### How to Quickly and Meaningfully Improve the Financial System’s Collective Ability to Detect Crimes

Complex financial crimes are hard to detect primarily because data related to different pieces of the overall puzzle are usually distributed across a network of financial institutions, regulators, and law-enforcement agencies. The problem is also rapidly increasing in complexity because new platforms are emerging all the time that facilitate the transfer of value across a range of industries. These include crypto-currencies, real-estate settlement services, peer-to-peer lending, gaming platforms, and more.

Most attempts at solving the problem of detecting complex financial crimes concentrate on the problem of integrating disparate datasets, either by attempting to centralise them in a data lake architecture or by building data access APIs across distributed datasets. This is likely necessary in the long run, but there is an easier approach we can take in the short term that will meaningfully improve the financial system’s collective ability to detect crimes. Hard to believe? Read on.

At a fundamental level, detecting financial crimes is really about building statistical risk models that can accurately quantify the riskiness of an entity $x$, based on the entity’s activities across the financial system and beyond. As every data scientists would know, the theoretical best such model is of course the Bayes Optimal Estimator, which is given by

$R(x) = \arg \max_{c \in C} \sum_{h \in H} P(c \,|\, h, x) P( D \,|\, h) P(h)$,

where $C$ is the set of all possible classes (in our setting, each class denotes a type of financial crime), $H$ is the space of all possible risk models, $P$ refers to a probability, $D$ is the training data, $P(h)$ is the prior probability of $h$ being the true model, $P(D \,|\, h)$ is the likelihood of $h$ based on the data, and $P(c \,|\, h,x)$ is the probabilistic prediction of model $h$ on $x$. (If you need a crash course on Bayesian probability theory, look here. The Wisdom of the Crowd concept is related too.) Of course, most interesting hypothesis space $H$ are too large for the Bayes optimal estimator to be constructed exactly, but there are plenty of ways we can build an ensemble model that approximates the Bayes optimal estimator by combining a subset of good and diverse models from some hypothesis space $H$. Bagging, Boosting, Stacking, Bayesian Model Averaging, possibly in combination with Random Subspace methods, are all very successfully machine learning algorithms that exploit this strategy in one way or another. (For example, Random forest combine Bagging with Random Subspace on decision trees to produce a still state-of-the-art learning algorithm for many problems.)

So how is the above relevant to the problem of detecting complex financial crimes?

Well, consider these facts:

1. Every financial institution maintains tens to hundreds of risk models of different kinds on their customers as part of their normal course of doing business .
2. The risk models between financial institutions can be quite different, giving us a diverse set of models when they are put together.
3. Each of these financial institutions has legislative obligation to send a subset of their data to financial intelligence units (FIU) in each country. (For example, financial institutions send all cash transactions exceeding \$10k, international fund transfers and suspicious matter reports to FIUs under the AML/CTF regime. Most law-enforcement agencies can also serve notices on financial institutions to obtain data on entities of interest).
4. There are now confidential computing technologies that allow organisations to do joint computations on their collective data in a privacy-preserving manner. (See, for example, this article from Data61.)

Together, these provide essentially all the ingredients we need for different institutions in the financial system to come together to construct an ensemble model that approximates the Bayes optimal estimator for detecting complex financial crimes.

Let’s flesh this out with a concrete illustration. In the standard AML/CTF setting, you have a financial intelligence unit and a population of reporting entities (banks, credit unions, casinos, etc). Using privacy-preserving data matching techniques (see for example this paper), it’s possible for them to link up their shared customers and arrive at a configuration shown in the following diagram.

The first step in constructing an approximation to the Bayes optimal estimator is to sum the risk scores across all the reporting entities. In other words, instead of summing over all models in a hypothesis class, we sum over all the actual risk models being used in the reporting entities. This can be done in a privacy-preserving manner with a partially homomorphic encryption scheme like the Paillier Cryptosystem, as shown in the next diagram.

Here, each reporting entity (RE) simply sums up its local risk scores, encrypts the result using the FIU’s public key, adds it to the encrypted value from the previous RE in the chain if one exists, and then passes on the encrypted sum to the next RE. The last RE in the chain then sends the final encrypted result to the FIU, which then decrypts the data using its private key to obtain the resulting sum.

At this point, if we made the simplifying assumption that the weighting $P( D \,|\, R_i) P(R_i)$ of each model $R_i$ is the same, then the predicted risk score of each entity in the financial system is simply the sum of risk scores divided by the total number of risk models, i.e. the average risk score. This is likely sufficient to give us an improved risk model for detecting financial crimes, one with lower variance than the individual models that make up the ensemble model. But we can do better than that.

The problem comes down to having a good way of estimating the value of $P(D \,|\, R_i)$ for each $R_i$. The fundamental difficulty is of course that the data $D$ is spread across the financial system in different institutions. If we think of $D$ as a $n \times m$ matrix, then each reporting entity only has a subset of the columns of the matrix and the financial intelligence unit only has a subset of the rows of the matrix. For each risk model $R_i$ built by a reporting entity $B$, we would of course have an estimate of $P( D_{|B} \,|\, R_i)$, the accuracy of $R_i$ on $D_{|B}$, the subset of $D$ available to $B$. We can approximate $P( D \,|\, R_i)$ by

$P( D \,|\, R_i) = \frac{1}{2} (P( D_{|B} \,|\, R_i) + P( D_{|F} \,|\, R_i))$,

where $D_{|F}$ is the subset of $D$ available to the financial intelligence unit (FIU). There are different ways $P( D_{|F} \,|\, R_i)$ can be approximated. If the FIU has its own risk model $R_F$ constructed based on $D_{|F}$, then one approximation of $P( D_{|F} \,|\, R_i)$ is simply the statistical correlation between the predictions of $R_i$ and $R_F$ on a common set of entities, which can be computed in a privacy-preserving manner because it involves only inner-product calculations. (See this post and this paper for details.)

To incorporate the $P( D \,|\, R_i)$ weighting into the above computation, each RE will first compute the weighting formula for each model in conjunction with the FIU in a privacy-preserving manner. The individual risk scores are then weighted accordingly and summed up using the homomorphic encryption scheme described above to obtain the ensemble model risk scores. Under mild conditions on the diversity and accuracy of the underlying risk models that make up the ensemble model, one can have mathematical guarantees that the ensemble model is more accurate than each individual risk model in the ensemble. In other words, the financial system as a whole have just obtained a risk model that is superior to anything that exists out there!

So what would it take to build such an ensemble model? The title of this blog post deliberately a bit flippant to attract, I hope, the right level of attention. In practice, I think we are actually not that far away from making the above a reality. There are a few possible obstacles. To begin with, confidential computing is one area where technology has likely advanced beyond the boundaries of existing legislations. While the algorithms come with cryptographic guarantees on privacy preservation, the act of anonymous data matching may still require amendments to existing legislations. Also, in the short term at least, any attempt to build an ensemble model in the manner described in this article will require the willing collaboration of a network of financial institutions and relevant regulators or financial intelligence units. Such collaboration is likely difficult to achieve, but Australia is possibly in the best position to achieve such a result with the recent establishment of the Fintel Alliance, which brings together AUSTRAC, major financial institutions, and law-enforcement agencies in a public-private partnership. Here’s hoping optimism pays.

## One thought on “How to Quickly and Meaningfully Improve the Financial System’s Collective Ability to Detect Crimes”

1. Very interesting vision Kee Siong. Would be interested to discuss the practicalities of PPRL per the paper you cite.

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