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Data Vault 2.0 – data model

After the first part of the article  series about Data Vault where we introduced the concept and the basicis of its architecture, we return to you with more in-depth look into data modeling. We will analyze concepts such as Business keys (BKEYs), hash keys (HKEYs), Hash diff (HDIF) and more!



Data Vault – technical columns



Business Key (BKEY)


In contrast to traditional data warehouses, Data Vault does not generate artificial keys on its own, nor does it use concepts such as sequences or key tables. Instead, it relies on a carefully selected attribute from the source system, known as the Business Key (BKEY). Ideally, the BKEY should not change over time and be the same across all source systems where the data is generated. While this may not always be possible, it greatly simplifies passive model integration. Furthermore, in the context of GDPR requirements, it is not advisable to choose business keys that contain sensitive data as it can be challenging to mask such data when exposing the data warehouse.


Examples of BKEYs may include the VAT invoice number, the accounting attachment number, or the account number. However, finding a suitable BKEY may not be an easy task. One best practice is to check how the business retrieves data from source systems and which values are used when entering data into the source system. Typically, these values, as they are known to the business, are good candidates for BKEYs. Often, the same data is processed in multiple source systems. For instance, in an organization with several systems for processing tax documents (invoices, receipts), natural document numbers (receipt/invoice numbers) may be used in some, while an artificial key (attachment number) may be used in others. In some cases, a sequential document number and an equivalent natural number are also used. In such situations, using an integration matrix can help identify the appropriate BKEY.


Matrix showcasing potential BKEY keys



As we can see from the matrix, there are several potential BKEY keys, but only the document number appears in the majority of the sources from which we retrieve document data. If we use a BKEY key based on the document number, the data in the Data Vault model will naturally integrate. However, what will we get for data from „System 2„? For this data, we need to design an appropriate same-as link (a Data Vault object) that will connect the same data. More on this in the later part of the article.


It is important that the same BKEY keys from different source systems are loaded in the same way. Even if we want to format such a key, for example, by adding a constant prefix, we should do it in the same way for data from all sources.



Hash key (HKEY)


In the DV model, all joins are performed using a hash key. The hash key is the result of applying a hash function (such as MD5) to the BKEY value. The hash key is ideal for use as a distribution key for architectures with multiple data nodes and/or buckets. Through distribution, we can efficiently scale queries (insert and select) and limit data shuffling, as data with the same BKEY values are stored on the same node (having received the same HKEY).


Example BKEY and HKEY:




Hash diff (HDIF)


In Data Vault objects that store historical data (SCD2), HDIF represents the next versions of a record. HDIF is calculated by computing a hash value on all the meaningful columns in the table.





Date and hour of record loading.





Indication that a record has been deleted. It is important to note that in Data Vault 2.0 it is not recommended to use validity periods (valid from – valid to) to maintain historical records. As this requires costly update operations that are not efficient, especially for real-time data. In addition, for some Big Data technologies, update operations may not be available, which further complicates the implementation of validity periods. Instead, Data Vault recommends an insert-only architecture based on technical columns such as LoadTime and DelFlag to indicate when a record has been deleted.





For Data Vault tables that receive data from multiple sources, the source column allows for additional partitioning (or sub-partitioning) to be established. Proper management of the physical structure of the table enables independent loading of data from multiple sources at the same time.

Different types of Data Vault objects have different sets of technical columns, which will be discussed further in the article.




Passive integration:


In classic warehouses, there are often so-called key tables in which keys assigned to business objects on a one-off basis are stored. Loading processes read the key table and, based on this, assign artificial keys in the warehouse. There are also sequences based on which keys are assigned, and sometimes a GUID is used.


All these solutions require additional logic to be implemented so that the value of the keys can be assigned consistently in the warehouse model. Often, these additional algorithms also limit the scalability of the warehouse resource. Passive integration is the opposite of this approach. Passive integration involves calculating a key on the fly during a table feed based only on the business key. With a deterministic transformation (hash function on BKEY), we can do this consistently in any dimension, e.g:


  • model dimension – the same BKEY in different warehouse objects will give us the same hkey so we can feed them independently and then combine them in any consistent way


  • time dimension – feeding the same BKEY at different points in time will give us the same result. Records powered up a year ago and today will get the same HKEY. Clearing the data and feeding it again will also have no effect on the calculated values (unlike, for example, in the case of sequences)


  • environment dimension – the same BKEY will have the same HKEY on different environments which facilitates testing and development.


The above is possible, but only if we choose the BKEY correctly, so the necessary effort should be made to make the choice optimal. We should consistently calculate it with the same algorithm for all HUB objects in the model. The exception can appear when we know that we have potential BKEYs in different formats in the source systems, but a simple transformation will make it consistent. It is important that this transformation is of the 'hard rule’ type.


For example:


In system 1 we have the key BKEY: „qwerty12345”


In system 2 we have the key BKEY: „QWERTY12345”


We know that business-wise they mean the same thing. In this case, we can apply a „hard rule” in the form of a LOWER or UPPER function to make the keys consistent.


Unfortunately, there are also situations where we have completely different BKEYs in different systems, for example:


In system 1 we have the key BKEY: „qwerty12345”


In system 2 we have the key BKEY: „7B9469F1-B181-400B-96F7-C0E8D3FB8EC0”


For such cases, we are forced to create so-called same-as links, which we will discuss later in this article.



Physical objects in Data Vault



Data Vault objects appear in the same form in both the RDV and BDV layers. The differences between them are only in the way the values in these objects are calculated (Hard rules and Soft rules). The objects of each layer should be distinguished at the level of naming convention and/or schema or database



  1. HUB
  2. LINK
    • Standard
    • Effectiveness
    • Multiactivity



  1. Business HUB
  2. Business LINK
  3. Business SATELLITE
    • Standard
    • Effectiveness
    • Multiactivity



HUB type objects


Hubs in the Data Vault warehouse are objects around which a grid of other related objects (satellites and links) is created. A Hub is a 'bag’ for business keys. A Hub cannot contain technical keys that the business does not understand, the keys must be unique. Examples of HUBs could be: customer, bill, document, employee, product, payment, etc.


We feed the Hubs with keys (BKEY) from the source systems, one BKEY can represent data from multiple source systems. We can use some rules to calculate BKEY but only those that meet the hard rules (usually UPPER, LOWER, TRIM). We never delete data from the HUB, if a record has disappeared from the source systems then its key should remain in the HUB. Even if the data is loaded into the hub in error, we do not need to delete unnecessary keys.



Example HUB structure, description of technical columns one chapter earlier.



Satellite type objects


It stores business attributes. We can have satellites with history (SCD2) or without history (SCD0/SCD1). We create a new satellite when we want to separate some group of attributes. We can do this for a number of reasons:


a) we want to store data of the same business importance (e.g. address data) in one place


b) we want to separate fast-changing attributes into a separate satellite. Fast-changing attributes are those that change frequently causing duplication of records in the satellite. Examples of such attributes could be e.g. interest rate, account balance, accrued interest, etc.


c) we want to segregate attributes with sensitive data for which we will apply restrictive permission policies or GDPR rules.


d) we want to add a new system to the warehouse and create a new satellite for it


e) others that for some reason will be optimal for us



Data Vault is very flexible in this respect. However, be sure to document the model well.



Example of a satellite with data recorded in SCD2 mode:




Multiactive satellite – a specific type of a satellite where the key is not only BKEY but also a special multiactivity determinant (one of the substantive attributes). An example of such a satellite is a satellite storing address data where the multiactivity determinant is the type of address (correspondence, main, residential).


We have one BKEY (e.g. login in the application) and several addresses. We can successfully replace the multiactivity satellite with a regular one by adding a multiactivity determinant column to the hashkey calculation. My experience shows that it is better to limit the use of multiactivity satellites for reasons of model readability and reading efficiency.


 Example of a multiactivity satellite with data recorded in SCD2 mode



Link type objects


Link objects come in several versions:


Relational link – represents relationships between two or more objects which can be powered by complex business logic. Relationships must be unique – this is achieved by generating a unique hash for the relationship which is calculated from the hashes of the records it links. A link does not contain business columns (the exception is an nonhistorized link).


If we want to show history then we need to attach a satellite with a timeline to the link (effectivity satellite). The performance satellite can also contain additional business columns describing relationships.





Hierarchical link – used to model parent-child relationships (e.g. organisational structure) This type of link can of course also store history. To achieve that – just add an efficiency satellite to the link.



An example of an organisational structure in the Data Vault model using a hierarchical link and an efficiency satellite:




Non-historicised link  (also known as transactional links) – a link that may contain business attributes within it, or may be associated with a satellite which has these attributes. The important thing is that it stores information about events that have occurred and will never be changed (like a classic fact table). Examples of such data are: system logs, invoice postings that can only be changed/withdrawn with another posting (storno accounting), etc.



and example of a Non-historicised link




Link same as – allows you to tag different BKEY keys in the HUB table that essentially mean the same thing business-wise. I have mentioned this in previous chapters when describing the selection of the optimal BKEY. It is very important to note that this link only combines BKEY keys that business mean the same thing, we do not use the same as to register relationships other than mutually explicit relationships. We can use advanced algorithms to calculate often non-obvious links and record the results of the calculation in the link.



Examples of “same as” link



Links such as „same as” can be used in situations when we want to indicate often non-obvious business relationships, but also in very mundane situations. For example, when two systems have completely different business keys that represent the same thing, or when a key changes over time and we want to capture and record that change.


PIT facility – The Data Vault model is fragmented, as we have many subject satellites correlated to HUBs. Queries in the warehouse often involve several HUBs and satellites correlated with them. Selecting data from a specific point in time can be a challenge for the database. To improve read performance we use Point In Time (PIT) objects. A PIT table is something like a business index.


The important point is that we create PITs for specific business requirements. We define a set of source data (hubs, satellites), combine selected tables of hubs, links and satellites in such an arrangement as the business expects, e.g. for a selected moment in time (selected timeline or other business parameter). These are objects that we can reload and clean at any time, depending on the requirements of the recipient and the limitations of the hardware/system platform. The PIT is constructed from keys that refer to the hub and satellites so that we can retrieve data from these objects with a simple „inner join„.


A PIT facility can also refer to links instead of HUBs and satellites attached to a link.


BRIDGE object – works similarly to the PIT object with the difference being that it does not speed up access to data on a specific date but speeds up reading of a specific HKEY. Like PIT objects, BRIDGE objects are also created for the specific requirements of the data recipient. Bridge objects contain keys from multiple links and associated HUBs.





The raw Data Vault model is not an easy model to use, it is difficult to navigate without documentation and therefore should not be made widely available to end users. The PIT as well as the Bridge objects help the end-user to read the DataVault data efficiently but it is important to remember that they are not a replacement for the Information Delivery (Data Mart) layers. They should be considered more as a bridge and/or optimisation object to produce higher layers. Of course, creating a PIT/Bridge object also costs money, so this optimisation method is used where there are many potential customers.


This concludes the second part of our series of articles about Data Vault and its implementation. Next week, you will be able to read about naming convention. Additionally, you will be able to find the summary of the information provided so far! To make sure you will not miss the next part of the series, be sure to follow us on our social media linked below. And if you have additional questions about data – let’s talk about it!


Data Vault Part 2 - Data modeling

What is Data Vault? How to implement it in your organization and how to harness its power in your organization? Take a look and learn!

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Data Vault, compared to other modelling methods is relatively new. There are not many specialists with experience when it comes to data warehouses in this architecture. The lack of practical knowledge often results in solutions that only partially comply with the guidelines. This results in achieved results not fulfilling expectations and not supporting business strategy properly. Implementation and performance are especially problematic and require in-depth consideration.


But if you are curious about enormous potential of Data Vault as a Data Governance tool – you came to right place. Tomasz Dratwa, BitPeak Senior Data Engineer and Data Governance expert with several years of experience in implementing and developing Data Vaults decided to write down the most vital issues that need to be considered while building DV in your organization. Issues such as implementation of modelling from the architecture level to the physical fields in the warehouse. We are sure that they will help anyone who considers a warehouse in a Data Vault architecture.


The article is mostly for people who have some experience in dealing with databases and data warehouses before. It does not explain the basics of creating a data warehouse, modeling, foreign keys, or what SCD1 and SCD2 are. For those unfamiliar with the concepts, the article may be a challenging lecture. However, for those well-versed in dealing with databases and data warehouses, or just determined and able to access the google – this will most certainly be a very valuable lecture.



What is Data Vault?


Data Vault is a set of rules/methodologies that allow for the comprehensive delivery of a modern, scalable data warehouse. Importantly, these methodologies are universal. For example, they allow for modeling both financial data warehouses where data is loaded on a daily basis, and where backward data corrections are important, as well as warehouses collecting user behavioral data loaded in micro-batches. Data Vault precisely defines the types of objects in which data is physically stored, how to connect them, and how to use them. Thanks to these rules, we can create a high-performance (in terms of reading and writing) fully scalable (in terms of computing power, space, and surprisingly, also manufacturing!) data warehouse. Proper use of Data Vault enables us to fully leverage the scaling capabilities of Cloud, Big Data, Appliance, RDBMS environments (in terms of space and computing power). Additionally, the structure of the model and its flexibility allows for parallel development of the data warehouse model by multiple teams simultaneously (e.g., in the Agile Nexus model).



The two logical layers of the integrated Data Vault model are:


  • Raw Data Vault – raw data organized based on business keys (BKEY) and „hard rules” transformations (explained later in the article).


  • Business Data Vault – transformed and organized data based on business rules.



Both layers can physically exist in one database schema, and it’s important to manage the naming convention of objects appropriately. An issue which I will explain later. The Information Delivery layer (Data Marts) should be built on top of the above layers in a way that corresponds to the business requirements. It doesn’t have to be in the Data Vault format, so I won’t focus on Information Delivery design in this article.


Currently, Data Vault is most popular in Scandinavian countries and the United States, but I believe it is a very good alternative to Kimball and Immon and will quickly gain popularity worldwide.


Data Vault is „Business Centric” data model, which follows the business relationships rather than the systems and technical data structure in the sources. The data is grouped into areas, of which the central points are the so-called Hub objects (which will be discussed later). The technical and business timelines are completely separated. We can have multiple timelines because the time attributes in Data Vault are ordinary attributes of the data warehouse and do not have to be technical fields. On the other hand, Data Vault ensures data retention in the format in which the source system produced it, without loss or unnecessary transformations. It seems impossible to reconcile, yet it can be done.


Data Vault is a single source of facts, but the information an often be multi-faceted. Variants are necessary, because the same data is often interpreted differently by different recipients, and all these interpretations are correct. Facts are data as it came from the source; Such data can be interpreted in many ways, and with time, new recipients may appear for whom calculated values are incomplete. With time, the algorithms used for calculations may also degrade. Data Vault is fully flexible and prepared for such cases.


Data Vault is based on three basic types of objects/tables:


  • Hub: stores only business keys (e.g. document number).
  • Relational Link: contains relationships between business keys (e.g. connection between document number and customer).
  • Satellite: stores data and attributes for the business key from the Hub. A satellite can be connected to either a Hub or a Link.



An example excerpt from a Data Vault model:


As you can see, the Data Vault model is not simple. Therefore, it is recommended to establish the appropriate rules for its development and documentation during the planning phase. It is also important to start modeling from a higher level. The best practice is to build a CDM (Corporate Data Model) in the company, which is a set of business entities and dependencies that function in the enterprise. The Data Vault model should refer to the high-level CDM in its detailed structure. Additionally, it is worth defining naming conventions for objects and columns. It is also necessary to document the model (e.g. in the Enterprise Architect tool).




Data Vault 2.0 – Architecture


In this article, we will focus only on the portion of the architecture highlighted on the diagram. To this end I will explain what the RDV and BDV layers are, how to model them logically and physically, and how to approach data modeling in relation to the entire organization. We will also discuss all types of Data Vault objects, good and bad practices for creating business keys, naming conventions, explain what passive integration is, and discuss hard rules and soft rules. I will try to cover all the key aspects of Data Vault, understanding of which enables the correct implementation of the data warehouse.


High-level diagram of a data warehouse architecture based on Data Vault.



Buisness hard and soft rules


A crucial aspect of a data warehouse is the storage and computation of facts and dimensions. To optimize this process, it’s very important to understand the differences between hard and soft rules transformations. Typically, the lower levels of any data warehouse store data in its least transformed state. This is due to practical considerations, as storing data in the form it was received in is crucial. Why? Because it allows us to use that data even after many years and calculate what we need at any given moment. On the other hand, some transformations are fully reversible and invariant over time, such as converting dates to the ISO format or converting decimal values from Decimal(14,2) to Decimal(18,4). These data transformations in Data Vault are called Hard Rules. Sometimes, we also consider irreversible transformations (for example trimming) as Hard Rules, but we must ensure that the data loss doesn’t have a business or technical impact. All other computations that involve column summation, data concatenation, dictionary-based calculations, or more complex algorithms fall under soft rule transformations. Data Vault clearly defines where we can apply specific transformations.



Raw Data Vault and Business Data Vault


In logical terms, the Data Vault model is divided into two layers:


Raw Data Vault (RDV) – Which contains raw data, with solely hard rules allowed for calculations. Despite this, the RDV model is fully business-oriented, with objects such as Hubs, Links, and Satellites arranged according to how the business understands the data. Technical data layouts, as found in the source system, are not allowed in this layer. This is known as the „Source System Data Vault (SSDV)”, which provides no benefits, such as passive model integration, which will be discussed later. This layer stores a longer history of data according to the needs of the data consumers. It is also a good practice to standardize the source system data types in this layer, for example, by having uniform date and currency formats.


Business Data Vault (BDV) – which allows for any type of data transformation (both hard and soft rules) and arranges the data in a business-oriented manner. The source of data for this layer is always the RDV layer. The fundamental rule of Data Vault is that the BDV layer can always be reconstructed based on the RDV layer. If all objects in the BDV layer are deleted, a well-constructed Data Vault model should allow for its re-population.


Both layers are accessible to users of the data warehouse and their objects can be easily combined. It is recommended to store tables from both the RDV and BDV layers in the same database (or schema) and differentiate them with an appropriate naming convention. 


This concludes the first part of our articles about Data Vault and its implementation. Next week, you will be able to read about data modelling. To make sure you will not miss the next part of the series, be sure to follow us on our social media linked below. And if you have additional questions about data – let’s talk about it!



Data Vault Part 1 - Introduction

What is Data Vault? How to implement it in your organization and how to harness its power in your organization? Take a look and learn!

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As Artificial Intelligence develops, the need for more and more complex models of machine learning and more efficient methods to deploy them arises. The will to stay ahead of the competition and the interest in the best achievable process automation require implemented methods to get increasingly effective. However, building a good model is not an easy task. Apart from all the effort associated with the collection and preparation of data, there is also a matter of proper algorithm configuration.


This configuration involves inter alia selecting appropriate hyperparameters – parameters which the model is not able to learn on its own from the provided data. An example of a hyperparameter is a number of neurons in one of the hidden layers of the neural network. The proper selection of hyperparameters requires a lot of expert knowledge and many experiments because every problem is unique to some extent. The trial and error method is usually not the most efficient, unfortunately. Therefore some ways to optimise the selection of hyperparameters for machine learning algorithms automatically have been developed in recent years.


The easiest approach to complete this task is grid search or random search. Grid search is based on testing every possible combination of specified hyperparameter values. Random search selects random values a specified number of times, as its name suggests. Both return the configuration of hyperparameters that got the most favourable result in the chosen error metric. Although these methods prove to be effective, they are not very efficient. Tested hyperparameter sets are chosen arbitrarily, so a large number of iterations is required to achieve satisfying results. Grid search is particularly troublesome since the number of possible configurations increases exponentially with the search space extension.


Grid search, random search and similar processes are computationally expensive. Training a single machine learning model can take a lot of time, therefore the optimisation of hyperparameters requiring hundreds of repetitions often proves impossible. In business situations, one can rarely spend indefinite time trying hundreds of hyperparameter configurations in search for the best one. The use of cross-validation only escalates the problem. That is why it is so important to keep the number of required iterations to a minimum. Therefore, there is a need for an algorithm, which will explore only the most promising points. This is exactly how Bayesian optimisation works. Before further explanation of the process, it is good to learn the theoretical basis of this method.



Mathematics on cloudy days

Imagine a situation when you see clouds outside the window before you go to work in the morning. We can expect it to rain during any day. On the other hand, we know that in our city there are many cloudy mornings, and yet the rain is quite rare. How certain can we be that this day will be rainy?


Such problems are related to conditional probability. This concept determines the probability that a certain event A will occur, provided that the event B has already occurred, i.e. P(A|B). In case of our cloudy morning, it can go as P(Rain| Clouds), i.e. the probability of precipitation provided the sky was cloudy in the morning. The calculation of such value may turn out to be very simple thanks to Bayes’ theorem.



Helpful Bayes’ theorem


This theorem presents how to express conditional probability using the probability of occurrence of individual events. In addition to P(A) and P(B), we need to know the probability of B occurring if A has occurred. Formally, the theorem can be written as:



This extremely simple equation is one of the foundations of mathematical statistics [1].


What does it mean? Having some knowledge of events A and B, we can determine the probability of A if we have just observed B. Coming back to the described problem, let’s assume that we had made some additional meteorological observations. It rains in our city only 6 times a month on average, while half of the days start cloudy. We also know that usually only 4 out of those 6 rainy days were foreshadowed by morning clouds. Therefore, we can calculate the probability of rain (P(Rain) = 6/30), cloudy morning (P(Clouds) = 1/2) and the probability that the rainy day began with clouds (P(Clouds|Rain) = 4/6). Basing on the formula from Bayes’ theorem we get:



The desired probability is 26.7%. This is a very simple example of using a priori knowledge (the right-hand part of the equation) to determine the probability of the occurrence of a particular phenomenon.



Let’s make a deal


An interesting application of this theorem is a problem inspired by the popular Let’s Make A Deal quiz show in the United States. Let’s imagine a situation in which a participant of the game chooses one of three doors. Two of them conceal no prize, while the third hides a big bounty. The player chooses a door blindly. The presenter opens one of the doors that conceal no prize. Only two concealed doors remain. The participant is then offered an option: to stay at their initial choice, or to take a risk and change the doors. What strategy should the participant follow to increase their chances of winning?


Contrary to the intuition, the probability of winning by choosing each of the remaining doors is not 50%. To find an explanation for this, perhaps surprising, statement, one can use Bayes’ theorem once again. Let’s assume that there were doors A, B and C to choose from. The player chose the first one. The presenter uncovered C, showing that it didn’t conceal any prize. Let’s mark this event as (Hc), while (Wb) should determine the situation in which the prize is behind the doors not selected by the player (in this case B). We look for the probability that the prize is behind B, provided that the presenter has revealed C:



The prize can be concealed behind any of the three doors, so (P(Wb) = 1/3). The presenter reveals one of the doors not selected by the player, therefore (P(Hc) = 1/2). Note also that if the prize is located behind B, the presenter has no choice in revealing the contents of the remaining doors – he must reveal C. Hence (P(Hc|Wb) = 1). Substituting into the formula:



Likewise, the chance of winning if the player stays at the initial choice is 1 to 3. So the strategy of changing doors doubles the chance of winning! The problem has been described in the literature dozens of times and it is known as the Monty Hall paradox from the name of the presenter of the original edition of the quiz show [2].


Bayesian optimisation


As it is not difficult to guess, the Bayesian algorithm is based on the Bayes’ theorem. It attempts to estimate the optimised function using previously evaluated values. In the case of machine learning models, the domain of this function is the hyperparameter space, while the set of values is a certain error metric. Translating that directly into Bayes’ theorem, we are looking for an answer to the question what will the f function value be in the point xₙ, if we know its value in the points: x₁, …, xₙ₋₁.


To visualize the mechanism, we will optimise a simple function of one variable. The algorithm consists of two auxiliary functions. They are constructed in such a way, that in relation to the objective function f they are much less computationally expensive and easy to optimise using simple methods.


The first is a surrogate function, with the task of determining potential f values in the candidate points. For this purpose, regression based on the Gaussian processes is often used. On the basis of the known points, the probable area in which the function can progress is determined. Figure 1 shows how the surrogate function has estimated the function f with one variable after three iterations of the algorithm. The black points present the previously estimated values of f, while the blue line determines the mean of the possible progressions. The shaded area is the confidence interval, which indicates how sure the assessment at each point is. The wider the confidence interval, the lower the certainty of how f progresses at a given point. Note that the further away we are from the points we have already known, the greater the uncertainty.



Figure 1: The progression of the surrogate function



The second necessary tool is the acquisition function. This function determines the point with the best potential, which will undergo an expensive evaluation. A popular choice, in an acquisition function, is the value of the expected improvement of f. This method takes into account both the estimated average and the uncertainty so that the algorithm is not afraid to „risk” searching for unknown areas. In this case, the greatest possible improvement can be expected at xₙ = -0.5, for which f will be calculated. The estimation of the surrogate function will be updated and the whole process will be repeated until a certain stop condition is reached. The progression of several such iterations is shown in Figure 3.



Figure 2: The progression of the acquisition function



Figure 3: The progression of the four iterations of the optimisation algorithm



The actual progression of the optimised function with the optimum found is shown in Figure 4. The algorithm was able to find a global maximum of the function in just a few iterations, avoiding falling into the local optimum.

Figure 4: The actual progression of the optimised function



This is not a particularly demanding example, but it illustrates the mechanism of the Bayesian optimisation well. Its unquestionable advantage is a relatively small number of iterations required to achieve satisfactory results in comparison to other methods. In addition, this method works well in a situation where there are many local optima [3]. The disadvantage may be the relatively difficult implementation of the solution. However, dynamically developed open source libraries such as Spearmint [4], Hyperopt [5] or SMAC [6] are very helpful. Of course, the optimisation of hyperparameters is not the only application of the algorithm. It is successfully applied in such areas as recommendation systems, robotics and computer graphics [7].




[1] „What Is Bayes’ Theorem? A Friendly Introduction”, Probabilistic World, February 22, 2016. (provided July 15, 2020).

[2] J. Rosenhouse, „The Monty Hall problem. The remarkable story of math’s most contentious brain teaser”, January. 2009.

[3] E. Brochu, V. M. Cora, i N. de Freitas, „A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning”, arXiv:1012.2599 [cs], December. 2010




[7] B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, i N. de Freitas, „Taking the Human Out of the Loop: A Review of Bayesian Optimization”, Proc. IEEE, t. 104, nr 1, s. 148–175, January 2016, doi: 10.1109/JPROC.2015.2494218.



Smarter Artificial Intelligence with Bayesian Optimization

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