Converting supervisory reports to Semantic Webs: from XBRL to RDF

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A growing number of supervisory reports across Europe are based on the XML Extensible Business Reporting Language standard (XBRL). Financial entities such as banks, insurance undertakings and pension institutions are required to submit their reports to their supervisors in this format.

XBRL is a language for modeling, exchanging and automatically processing business and financial information. Reports in this format (called instance documents) are based on metadata (set out in taxonomies) that add semantic meaning to the data points that are reported. You can choose different implementations but overall an XBRL taxonomy provides a semantically rich data model and that has always been one of the main advantages of XBRL.

However, in its raw format (an XML file) each report is basically a machine readable document with a tree structure that does not enable easy integration with related data from other sources or integration with text documents and their contents.

In this blog, I will show that converting the XBRL reports to another format allows easier integration and understanding. That other format is based on Semantic Webs. It has been shown that XBRL converted to Semantic Webs can be done without any loss of information (see for example this article). So if we convert the XBRL format to a Semantic Web then we keep the structure and the meaning provided by the taxonomy. The result is basically a graph and this format enables integration with other linked data that is much easier.

A Semantic Web consists of formats and technologies that are rather old (from a computer science perspective): it originated around the same time as XBRL, some twenty years ago. And because it tried to solve similar problems (lack of semantic meaning in the World Wide Web) as the XBRL standard (lack of semantic meaning in business and financial data), to some extent it is based on similar concepts. It was however developed completely separate from XBRL.

The general concept of a Semantic Webs, where data is linked together to provide semantic meaning, is also known as a knowledge graph.

How does a Semantic Web work? One of the formats of the Semantic Web is the Resource Description Framework (RDF), originally designed as a metadata data model. RDF was adopted as a World Wide Web Consortium recommendation in 1999. The RDF 1.0 specification was published in 2004, and RDF 1.1 followed in 2014.

The RDF format is based on expressions in the form of subject-predicate-object, called triples. The subject and object denote (web) resources and the predicate denotes the relationship between the subject and the object. For example the expression ‘Spinoza has written the book Ethica Ordine Geometrico Demonstrata’ in RDF is a triple with a subject denoting “Spinoza”, a predicate denoting “has written”, and an object denoting “the book Ethica Ordine Geometrico Demonstrata”. This is a different approach than for example object-oriented models with an entity (Spinoza), attribute (book) and value (Ethica).

The RDF format could potentially solve some problems with the XBRL format. To explain this, I converted an XBRL-instance (a test instance file from EIOPA for Solvency 2) to RDF format.

Below you see the representation of one arbitrary data point in the report (called a fact) in RDF format and visualized as a network (I used the Python package networkx). The predicates contain the complete web resource so I limited the name to the last word to make it readable.

The red node is the starting point of the data point. The red labels on the lines describe the predicate between subject and object. You see that the fact (subject) ‘has decimals’ (predicate) 2 (object), and furthermore has unit EUR, has value 838522076.03, has type metmi503 (an internal code describing Payments for reported but not settled claims) and some other properties.

The data point also has a so-called context that defines the entity to which the fact applies, the period of time the fact is relevant (in this case 2019-12-31) and also a scenario, which consists of additional metadata of the data point. In this case we see that the data point is related to statutory accounts, non-life and health non-STL, direct business and accepted during the period (and a node without a label).

All facts in every XBRL instance are structured in this way, which means that for example you can search all facts with the label statutory accounts. Furthermore, because XBRL uses namespaces you can unambiguously identify predicates and objects in the report. For example, you see that the entity node has an identifier (starting with 0LFF1…) and a scheme (17442). The scheme refers to the web resource for the ISO standard 17442 which specifies the Legal Entity Identifier (LEI), so the entity is unambiguously identified with the given (LEI-)code. If you add other XBRL instances with references to that entity then the data is automatically linked because other instances will contain exactly the same entity node.

The RDF representation of the XBRL fact above is:

_:provenance1 xl:instance "filename".
_:unit_u xbrli:measure iso4217:EUR.
  xl:provenance :provenance1;
  xl:type xbrli:fact; 
  rdf:type s2md_met:mi503;
  rdf:value "838522076.03"^^xsd:decimal;
  xbrli:decimals "2"^^xsd:integer;
  xbrli:unit :unit_u; 
  xbrli:context :context_BLx79_DIx5_IZx1_TBx28_VGx84.
  xl:type xbrli:context;
  xbrli:entity [
    xbrli:identifier "0LFF1WMNTWG5PTIYYI38";
  xbrli:scenario [
    xbrldi:explicitMember "s2c_LB:x79"^^rdf:XMLLiteral;
    xbrldi:explicitMember "s2c_DI:x5"^^rdf:XMLLiteral;
    xbrldi:explicitMember "s2c_RT:x1"^^rdf:XMLLiteral;
    xbrldi:explicitMember "s2c_LB:x28"^^rdf:XMLLiteral;
    xbrldi:explicitMember "s2c_AM:x84"^^rdf:XMLLiteral;
  xbrli:instant "2019-12-31"^^xsd:date.

Instead of storing the data in separate templates with often unclear code names you can also convert the XBRL data to one large Semantic Web where all facts are linked together. The RDF format thus provides a graph model which allows easier integration and visualization (and, for me at least, easier understanding). It allows adding and linking data from other sources, such as Solvency 2 documents and external data, in the same graph.

Typically, supervisory reports consists of thousands of data points and supervisors receive reports from many entities each period. How would you store that information? I think that the natural way to store an XBRL instance is not a relational database but a graph database (like graphDB or Neo4j). These databases can store the facts with all the metadata in a structured way and enable to query the graph efficiently. Next blog, I will explore graph databases and query languages for XBRL reports converted to the RDF format.

Pilot Data Quality Rules

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Data Quality is receiving more and more attention within the financial sector, and deservedly so. That’s why DNB will start a pilot in September with the insurance sector to enable entities to run locally the required open source code and to evaluate Solvency 2 quantitative reports with our Data Quality Rules.

In the coming weeks we will:

With these tools you are able to assess the data quality of your Solvency 2 quantitative reports before submitting them to DNB. You can do that within your own data science environment.

We worked hard to make this as easy as possible; the only thing you need is Anaconda / Jupyter Notebooks (Python) and Git to clone our repositories from Github (all free and open source software). And of course the data you want to check. We also provide code to evaluate the XBRL instance files.

We are planning workshops to explain how to use the code and validation rules and to go through the process step by step.

Want to join or know more, please let me know (w.j.willemse at

Code moved to GitHub/DNB

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It has been a bit quiet here on my side. But I have been busy moving the source code from the notebooks here to the GitHub-account of DNB. And in doing so we improved the code in many areas. Code development can now be done efficiently by using tools for Continuous Integration and Deployment. This enables everyone to work with us to explore new ideas and to test, improve and expand the code.

Let me shortly introduce our repositories (these are all based on code that I wrote for the blogs on this website).

Our insurance repositories


A package for retrieving Solvency 2-data. Our idea is to provide you with one package for all Solvency 2-data retrieval.

Currently it is able to download the Risk Free Interest Term Structures from the EIOPA website, so you don’t need to search on the EIOPA website. And it implements the Smith-Wilson algorithm so you can make your own curves with different parameters.

This code is deployed as a package to the Python Package Index (a.k.a. the cheese shop), so you can install it with pip.


A package aimed to improve data quality of your reports. With this code you can generate and evaluate patterns, and we plan to publish validation and plausibility patterns in addition to the existing ones in the taxonomies. With this package you can evaluate your reports with these patterns.

This package is also deployed to the Python Package Index.


A project with data science applications and tutorials on using the packages above. Currently, we have a data science tutorial using the public Solvency 2 data and a tutorial for the data-patterns package.


Our experimental Natural Language Processing projects with Solvency 2 documents. I already published some results here with NLP (reading the Solvency 2 legislation documents and Word2Vec and Topic Modelling with SFCR documents) and we are planning to provide these and other applications in this repository.

All repositories were made from cookiecutter templates, which is a very easy way to set up your projects.

Take a look at the repositories. If you have suggestions for further improvements or ideas for new features, do not hesitate to raise an issue on the GitHub-site. In the documentation of each repository you can find more information on how to contribute.

Word2vec models for SFCRs

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Word2vec is a well-known algorithm for natural language processing that often leads to surprisingly good results, if trained properly. It consists of a shallow neural network that maps words to a n-dimensional number space, i.e. it produces vector representations of words (so-called word embeddings). Word2vec does this in a way that words used in the same context are embedded near to each other (their respective vectors are close to each other). In this blog I will show you some of the results of word2vec models trained with Wikipedia and insurance-related documents.

One of the nice properties of a word2vec model is that it allows us to do calculations with words. The distance between two word vectors provides a measure for linguistic or semantic similarity of the corresponding words. So if we calculate the nearest neighbors of the word vector then we find similar words of that word. It is also possible to calculate vector differences between two word vectors. For example, it appears that for word2vec model trained with a large data set, the vector difference between man and woman is roughly equal to the difference between king and queen, or in vector notation kingman + woman = queen. If you find this utterly strange then you are not alone. Besides some intuitive and informal explanations, it is not yet completely clear why word2vec models in general yield these results.

Word2vec models need to be trained with a large corpus of text data in order to achieve word embeddings that allow these kind of calculations. There are some large pre-trained word vectors available, such as the GloVe Twitter word vectors, trained with 2 billion tweets, and the word2vec based on google news (trained with 100 billion words). However, most of them are in the English language and are often trained on words that are generally used, and not domain specific.

So let’s see if we can train word2vec models specifically for non-English European languages and trained with specific insurance vocabulary. A way to do this is to train a word2vec model with Wikipedia pages of a specific language and additionally train the model with sentences we found in public documents of insurance undertakings (SFCRs) and in the insurance legislation. In doing so the word2vec model should be able to capture the specific language domain of insurance.

The Wikipedia word2vec model

Data dumps of all Wikimedia wikis, in the form of a XML-files, are provided here. I obtained the latest Wikipedia pages and articles of all official European languages (bg, es, cs, da, de, et, el, en, fr, hr, it, lv, lt, hu, mt, nl, pl pt, ro, sk, sl, fi, sv). These are compressed files and their size range from 8.6 MB (Maltese) to 16.9 GB (English). The Dutch file is around 1.5 GB. These files are bz2-compressed; the uncompressed Dutch file is about 5 times the compressed size and contains more than 2.5 million Wikipedia pages. This is too large to store into memory (at least on my computer), so you need to use Python generator-functions to process the files without the need to store them completely into memory.

The downloaded XML-files are parsed and page titles and texts are then processed with the nltk-package (stop words are deleted and sentences are tokenized and preprocessed). No n-grams were applied. For the word2vec model I used the implementation in the gensim-package.

Let’s look at some results of the resulting Wikipedia word2vec models. If we get the top ten nearest word vectors of the Dutch word for elephant then we get:

In []: model.wv.most_similar('olifant', topn = 10)
Out[]: [('olifanten', 0.704888105392456),
        ('neushoorn', 0.6430075168609619),
        ('tijger', 0.6399451494216919),
        ('luipaard', 0.6376790404319763),
        ('nijlpaard', 0.6358680725097656),
        ('kameel', 0.5886276960372925),
        ('neushoorns', 0.5880545377731323),
        ('ezel', 0.5879943370819092),
        ('giraf', 0.5807977914810181),
        ('struisvogel', 0.5724758505821228)]

These are all general Dutch names for (wild) animals. So, the Dutch word2vec model appears to map animal names in the same area of the vector space. The word2vec models of other languages appear to do the same, for example norsut (Finnish for elephant) has the following top ten similar words: krokotiilit, sarvikuonot, käärmeet, virtahevot, apinat, hylkeet, hyeenat, kilpikonnat, jänikset and merileijonat. Again, these are all names for animals (with a slight preference for Nordic sea animals).

In the Danish word2vec model, the top 10 most similar words for mads (in Danish a first name derived from matthew) are:

In []: model.wv.most_similar('mads', topn = 10)
Out[]: [('mikkel', 0.6680521965026855),
        ('nicolaj', 0.6564826965332031),
        ('kasper', 0.6114416122436523),
        ('mathias', 0.6102851033210754),
        ('rasmus', 0.6025335788726807),
        ('theis', 0.6013824343681335),
        ('rikke', 0.5957099199295044),
        ('janni', 0.5956574082374573),
        ('refslund', 0.5891965627670288),
        ('kristoffer', 0.5842193365097046)]

Almost all are first names except for Refslund, a former Danish chef whose first name was Mads. The Danish word2vec model appears to map first names in the same domain in the vector space, resulting is a high similarity between first names.

Re-training the Wikipedia Word2vec with SFCRs

The second step is to train the word2vec models with the insurance related text documents. Although the Wikipedia pages for many languages contain some pages on insurance and insurance undertakings, it is difficult to derive the specific language of this domain from these pages. For example the Dutch word for risk margin does not occur in the Dutch Wikipedia pages, and the same holds for many other technical terms. In addition to the Wikipedia pages, we should therefore train the model with insurance specific documents. For this I used the public Solvency and Financial Condition Reports (SFCRs) of Dutch insurance undertakings and the Dutch text of the Solvency II Delegated Acts (here is how to download and read it).

The SFCR sentences are processed in the same manner as the Wikipedia pages, although here I applied bi- and trigrams to be able to distinguish insurance terms rather than separate words (for example technical provisions is a bigram and treated as one word, technical_provisions).

Now the model is able to derive similar words to the Dutch word for risk margin.

In []: model.wv.most_similar('risicomarge')
Out[]: [('beste_schatting', 0.43119704723358154),
        ('technische_voorziening', 0.42812830209732056),
        ('technische_voorzieningen', 0.4108312726020813),
        ('inproduct', 0.409644216299057),
        ('heffingskorting', 0.4008549451828003),
        ('voorziening', 0.3887258470058441),
        ('best_estimate', 0.3886040449142456),
        ('contant_maken', 0.37772029638290405),
        ('optelling', 0.3554660379886627),
        ('brutowinst', 0.3554105758666992)]

This already looks nice. Closest to risk margin is the Dutch term beste_schatting (English: best estimate) and technische_voorziening(en) (English: technical provision, singular and plural). The relation to heffingskorting is strange here. Perhaps the word risk margin is not solely being used in insurance.

Let’s do another one. The acronym skv is the same as scr (solvency capital requirement) in English.

In []: model.wv.most_similar('skv')
Out[]: [('mkv', 0.6492390036582947),
        ('mcr_ratio', 0.4787723124027252),
        ('kapitaalseis', 0.46219778060913086),
        ('mcr', 0.440476655960083),
        ('bscr', 0.4224048852920532),
        ('scr_ratio', 0.41769397258758545),
        ('ðhail', 0.41652536392211914),
        ('solvency_capital', 0.4136047661304474),
        ('mcr_scr', 0.40923237800598145),
        ('solvabiliteits', 0.406883180141449)]

The SFCR documents were sufficient to derive an association between skv and mkv (English equivalent of mcr), and the English acronyms scr and mcr (apparently the Dutch documents sometimes use scr and mcr in the same context). Other similar words are kapitaalseis (English: capital requirement) and bscr. Because they learn from context, the word2vec models are able to learn words that are synonyms and sometimes antonyms (for example we say ‘today is a cold day’ and ‘today is a hot day’, where hot and cold are used in the same manner).

For an example of a vector calculation look at the following result.

In []: model.wv.most_similar(positive = ['dnb', 'duitsland'], 
                             negative = ['nederland'], topn = 5)
Out[]: [('bundesbank', 0.4988047778606415),
        ('bundestag', 0.4865422248840332),
        ('simplesearch', 0.452720582485199),
        ('deutsche', 0.437085896730423),
        ('bondsdag', 0.43249475955963135)]

This function finds the top five similar words of the vector DNBNederland + Duitsland. This expression basically asks for the German equivalent of De Nederlandsche Bank (DNB). The model generates the correct answer: the German analogy of DNB as a central bank is the Bundesbank. I think this is somehow incorporated in the Wikipedia pages, because the German equivalent of DNB as a insurance supervisor is not the Bundesbank but Bafin, and this was not picked up by the model. It is not perfect (the other words in the list are less related and for other countries this does not work as well). We need more documents to find more stable associations. But this to me is already pretty surprising.

There has been some research where the word vectors of word2vec models of two languages were mapped onto each other with a linear transformation (see for example Exploiting Similarities among Languages for Machine Translation, Mikolov, et al). In doing so, it was possible to obtain a model for machine translation. So perhaps it is possible for some European languages with a sufficiently large corpus of SFCRs to generate one large model that is to some extent language independent. To derive the translation matrices we could use the different translations of European legislative texts because in their nature these texts provide one of the most reliable translations available.

But that’s it for me for now. Word2vec is a versatile and powerful algorithm that can be used in numerous natural language applications. It is relatively easy to generate these models in other languages than the English language and it is possible to train these models that can deal with the specifics of insurance terminology, as I showed in this blog.

Pattern discovery in Solvency 2 data (2)

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Pattern discovery is a general technique to derive patterns from the data itself, without using explicit knowledge about the data. Previously, I described how to discover patterns in Solvency 2 data, for example that values of column x are most of the time or (almost) always equal to the values of column y, or higher, or lower, etc. I also showed how to find columns whose values are the sum of values of other columns, which often occurs in financial reports.

Here I will take pattern discovery one step further and discover constant ratios between values of columns. That is, patterns where the quotient between values of two columns equals a constant.

An example will clarify this. We take the own funds data of Dutch insurance undertakings (sheet 20 of the Excel file) and select the last year of data.

df = get_sheet(20)
df = df.xs(datetime(2017,12,31), axis = 0, level = 1, drop_level = False)

Now we run the generate-function from the insurlib package on Github. The generate-function allows the parameter pattern = “ratio”. Make sure the minimum support is higher than one otherwise you end up with a lot of ratio-patterns. Patterns are generated with the following code, with minimum support 3 and minimum confidence 10%.

rules = patterns.generate(dataframe = df,
                          pattern = "ratio",
                          parameters = {"min_confidence": 0.1, 
                                        "min_support": 3}))
rules = list(rules)

The first two patterns in the list are

['ratio', '9/20', ['mcr , total', 'scr , total']], 19, 120, 0.1367]


['ratio', '1/4', ['mcr , total', 'scr , total']], 36, 103, 0.259]

The two patterns state that the quotient between the values of the columns ‘mcr , total’ and ‘scr , total’ is 9/20 in 19 cases with confidence of almost 14% and is 1/4 (with 120 exception to this rule) is 36 cases with confidence of almost 26% (with 103 exceptions). In Solvency 2, the acronym MCR stands for Minimum Capital Requirement, and SCR stand for Solvency Capital Requirement (the solvency 2 risk-based capital requirement with VaR 99,5%). So the identified ratios are 9/20 (i.e. 45%) and 1/4 (i.e. 25%).

It is not desirable that the MCR is too low or too high in relation to the SCR. Solvency 2 legislation therefore prescribes that the MCR is bounded between 25% and 45% of the SCR. We see that these legal boundaries are found in the data itself. We have 36 insurance undertakings where the ratio is 25%, 19 undertaking where the ratio is 45%. The rest (should) have a ratio somewhere between 25% and 45%.

The algorithm applies a brute-force search for ratios between columns. It uses the fraction module of Python’s standard library to convert every quotient to a fraction, which enables the use of rational number arithmetic. For example

>>> Fraction(9,4)

The fraction expression you see in the pattern definition is the string representation of the fraction object.

A common problem with dealing with quotients is that often the original data set contains quotients like 0.2499999 and 0.2500001 because values are rounded off to euros. In the fraction module, this can be overcome by putting a limit on the denominator (default is 1e7, but you can pass this as a parameter). The result is that the nearest fraction is found given the limit on the denominator.

The other rules that were found in the own funds data are

['ratio', '9/100', ['available and eligible own funds|total eligible own funds to meet the mcr , tier 2', 'scr , total']], 3, 12, 0.2]

['ratio', '1/5', ['available and eligible own funds|total eligible own funds to meet the mcr , tier 2', 'mcr , total']], 12, 3, 0.8]

['ratio', '3/20', ['available and eligible own funds|total eligible own funds to meet the scr , tier 3', 'scr , total']], 6, 15, 0.2857]

['ratio', '1/3', ['available and eligible own funds|total eligible own funds to meet the scr , tier 3', 'mcr , total']], 3, 18, 0.1429]

These ratio-patterns are boundaries on the available and eligible own funds and are prescribed by Solvency 2 legislation. In the Netherlands, they have a relatively low support because a limited number of Dutch insurance undertakings hit the legal boundaries of tier two and tier three capital.

Here we looked at the own funds data. But many more patterns of this type can be found if you run the complete data set of Dutch insurance undertakings. It takes some time but then you will find in total 121 ratio-patterns (with minimum support of 3) covering loss-absorbing capacity of deferred taxes, impact of transitional measures, operational risk capital, etc. And of course other data sets than Solvency 2 data are possible.

These ratio-patterns work well because the Solvency 2 legislation contains legal boundaries that are represented in the data. Also other nonlegal constant ratios can be found, such as entity-specific ratios. You can find ratio-patterns for each insurance undertaking separately and then signal when a pattern is violated. This would work with a relatively low limit on the denominator of the fractions, because we want to find constant ratios with a high confidence. But for this to work well you will need more than two years of data.

A brute-force approach works well for the Dutch public Solvency 2 data set (around 1270 dimensions). But for high dimensional data it will take some time because of the possible combinations. Perhaps smart ways exist to detect ratios more easily, for example via statistical correlations.

The ratio-patterns that were discovered could be related to the Solvency 2 legislation by automatically reading ratios and percents in the text. And in the same manner, entity-specific ratios could be related to the SFCR documents of that entity. But that is for future work.

Pattern discovery in Solvency 2 data (1)

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This blog describes some results with algorithms for pattern discovery in Solvency 2 quantitative reports. The main idea here is to automatically uncover patterns that are present in these reports. We want to find patterns that represent widely or commonly occurring situations, and possibly represent business rules and relations prescribed by the underlying legislation. If we are able to find these patterns, then we are also able to identify when data satisfy and do not satisfy the patterns.

How can we find these patterns? Initially, I started with association rules. This is a rule-based machine learning approach that leads to transparent and explainable results. However, for this approach the quantitative data has to be encoded to a set of features (for example by replacing every quantitative value with an appropriate nominal value) and with high dimensional data this quickly becomes computationally expensive.

After some increments I decided to program a pattern discovery algorithm especially designed for analyzing the quantitative data points of reports. The goal was to speed up the process, while maintaining the association rules mining approach and performance measures. Below I will give some examples of how and which patterns can be found. The code is part of the insurlib package on Github. I used the public Solvency 2 data of Dutch insurers to find patterns in the quantitative data of these insurers (but applications to other data sets are possible).

First read the pandas and the insurlib package. The patterns-part consists of functions to generate patterns in numerical columns of dataframes.

import pandas as pd
from insurlib import patterns

Now read the public Solvency 2 data as was described in How to analyze public Solvency 2 data of Dutch insurers (by reading the Excel file and defining the read_sheet function). To recall, the Excel consists of the following worksheets:

  • Worksheet 14: balance sheet
  • Worksheet 15: premiums – life
  • Worksheet 16: premiums – non-life
  • Worksheet 17: technical provisions – life
  • Worksheet 18: technical provisions – non-life
  • Worksheet 19: transition and adjustments
  • Worksheet 20: own funds
  • Worksheet 21: solvency capital requirements – 1
  • Worksheet 22: solvency capital requirements – 2
  • Worksheet 23: minimum capital requirements
  • Worksheet 24: additional information life
  • Worksheet 25: additional information non-life
  • Worksheet 26: additional information reinsurance

Example 1: comparing two dataframes

Suppose we want to compare the worksheet balance sheet and the worksheet non-life technical provision and find the relations between the contents in these worksheets.

df1 = get_sheet(14)
df2 = get_sheet(18)
df2.columns = [str(df2.columns[i]) for i in range(len(df2.columns))]

The last line is to convert the multiple level columns to one level (so that we can compare it more easily with other dataframes).

You can generate patterns with the generate-function. Patterns that are found have the ‘association rule’-structure P -> Q. If you input two dataframes (P_dataframe and Q_dataframe) then all columns of P_dataframe are compared to all columns of Q_dataframe. The pattern we are looking for is ‘=’, so patterns with corresponding values are found. You can also use other patterns, such as ‘<‘, ‘<=’ , ‘>’, ‘>=’ and ‘!=’. Also a dict of parameters is used as input, with in this case the minimum confidence and the minimum support.

rules = patterns.generate(P_dataframe = df1,
                          Q_dataframe = df2,
                          pattern = "=",
                          parameters = {"min_confidence": 0.75, 
                                        "min_support": 10}))
rules = list(rules)
print("Number of rules: " + str(len(rules)))
Number of rules: 2

The output is a generator that we can convert to a list of rules. Two rules are found in this case. Let’s look a the first rule.

    'assets|reinsurance recoverables from:|non-life and health 
    similar to non-life , solvency ii value', 
    "('total non-life obligation', 'Technical provisions -
    total|Recoverable from reinsurance contract/SPV and Finite
    Re after the adjustment for expected losses due to counterparty
    - total')"], 

The first pattern states that the value of the reinsurance recoverables on the asset side for non-life on the balance sheet equates the value of the recoverable from reinsurance contracts in the technical provision for non-life obligations in the technical provisions sheet. The rule has confidence of almost 97%, and a support of 127. This means that there are 127 occurrences of this pattern in the data and in 97% of all occurrences (with nonzero data points) the patterns holds. We also see that in four cases the patterns are not present, i.e. the reinsurance recoverables does not equate to the recoverable in the technical provision (these are presumably data errors).

The second rule that was found reads:

    'liabilities|technical provisions – non-life , solvency ii value',
    "('total non-life obligation', 'Technical provisions -
    total|Technical provisions - total')"], 

This rule also has a high confidence. It says that the value of the technical provisions for non-life in the balance sheet equals the value of the total technical provisions in the technical provision sheet. This is a plain consistency rule between the sheets. The six exceptions are presumably data errors.

Both rules were, at the moment of publication, not part of the automatic and predefined validation rules of the Solvency II reports (otherwise the confidence would be 100%), as part of the XBRL-taxonomy. But by analyzing the reports in this manner we were able to uncover them automatically.

Example 2: patterns of sums

Often financial reports contain sums within the report. We can analyze the column names to detect potential sums (often a hierarchy in the columns name can be identified), but we can also find patterns of sums. The following code does that. We input the balance sheet dataframe and let the algorithm search for ‘sum’-patterns. The parameters sum_elements states the maximum elements in the sum (in this case three).

rules = patterns.generate(dataframe = df1,
                          pattern = "sum",
                          parameters = {"sum_elements": 3})
rules = list(rules)
print("Number of rules: " + str(len(rules)))
Number of rules: 7

Let’s take a look at the first rule:

    ['assets|investments (other than assets held for index-linked and 
     unit-linked contracts)|equities|equities - listed , solvency ii 
     'assets|investments (other than assets held for index-linked and 
     unit-linked contracts)|equities|equities - unlisted , solvency ii
    'assets|investments (other than assets held for index-linked and 
     unit-linked contracts)|equities , solvency ii value'], 

The rule states that the sum of the listed and unlisted equities equals to the equities (so equities are either listed or non-listed). This rule has a confidence of 100%, and there is presumably a validation rule within the reports. Six rules in this structure were found in this way. This is however somewhat computationally expensive.

Example 3: patterns with a given value

The last example searches for patterns with specific values. In this case we want to know in how many cases the investments are higher than zero. We can do this in the following way. We input the dataframe like in example 2 and we add a parameter columns and set it to the name of the column we want to investigate (in fact you can input a list of columns).

P = ['assets|investments (other than assets held for index-linked and 
      unit-linked contracts) , solvency ii value']
 rules = patterns.generate(dataframe = df1, 
                           pattern = ">", 
                           columns = P, 
                           value = 0, 
                           parameters = {'min_confidence': 0.75,
                                         'min_support': 1})
 rules = list(rules)
     'assets|investments (other than assets held for index-linked and 
     unit-linked contracts) , solvency ii value', 

The value of investment is, with confidence of 96%, higher than zero. In eleven cases the value is not higher than zero. This rule has a high confidence because, normally, insurers invest premiums collected for insurance policies into a wide range of investment assets. If no list of columns is added, patterns in all numerical columns in the dataframe returned.

The aim of these examples is to give a general idea of pattern discovery in Solvency 2 quantitative data. Numerous patterns can be found in this way by using the complete data set. And by using the measures confidence and support we can find patterns that are not exactly perfect but do provide information about the data, without taking recourse to statistical methods. Data errors and specific situations that lead to exceptions in the data are not expressions of pure randomness and should therefore not be analyzed by statistical methods. With these patterns we are able to reconstruct basic patterns in the data that provide information about the data.

Of course, many improvements are possible in order to find more complex patterns (and that why there is a (1) in the title of this blog). Presumably all existing validation rules can be found in this manner, and much more. Hopefully I will be able to implement these improvements and present them in a new blog.

Text modeling with S2 SFCRs

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European insurance undertakings are required to publish each year a Solvency and Financial Condition Report (SFCR). These SFCRs are often made available via the insurance undertaking’s website. In this blog I will show some first results of a text modeling exercise using these SFCRs.

Text modeling was done with Latent Dirichlet Allocation (LDA) with the Mallet’s implementation, via the gensim-package (found here: A description you can find here: LDA is an unsupervised learning algorithm that generates latent (hidden) distributions over topics for each document or sentence and a distribution over words for each topic.

To get the data I scraped as many SFCRs (in all European languages) as I could find on the Internet. As a result of this I have a data set of 4.36 GB with around 2,500 SFCR documents in PDF-format (until proven otherwise, I probably have the largest library of SFCR documents in Europe). Among these are 395 SFCRs in the English language, consisting in total of 287,579 sentences and 8.1 million words.

In a SFCR an insurance undertaking publicly discloses information about a number of topics prescribed by the Solvency II legislation, such as its business and performance, system of governance, risk profile, valuation and capital management. Every SFCR therefore contains the same topics.

The LDA algorithm is able to find dominant keywords that represents each topic, given a set of documents. It is assumed that each document is about one topic. We want to use the LDA algorithm to identify the different topics within the SFCRs, such that, for example, we can extracts all sentences about the solvency requirements. To do so, I will run the LDA algorithm with sentences from the SFCRs (and thereby assuming that each sentence is about one topic).

I followed the usual steps; some data preparation to read the pdf files properly. Then I selected the top 9.000 words and I selected the sentences with more than 10 words (it is known that the LDA algorithm does not work very good with words that are not often used and very short documents/sentences). I did not built bigram and trigram models because this did not really change the outcome. Then the data was lemmatized such that only nouns, adjectives, verbs and adverbs were selected. The spacy-package provides functions to tag the data and select the allowed postags.

The main inputs for the LDA algorithm is a dictionary and a corpus. The dictionary contains all lemmatized words used in the documents with a unique id for each word. The corpus is a mapping of word id to word frequency in each sentence. After we generated these, we can run the LDA algorithm with the number of topics as one of the parameters.

The quality of the topic modeling is measured by the coherence score.

The coherence score per number of topics

Therefore, a low number of topics that performs well would be nine topics (0.65) and the highest coherence score is attained at 22 topics (0.67), which is pretty high in general. From this we conclude that nine topics would be a good start.

What does the LDA algorithm produce? It generates for each topic a list of keywords with weights that represent that topic. The weights indicate how strong the relation between the keyword and the topic is: the higher the weight the more representative the word is for that specific topic. Below the first ten keywords are listed with their weights. The algorithm does not classify the topic with one or two words, so per topic I determined a description that more or less covers the topic (with the main subjects of the Solvency II legislation in mind).

Topic 0 ‘Governance’: 0.057*”management” + 0.051*”board” + 0.049*”function” + 0.046*”internal” + 0.038*”committee” + 0.035*”audit” + 0.034*”control” + 0.032*”system” + 0.030*”compliance” + 0.025*”director”

Topic 1 ‘Valuation’: 0.067*”asset” + 0.054*”investment” + 0.036*”liability” + 0.030*”valuation” + 0.024*”cash” + 0.022*”balance” + 0.020*”tax” + 0.019*”cost” + 0.017*”account” + 0.016*”difference”

Topic 2 ‘Reporting and performance’: 0.083*”report” + 0.077*”solvency” + 0.077*”financial” + 0.038*”condition” + 0.032*”information” + 0.026*”performance” + 0.026*”group” + 0.025*”material” + 0.021*”december” + 0.018*”company”

Topic 3 ‘Solvency’: 0.092*”capital” + 0.059*”requirement” + 0.049*”solvency” + 0.039*”year” + 0.032*”scr” + 0.030*”fund” + 0.027*”model” + 0.024*”standard” + 0.021*”result” + 0.018*”base”

Topic 4 ‘Claims and assumptions’: 0.023*”claim” + 0.021*”term” + 0.019*”business” + 0.016*”assumption” + 0.016*”market” + 0.015*”future” + 0.014*”base” + 0.014*”product” + 0.013*”make” + 0.012*”increase”

Topic 5 ‘Undertaking’s strategy’: 0.039*”policy” + 0.031*”process” + 0.031*”business” + 0.030*”company” + 0.025*”ensure” + 0.022*”management” + 0.017*”plan” + 0.015*”manage” + 0.015*”strategy” + 0.015*”orsa”

Topic 6 ‘Risk management’: 0.325*”risk” + 0.030*”market” + 0.027*”rate” + 0.024*”change” + 0.022*”operational” + 0.021*”underwriting” + 0.019*”credit” + 0.019*”exposure” + 0.013*”interest” + 0.013*”liquidity”

Topic 7 ‘Insurance and technical provisions’: 0.049*”insurance” + 0.045*”reinsurance” + 0.043*”provision” + 0.039*”life” + 0.034*”technical” + 0.029*”total” + 0.025*”premium” + 0.023*”fund” + 0.020*”gross” + 0.019*”estimate”

Topic 8 ‘Undertaking’: 0.065*”company” + 0.063*”group” + 0.029*”insurance” + 0.029*”method” + 0.023*”limit” + 0.022*”include” + 0.017*”service” + 0.016*”limited” + 0.015*”specific” + 0.013*”mutual”

To determine the topic of a sentences we calculate for each topic the weight of the words in the sentences. The main topic of the sentence is then expected to be the topic with the highest sum.

If we run the following sentence (found in one of the SFCRs) through the model

"For the purposes of solvency, the Insurance Group’s insurance obligations
are divided into the following business segments: 1. Insurance with profit
participation 2. Unit-linked and index-linked insurance 3. Other life
insurance 4. Health insurance 5. Medical expence insurance for non-life
insurance 6. Income protection insurance for non-life insurance Pension &
Försäkring (Sweden) Pension & Försäkring offers insurance solutions on the
Swedish market within risk and unit-linked insurance and traditional life

then we get the following results per topic:

[(0, 0.08960573476702509), 
(1, 0.0692951015531661),
(2, 0.0692951015531661),
(3, 0.06332138590203108),
(4, 0.08363201911589009),
(5, 0.0692951015531661),
(6, 0.08004778972520908),
(7, 0.3369175627240143),
(8, 0.13859020310633216)]

Topic seven (‘Insurance and technical provisions’) has clearly the highest score 0.34 , followed by topic eight (‘Undertaking’). This suggests that these sentences are about the insurances and technical provisions of the undertaking (that we can verify).

Likewise, for the sentence

"Chief Risk Officer and Risk Function 
The Board has appointed a Chief Risk Officer (CRO) who reports directly to
the Board and has responsibility for managing the risk function and
monitoring the effectiveness of the risk management system."

we get the following results:

[(0, 0.2926447574334898), 
(1, 0.08294209702660407),
(2, 0.07824726134585289),
(3, 0.07824726134585289),
(4, 0.07824726134585289),
(5, 0.08450704225352113),
(6, 0.14866979655712048),
(7, 0.07824726134585289),
(8, 0.07824726134585289)]

Therefore, topic zero (‘Governance’) and topic six (‘Risk management’) have the highest score and this suggests that this sentence is about the governance of the insurance undertaking and to a lesser extent risk management.

The nine topics that were identified reflect fairly different elements in the SFCR, but we also see that some topics consist of several subtopics that could be identified separately. For example, the topic that I described as ‘Valuation’ covers assets and investments but it might be more appropriate to distinguish investment strategies from valuation. The topic ‘Solvency’ covers own funds as well as solvency requirements. If we increase the number of topics then some of the above topics will be split into more topics and the topic determination will be more accurate.

Once we have made the LDA model we can use the results for several applications. First, of course, we can use the model to determine the topics of previously unseen documents and sentences. We can also analyze topic distributions across different SFCRs, we can get similar sentences for any given sentence (based on the distance of the probability scores of the given sentence to other sentences).

In this blog I described first steps in text modeling of Solvency and Financial Condition Reports of insurance undertakings. The coherence scores were fairly high and the identified topics represented genuine topics from the Solvency II legislation, especially with a sufficient number of topics. Some examples showed that the LDA model is able to identify the topic of specific sentences. However, this does not yet work perfectly; an important element of SFCR documents are the numerical information often stored in table form in the PDF. These are difficult to analyze with the LDA algorithm.

How to analyze public Solvency 2 data of Dutch insurers

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In this blog we will use the public Solvency II data of all Dutch insurance undertakings and present it in one large data vector per undertaking. In doing so, we are able to use some easy but powerful machine learning algorithms to analyze the data. The notebook can be found here.

Solvency II data of individual insurance undertakings is published yearly by the Statistics department of DNB. The data represents the financial and solvency situation of each insurance undertaking per the end of each year. Currently, we have two years of data: ultimo 2016 and ultimo 2017. The publication of DNB is in the form of an Excel file with a number of worksheets containing the aggregated data and the individual data. Here we will use the individual data.

We will read the data in a Pandas Data Frame en use Numpy for data manipulations. Furthermore we need the datetime object

import pandas as pd
import numpy as np
from datetime import datetime

You can find the data with the following url

Download the file and make sure that the Excel file is accessible.

data_path = "../../20_local_data/"
xls = pd.ExcelFile(data_path + "Data individual insurers

The Excel file contains several worksheets with data. We want to combine all the data together in one Data Frame. To do that we need some data preparation and data cleaning for each worksheet.

In the following function a worksheet is put into a Data Frame and the columns names are set to lower case. Then an index of the data frame is set to the insurance undertaking name and the reporting period. Then we perform some cleaning (the original worksheets contain some process information). In addition, some worksheets in the file contain 2-dimensional data, that need to be pivoted such that we obtain one large vector with all the data per insurance undertaking in one row.

def get_sheet(num):
    # read entire Excel sheet
    df = xls.parse(num)
    # columns names to lower case
    df.columns = [c.lower() for c in df.columns]
    # set index to name and period
    df.set_index(['name', 'period'], inplace = True)
    # data cleaning (the excel sheet contains some
                     additional data that we don't need)
    drop_list = [i for i in df.columns 
                     if 'unnamed' in i or 'selectielijst' in i]
    df.drop(drop_list, axis = 1, inplace = True)
    # pivot data frame
    if "row_name" in df.columns:
        df.drop("row_name", axis = 1, inplace = True)
        df = df.pivot(columns = 'row_header')
    if df.columns.nlevels > 1:
        df.columns = [str(df.columns[i]) for i in
    return df

Creating one large vector per insurer

With the function above we can read a part of the Excel file and store it in a Pandas data frame. The following worksheets are contained in the Excel file published by DNB.

  • Worksheet 14: balance sheet
  • Worksheet 15: premiums – life
  • Worksheet 16: premiums – non-life
  • Worksheet 17: technical provisions – 1
  • Worksheet 18: technical provisions – 2
  • Worksheet 19: transition and adjustments
  • Worksheet 20: own funds
  • Worksheet 21: solvency capital requirements – 1
  • Worksheet 22: solvency capital requirements – 2
  • Worksheet 23: minimum capital requirements
  • Worksheet 24: additional information life
  • Worksheet 25: additional information non-life
  • Worksheet 26: additional information reinsurance

Let’s read the first worksheet with data and then append the other sheets to it. We shall not read the last three worksheets, because these contain the country specific reports.

df = get_sheet(14)
for l in range(15, 24):
    df_temp = get_sheet(l)
    df = df.join(df_temp, rsuffix = "_"+ str(l))

Let’s get the shape of the Data Frame.

print("Number of rows   : " + str(len(df.index)))
print("Number of columns: " + str(len(df.columns)))

Out: Number of rows   : 286
     Number of columns: 1273

So we have 286 rows of insurance undertakings data for ultimo 2016 and ultimo 2017. And we have 1273 columns with financial and solvency data about each insurance undertaking. Let’s take the data from the year 2017, and select all columns that have floating numbers in them.

df = df.xs(datetime(2017,12,31), 
           axis = 0, 
           level = 1,
           drop_level = True)
df = df[[df.columns[c] for c in range(len(df.columns)) 
          if df.dtypes[c]=='float64']]
df.fillna(0, inplace = True)
print("Number of rows   : " + str(len(df.index)))
print("Number of columns: " + str(len(df.columns)))

Out: Number of rows   : 139
     Number of columns: 1272

Apparently there is one columns with a non-floating values. For ultimo 2017 we have the data of 139 insurance undertaking.

Now we can perform all kinds of numerical analysis. Let’s calculate the total amount of assets of all Dutch insurance undertakings.

df['assets|total assets , solvency ii value'].sum()

Out: 486702222727.1401

That’s almost 487 billion euro at the end of 2017.

Finding similar insurers

Now let’s apply some algorithms to this data set. Suppose we want to know what insurance undertakings are similar with respect to their financial and solvency structure. To do that we can calculate the distances between all the data points of each insurance undertakings. An insurance undertaking with a low distance to another insurance undertaking might be similar to that undertaking.

If we divide each row by the total assets we do as if all insurance undertakings have equal size, and then the distances indicate similarity in financial and solvency structure (and not similarity in size).

X = df.div(df['assets|total assets , solvency ii value'],
              axis = 0)

The scikit-learn package provides numerous algorithms to do calculations with distances. Below we apply the NearestNeighbors algorithm to find the neighbors of each insurance undertaking. Then we get the distances and the indices of the data set and store them.

from sklearn.neighbors import NearestNeighbors
nbrs = NearestNeighbors(n_neighbors = 2, 
                        algorithm = 'brute').fit(X.values)
distances, indices = nbrs.kneighbors(X)

What are the nearest neighbors of the first ten insurance undertakings in the list?

for i in indices[0:10]:
     print(X.index[i[0]] + " --> " + X.index[i[1]])

ABN AMRO Captive N.V. --> Rabo Herverzekeringsmaatschappij N.V.
ABN AMRO Levensverzekering N.V. --> Delta Lloyd Levensverzekering N.V.
ABN AMRO Schadeverzekering N.V. --> Ansvar Verzekeringsmaatschappij N.V.
AEGON Levensverzekering N.V. --> ASR Levensverzekering N.V.
AEGON Schadeverzekering N.V. --> Nationale-Nederlanden Schadeverzekering Maatschappij N.V.
AEGON Spaarkas N.V. --> Robein Leven N.V.
ASR Aanvullende Ziektekostenverzekeringen N.V. --> ONVZ Aanvullende Verzekering N.V.
ASR Basis Ziektekostenverzekeringen N.V. --> VGZ Zorgverzekeraar N.V.
ASR Levensverzekering N.V. --> Achmea Pensioen- en Levensverzekeringen N.V.
ASR Schadeverzekering N.V. --> Veherex Schade N.V.

And with the shortest distance between two insurance undertakings we can find the two insurance undertakings that have the highest similarity in their structure.

min_list = np.where(distances[:,1] == distances[:,1].min())

Out: ['IZA Zorgverzekeraar N.V.', 'Univé Zorg, N.V.']

If you want to understand the financial performance it is of course handy to know which insurance undertakings are similar. A more general approach when comparing insurance undertakings is to cluster them into a small number of peer groups.

Clustering the insurers

Can we cluster the insurance undertakings based on the 1272-dimensional data? To do this we apply the t-sne algorithm (that we used before).

First we import all the packages required.

import matplotlib.pyplot as pyplot
from sklearn.manifold import TSNE
from sklearn.cluster import KMeans

Then we run the t-sne algorithm.

Y = TSNE(n_components = 2, 
         perplexity = 5, 
         verbose = 0, 
         random_state = 1).fit_transform(X.values)

And we plot the results

pyplot.figure(figsize = (7, 7))
pyplot.scatter(x = Y[:, 0], 
               y = Y[:, 1], 
               s = 7)

Depending on how you zoom in you see different clusters in this picture. In the above left you see the health insurance undertakings (with more clusters within that set: those offering basic health insurance and other offering additional health insurances, or both). On the right are (mostly) life insurance undertakings, and on the left (middle to below) are non-life insurance undertakings. And both clusters can be divided into several more sub clusters. These clusters can be used in further analysis. For example, you could use these as peer groups of similar insurance undertakings.

Clustering the features

Given that we have a 1272-dimensional vector of each insurance undertaking we might wish somehow to cluster the features in the data set. That is, we want to know which columns belong to each other and what columns are different.

An initial form of clustering were the different worksheets in the original Excel file. The data was clustered around the balance sheet, premiums, technical provisions, etc. But can we also find clusters within the total vector without any prior knowledge of the different worksheets?

A simple and effective way is to transpose the data matrix and feed it into the t-sne algorithm. That is, instead of assuming that each feature provides additional information about an insurance undertaking, we assume that each insurance undertaking provides additional information about a feature.

Let’s do this for only the balance sheet. In a balance sheet it is not immediately straightforward how the left side is related to the right side of the balance sheet, i.e. which assets are related to which liabilities. If you cluster all the data of the balance sheet then related items are clustered (irrespective of whether they are assets or liabilities).

df = get_sheet(14)

Instead of the scaled values we now take whether or not a data point was reported or not, and then transpose the matrix.

X = (df != 0).T

Then we apply the t-sne algorithm. In this case with a lower perplexity.

Y = TSNE(n_components = 2, 
         perplexity = 1.0, 
         verbose = 0, 
         random_state = 0, 
         learning_rate = 20, 
         n_iter = 10000).fit_transform(X.values)

And we plot the result with 15 identified clusters.

pyplot.figure(figsize = (7, 7))
pyplot.scatter(x = Y[:, 0], 
              y = Y[:, 1], 
              s = 5)
kmeans = KMeans(n_clusters = 15, random_state = 0, n_init  = 10).fit(Y)
for i in range(len(kmeans.cluster_centers_)):
    pyplot.scatter(x = kmeans.cluster_centers_[i,0],
                   y = kmeans.cluster_centers_[i,1],
                   s = 1,
                   c = 'yellow')
                   xy = (kmeans.cluster_centers_[i, 0], kmeans.cluster_centers_[i, 1]), 
                   size = 13)

Then we get this.

We see are large number of different clusters.

for i in df.T.loc[kmeans.labels_ == 6].index:

assets|assets held for index-linked and unit-linked contracts , solvency ii value
assets|loans and mortgages|loans and mortgages to individuals , solvency ii value
assets|reinsurance recoverables from:|life and health similar to life, excl health,index-linked,unit-linked|life excluding health,index-linked,unit-linked , solvency ii value
liabilities|technical provisions – index-linked and unit-linked , solvency ii value
liabilities|technical provisions – index-linked and unit-linked|best estimate , solvency ii value
liabilities|technical provisions – index-linked and unit-linked|risk margin , solvency ii value

So the assets held for index-linked and unit-linked contracts are in the same cluster as the technical provisions for index-linked and unit-linked items (and some other related items are found).

However, the relations found are not always perfect. To improve the clustering we should cluster the data that is related in their changes over time. But because we have just two years available (and so just one yearly difference) we presumably do not have enough data to do that.

What is learning in ‘deep learning’?

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The general process in an artificial neural network when it is trained is called deep learning. The adjective deep in this case refers to neural networks consisting of several layers with a large number of weights that are calibrated with input and output examples. But what does learning here mean? The question I want to discuss here is whether the learning in a deep learning network is learning in the genuine sense: does a deep learning algorithm learn in the way human beings do? And if a network learns it must learn something, then: what is it that a deep learning network learns?

Suppose you have an artificial neural network with a suitable architecture for image detection and you want to train it to detect cats in pictures. You have a training set of labelled pictures. You can train the network by back propagating through the network and change the weights between the nodes to minimize the output error. During the training process the parameters of each node in the network are changed in a similar way as would be done in fitting a (linear) regression model: the output of an error function is minimized by changing weights, and this is done for each picture in the training set, for each node in the network, and in a number of iterations. If you have done that then, with a sufficiently large training set, the network would be able to detect cats in pictures.

The question is: would it be correct to say that the structure of the network with all its hyper parameters somehow learned the basic properties of cats such that it can detect them in pictures? And to take this one step further, would it be correct to say that the network with trained weights and other parameters somehow knows what cats are?

It depends, of course, on what we understand by learning. If we would define the result of learning as the ability to recognize cats in specific pictures then it would qualify as learning. But if the result of learning is the ability to explain or to know what a cat is then I don’t think what the network does comes anywhere near this definition. A trained neural network calculates a complex function. There is no knowledge in or above the network about what cats are, at least not in a form that we can easily understand. Nowhere during the learning phase there occurs a magical jump from data to knowledge; nowhere becomes the pile of sand a heap. And yet it is able to recognize cats.

What kind of learning it this? Perhaps a better word for the way in which artificial neural networks learn is that they are being conditioned in a certain manner. The basic mode of learning of artificial neural networks, I would say, is conditioning and not learning in a genuine sense (where it would be able to explain what a cat is). In conditioning an association is formed between action (or output) and reward (or desired output); this is similar to the way animals learn.

This mode of learning results is an ability without knowledge. And there has yet to be found a general way to reconstruct knowledge that is tacitly present in the network. If an artificial network learns then it learns in such a way that what is learned remains concealed for us (until somehow we are able to extract from the network the knowledge it learned, but that would be our learning and not the networks learning).

By calling deep learning a form of learning we project a certain idea of learning onto the training process of neural networks. I think the reason for this is the apparent analogy with human brains, and natural neural networks in general, and artificial ones. For this analogy the reasoning is: because a human brain is able to learn and because an artificial neural network mimics the human brain processes, it is only logical to conclude that artificial neural networks are also able to learn. But there is a difference between human learning and the biological process during this learning. I myself am able to learn in the sense that I can explain what I learned (I hope); my brain is conditioned during this learning.

From this perspective a neural network is similar to any non human brain. During a learning phase it is conditioned for an ability. It does not acquire any knowledge during this process about what it has learned.

What is a black box?

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In discussions about the use of machine learning and deep learning algorithms the issue is often raised that many of these algorithms are black boxes and that we do not know how they work. What do we mean by a black box in relation to machine learning algorithms? What is a black box in itself?

Literally a black box is something that does not emit any light such that we are unable to see what is going on. An initial definition of a black box might be that it is an process or algorithm with observable input and output where the causal mechanism between input and output is unknown. This lack of knowledge implies that we are unable to see and explain what happens within the process or how the algorithm works.

But that is not a formal and satisfying definition, for we can ask: by whom should this causal mechanism be known and what constitutes this knowledge? Is it a not-knowing of an arbitrary individual, or is it a not-knowing of a group of experts of the matter at hand after a sufficient amount of time and resources? And is knowledge expressed in logic, math and natural language, or do we also count something like intuition to knowledge?

And furthermore, in practice there are different levels of knowledge of a process or algorithm. You might be able to explain only a small part of the process or algorithm in isolation, but not the full process from input to output with all interactions between the parts within the process. You might be able to explain how one particular input resulted in an output or how a set of related inputs led to the outputs. And you might be able to explain how changes in the input or conditions of the process or parameters of the algorithm change the output (the causal mechanism behind changes in input and conditions). This all constitutes some form of knowledge about an algorithm or process.

A definition of a black box based on this lack of knowledge experienced by someone is not a good idea. It depends on who is experiencing the black box. And more important, by defining a black box as the absence of something else we have not said what a black box in itself is. So in this way the definition of a black box remains hidden.

Another way to look at it is to see a complex deep learning algorithm as a very complex natural process, like a changing atmosphere, motion of fluids or a neurological process in a human brain. In these cases we observe input and output, but the internal mechanism depends on many factors and is extremely complex. It is not that we do not understand how these processes in general behave; for isolated parts we sometimes know precisely what happens. But because of the size and complexity of these processes and the huge amount of input data that could determine the outcome the causal relations between input and output are simply too complex to comprehend and to express in a succinct form. (I called it an analogy because we do know that a deep learning network is deterministic but for natural processes we do not know that). We often have some knowledge and understanding how certain simple processes in their isolated form behave, but when it comes to any precise prediction many processes are too complex. The same we see in deep learning algorithms; large amounts of input data and several layers with incomprehensible weights.

In light of this analogy it is perhaps better to see a black box algorithm as something that is open for investigation, just like any natural process is. What are the rules of a deep learning algorithm? How can we extract knowledge from a trained neural network? Of course the structure of these algorithm makes it particular hard to extract knowledge but it is not impossible. At least we should not dismiss the problem altogether to call a deep learning algorithm a black box and stop investigating.

And there has been made some progress in this area; some deep learning algorithms emit some light of their internal processes. We can try to generalize an algorithm and look at feature importance, we could use techniques such as LIME, and we could works backwards from the output to the input by back-propagation to learn the feature selection inside the algorithm. But this is just the beginning.

We currently lack a proper terminology to describe the processes in deep neural networks. Terms like interpretability and explainability that have been introduced in the area of deep learning are simply not well defined and too vague to describe what is going on. We need a proper science of neural networks that is able to rationally reconstruct the knowledge that is hidden inside in the weights and other parameters of the deep learning network.

So let’s change the definition of the term black box. Instead of absence of knowledge, basically a form of nothingness, we should see a black box in a more positive sense like nature before we understood (some of) her laws: open to be discovered. In the meantime, what do we do when we lack knowledge of a deep learning process? For me the answer lies in the analogy presented above; we should view the outcome as the outcome of a natural process. What that means is something for another blog.