| \rho \star \Theta_{\smallsetminus j,j} \right\| 1}$$
Here ϱ is a matrix of penalty parameters and ⋆ denotes component-wise multiplication. An edge is determined to exist between nodes j and k if θ̂jk > 0 and/or θ̂kj > 0. The tuning parameter ϱ can be the same for all elements and can be chosen, for example, by stability selection [Meinshausen and Bühlmann 2010]. Later we will allow elements of the ϱ matrix to differ.

## Modifications

The motivating data for Allen and Liu are the RNA-sequencing measurements from p genes in n experiments; their goal is to determine which genes are “connected” to each other in a metabolic process [Allen and Liu 2012]. Here we have the (noisy) counts of p names in n biographies; our goal is to determine which historical figures had "connections" to each other in a variety of social contexts. Two modeling considerations unique to this type of data and practical objective, which lead us to slight modifications in method, are the variance of document lengths and the irrelevance of negative edge estimates.
Documents in the ODNB vary greatly in length. People tend to have longer biographies when biographers know more about them or have deemed them historically significant. Allen and Liu note that it is important to normalize the data to be approximately independent and identically distributed Poisson random variables, since their model is sensitive to deviations from this assumption [Allen and Liu 2012]. To achieve this, we break the longer documents into 500 word sections and count each section as an observation. This introduces weak dependence among some observations, but the chronological nature of the documents may lessen this effect. That is, the people mentioned in the first section of Bacon’s biography may be very different from those mentioned in the last section. Being mentioned in the same section of a document may also be greater evidence of a connection than simply being mentioned in the same document.
As a preliminary test of this method, we calculate the Spearman correlation between lists of relationships provided by humanities scholars and
1. relationships produced by simple correlation
2. relationships produced by our model with document sectioning
3. relationships produced by our model without document sectioning
For our test set, simple correlation fails first, while those for our model – with and without sectioning – remain similar. Sectioning fails to improve correlation on some historical actors, but it leads to slight improvements in correlation for others.
Furthermore, when fitting the model, a large fraction of θ̂jk values are negative. When this coefficient is negative, it does not make sense to estimate a resulting edge, since negative coefficients imply a negative relationship between the counts of name j and name k. Because any specific person appears only in a small portion of the documents, and is presumably related to only a small fraction of all the people in the network, fitting this model tends to produce a large amount of negative coefficients compared to positive coefficients.

## Confidence Estimate Procedure

We want to be able to attach a confidence estimate to all edges (which can be used to rank connections), instead of just obtaining a yes or no estimate for each potential edge. Let the matrix C represent a symmetric confidence matrix (where each entry Cjk = Ckj = confidence attached to edge existing between person j and k). An informal confidence estimate can be obtained by refitting the model many times on random subsets of the data and computing the fraction of models in which a specific edge is found in the model.
The method of estimating the final edge confidences is as follows:
1. Sample half of the rows in the data matrix
2. Fit Poisson Graphical Lasso on this data as follows:
• For each j (column), fit the model in Equation 3, and obtain the coefficient estimates for ϱ=0.001
• Ignore any coefficient that has been estimated as negative
3. Repeat steps (1) and (2) 100 times.
4. Estimate the confidence of an edge between node j and k as $${\widehat{C}}_{\text{ij}} = \frac{\Sigma_{t = 1}^{B}\left\lbrack I\left( {\widehat{\theta}}_{\text{jk}}^{(t)} > 0\text{\ or\ }{\widehat{\theta}}_{\text{kj}}^{(t)} > 0 \right) \right\rbrack}{B}$$
Note that θ̂(t)jk is the estimate for the coefficient on the tth repetition of the model fitting in Step 2.
There are a number of methods described in the literature for selecting the tuning parameter ϱ. When the goal is prediction of the response variable, cross-validation is a natural choice. When the goal is network inference – specifically, we want to know whether each edge is “in” or “out” – stability selection can be used instead, as is done in Allen and Liu [Meinshausen and Bühlmann 2010] [Allen and Liu 2012]. Of most use to humanities scholars, however, is an organization of the current knowledge about relationships. Some scholars may wish to explore numerous potential relationships to one actor. Ordering the relationships correctly – in order of likelihood – is therefore more important than determining a cutoff point and excluding all edges that do not make the cut.
Our confidence estimates for a specific value of ϱ correspond to a single point on the stability paths mentioned in Meinshausen and Bühlmann [Meinshausen and Bühlmann 2010]. They note that the choice of range of ϱ to use when computing the “stable variables” – or in this case, edges – does not matter significantly. In our experiments with values of ϱ ranging from 0.001 (many edges) to 100 (no edges), we also find the confidence estimates tend to not vary too much for different reasonable values of ϱ, where reasonable is defined as a low enough penalty such that variables are actually added, but high enough penalty so that the algorithm converges rapidly.

## Name Disambiguation

Different people sometimes have the same names, and disambiguating them is difficult. When name duplication only happens rarely, it may be feasible to disambiguate manually. However, there are no less than twelve John Smith’s and ten Archibald Campbell’s in our node set; overall nearly a thousand names refer to multiple people. Furthermore, many of the people with these names overlap in lifespans, including a large number of parents who gave their own names to their children.
To process these duplicate names, we use a twofold method. First, we employ chronological filters on all our potential relationship edges. Two people cannot have a relationship if their lifespans did not overlap. We do, however, allow a one-year margin of error so that posthumous children may still have edges to their biological fathers. For people with unknown birth and death dates, we allow a twenty-year span before and after their known period of activity. For people for whom only a birth or a death date is known, we allow for up to a 110-year lifespan, erring on the side of inclusivity rather than exclusivity.
In the cases where there is chronological overlap in the lifespans of people with duplicate names, we fall back on probabilities. If the name was generated by NER, we evenly split the mentions among each of the people with that name – that is, we assign them each an equal probability. However, if our duplicates all have biographical entries, we assign each person a probability based on the length of their biography. This serves as an approximation of the relative frequency we expect each person to appear in the overall ODNB, which we use to weight the mentions accordingly.
For example, Francis Walsingham, the principal secretary, has a biography that is 30 times the length of Francis Walsingham, the Jesuit. Therefore we argue a mention of Francis Walsingham in some other ODNB biography is 30 times more likely to refer to the former rather than the latter. To follow this logic through, we would assign weights of 97% to the principal secretary and 3% to the Jesuit. Yet we don’t want to obscure the lesser-known Jesuit so thoroughly. Therefore, we cap the percentages at a max/min of 75% and 25% so that someone with an extremely long biography cannot dominate the probabilities completely. Thus in the period of overlap between their two lifespans, 75% of the instances of “Francis Walsingham” are attached to the principal secretary and 25% are attached to the Jesuit. In practice, this does yield lower confidence estimates and more false positives for “split-mention” nodes’ relationships, but we consider this an acceptable as a starting point for further, manual curation.

## Incorporating Humanist Knowledge

Prospectively, after enough humanists contribute their expert knowledge to the network via our crowd-sourcing website, it will be possible to use their contributions to refine our inference model by making local changes to the penalty parameter. We could do this by allowing the penalty matrix, ϱ, to vary for different relationships. If our experts confirm a relationship between actors j and k, we set ϱjkkj=0, which usually ensures that θ̂jk, θ̂kj ≠ 0. Similarly, for a confirmed non-relationship – that two figures are not connected – we would set ϱjkkj=∞, ensuring θ̂jk, θ̂kj = 0. As more experts label more potential relationships, we could continue to refine our model iteratively. By helping us to tune the penalty parameter, the contributions of (say) a hundred experts could help us to assess millions of relations more accurately.

## Network Code

Further information on how we generated our network can be found, along with our R code, at: https://github.com/sdfb/sdfb_network[5]

## Notes

[1] Our R code for both the pre-processing and statistical analysis of our dataset is at https://github.com/sdfb/sdfb_network/tree/master/code/ODNB.
[2]  Our R code for the topic modeling is at https://github.com/sdfb/sdfb_network/tree/master/code/topic_models
[3] For several of the known limitations of topic models in digital humanities, see [Meeks and Weingart 2012].
[4] We judged validating the additional 176 inferred relationships in the 10-39 confidence interval to be too labor-intensive, with little added benefit, to be worth calculating. Given the number of already-validated relationships in the 40-100 confidence interval, we calculated the lowest possible precision rate in our 10-100 confidence interval to be 28.27%. It is very likely higher.
[5] Research for this article was supported by a grant from the Council for Library and Information Resources Award (Con_505), by Google Faculty Awards 2012_R1_189 and 2013_R1_26, and by a Falk Fellowship from Carnegie Mellon University’s Dietrich College of Humanities and Social Sciences.

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