How to construct non-black box machine learning in algorithmic trading

This article discusses simple steps to construct explainable ML models, especially on noisy data. I use an example from the development process of our systematic trading research in  Comfort Zone Investments, osoba rizikového kapitálu, a.s.  In the example, I show how you can deal with model fingerprints, respectively 'whiten the black box.'

A black box is simply an input-output model where we don't know what is happening inside. With the rise of AI and ML in recent years, many predictions have been made with black boxes. Even some researchers don't know what is happening inside. Any ML model is just a complex optimization problem, but most algorithms we use do not have as simple interpretations as linear or logistic regression. People outside the field understand the black box as lacking interpretation.

A single-node neural network is easily interpretable, but a deep neural network cannot be interpreted. When adding recurrent layers, the interpretation is even worse. Thanks to visualizations, the convolution layers are making the task easier. Interpreting decision trees is straightforward, but a random forest consisting of 1000 trees or an XGBoost may be a headache. With more complex models, our loss is in direct explainability, but the gain is that we can solve more complex problems.

Our steps are similar for any ML project on highly noisy data:

1. What do you expect from the machine learning model? One of the most critical questions any data scientist should ask. Another similar question is, do I really need an ML model or just want to feel fancy? Your expectations should be around the solution for some particular task inside the project. If you are creative enough, you can define your problem to suit you better for ML. In algorithmic trading, it is way better to have some primitive [base] strategy that is functional. The idea can be based on price patter, news, fundamentals, options, or alternative data. The important is having the strategy itself. Do you have hundreds of potential signals daily? Great, that’s a lot of data – good for ML. Do you need to tune the strategy because trading costs destroy the average trade? Perfect, better use ML than doing it yourself with dozens of human biases.
2. Keep it simple! In this case, it is not only about interpretation, but also deep complex models tend to overfit on randomness. We don’t construct deep models to solve problems from the beginning to the end. We choose tasks that need ML solutions and prepare the data necessary for these tasks, so we add human experience. We avoid deep neural networks. With highly noisy data, if a simple 3-layer neural network with less than 200 nodes in each layer doesn’t provide significantly better results than the average, neither 5-layer network will. *You may disagree with this one when you are experienced with deep neural networks, so you can share some papers proving that deeper models work better with low signal-to-noise data. I would love to study them to correct my experience and biases.
3. Feature engineering (or follow the saying 'garbage in, garbage out'). Every feature that enters our models is constructed, tested, and deeply analyzed. When we see that the feature is significantly affecting the label, we may start asking questions: is there a fundamental explanation to prove this effect? Is the effect strong enough or just random because of data selection? Does this effect work on an unseen part of in-sample data? You may ask what an unseen part of the in-sample is. Before you start modeling, you should prepare in-sample [IS] and out-of-sample [OOS] data, even for basic data analysis. IS is necessary for model training and data analysis, and OOS is used as unseen data for model validation and analysis of results. You can divide IS into smaller parts to test the features (never use OOS for constructing and selecting features). In our development, we also use another OOS, named super-OOS [SOOS] or also known as simulation trading. The idea of SOOS is the final test of the functionality of the whole approach and the construction of the backtest.
4. Model fingerprints. When the model is trained, and the interpretability is not straightforward, you can analyze the effect of the change in features on model output. You can analyze linear, non-linear, and pairwise effects very simply (Beyond The Black Box: An Intuitive Approach to Investment Prediction with Machine Learning by Yimou (Andrew) Li, CFA , David Turkington, CFA , and Al Yazdani ). Or you can construct your approach by looking inside the model. Then you can ask other questions. How is the change in a feature affecting the model? Is that correct? Is the impact linear or non-linear? What is pair / multi-effect? What happens with these extreme values? For more information about feature importance, see chapter 8 of Advances in Financial Machine Learning by Marcos Lopez de Prado .

Example from Stock Pairs trading strategy

Stock Pairs is a simple mean-reversions strategy where we sell one stock and buy another, so we are market neutral. Both stocks should be correlated and have some fundamental relationship - the same industry or supply-demand relationship. We watch prices, and if the spread between prices is too wide, we enter a trade expecting the spread to reverse to the mean.

We solve two different problems here. The first is finding suitable pairs; the second is choosing the signal with the highest expected return. We separate these problems, and both use ML inside. Let's describe mentioned points practically. * I will only go inside a little to protect our know-how. For the pair selection problem, I describe only the first point:

Why do we need ML for finding pairs? After using fundamental data like sectors and industries, we still have potentially millions of stock pairs on US exchanges only. We need to analyze if the stocks have a mean-reversion relationship. Many methodologies include co-integration, Hurst exponent, correlations, or dynamic time warping. Since we cannot simply apply it and find pairs to prevent look-ahead bias, we have to do it with a walk-forward approach - every month (quarter, year), we use only the data available and select the right pairs. That makes a lot of computations for millions of stock pairs. Computationally heavy methodologies cannot be used, and correlation cannot describe lagged relationships. When human traders are looking for correlated assets, they look at both plots and see if they have similar traces. Simple distance of traces is problematic in this task and does not solve the problem. We took the traces as pictures and applied convolutional auto-encoders to obtain lower-dimension representation (latent vector space). Now we calculate the distance between the stocks in latent vector space. Once the neural network is trained, then it is computationally easy. Within a second, we can filter more suitable stock pairs where we may apply computationally heavier methodologies. The methodology is unsupervised, so there are fewer overfitting problems and biases than in supervised learning.

Why do we need ML for signal selection? With a basic selection of available stock pairs, we sometimes have hundreds of trading signals daily. The average signal return is mostly higher than the average cost, and the winning ratio is as expected for a mean-reversion strategy. We have a lot of data for developing models. Using just simple rules to select signals will not give us a competitive advantage; that is another point for ML.

We construct simple models of Artificial Neural Networks (with few layers and a smaller number of nodes) and GPU-accelerated Random Forests (again, not too large and not too deep). We only do a little hyper-parameter tuning because it is another step for overfitting, even when done with cross-validation. Many models are based on some random seed, so new trains or using different parts of IS will make slightly different outputs. We always train various models with the same set-up on different subsets on IS, and we closely watch the variance of the results. With bigger and deeper models, we observe the rise of overfitting with bigger variance in the results of various models on OOS (in this case, it is still part of a wider in-sample, explained more deeply in another article).

Feature engineering is a critical part of our development process because this is where the edge is created. Some deep models are good in feature extraction and may do a lot of work, but many fail due to high noise in stock prices and, in our case, the complexity of the strategy. We need to use a combination of two different price series, the fundamentals of both stocks, the historical performance that is not calculated trivially from the data, and so on. Most of the features can't be constructed by automatic feature extraction. Our features are built and tested by various approaches and may be divided into these groups: performance, spread, price distribution, volume, correlation, alternative, trend, earnings, and volatility. Most fundamental features are used as base filters.

A bit deeper into Model Fingerprints

Analyzing feature effects or model influences is necessary to prove the model uses all inputs and may be taken as a control mechanism if the given influences are logical. In linear models, we have straightforward information directly from the beta coefficient. In other models, we don't see it straight, but there are methodologies to analyze the effect. This effect may be linear, nonlinear, pairwise, or based on a combination of multiple features (hard to construct in linear models by hand because of too many combinations). I would like to present the result of an article, Beyond the Black Box, that was presented in the Journal of Financial Data Science Winter 2020. There was introduced an exciting way to analyze the feature effects with the regression model. I modified the computations to work with the binary classification model used in my prediction. I show only the results from my example because the article is not freely available.

Next to these effects, I also use simplified approaches to analyze the effect of each feature. The primitive effect of a feature is simply the difference between the outputs where we added and removed 2 standard deviations to a given feature and left other features unchanged. The effect is the absolute value between the extreme positive input (+2 standard deviations) and the extreme negative input (-2 standard deviations). Since most input data are standardized, the calculation is trivial.

The other effect is mean-based. We set all other features to zero (mean value for standardized input) and leave only the analyzed feature unchanged. The standard deviation of the output is then the mean-based effect. Here is an example from the Random Forest model used in our development.

You can analyze all your features and their direct effects. Calculating primitive effects, you can also explore the direction of the effect. Or you can plot partial dependences for all features (to see non-linearity). Still, by this analysis, we can see only the basic influence of one input. The interaction of various features is an essential part of the model. The pairwise interaction effect is calculated intuitively for both regression and classification problems. Higher-order interactions are presented in ML models, too, but are much harder to compute and interpret. When having a lot of features, simply comparing the most potent pairwise effect may give you clues for solid higher-order interactions. The following plot is an example of group features.

In your research, you can plot a heat map of the output while X and Y axis represents changes in feature inputs. That is, in our case, a grid where both axes are inside the interval [-2,2] (standardized data).

Avoiding the black box may be tricky sometimes, but with these techniques, it is more convenient. Applying these four simple steps may help to create more interpretable machine learning. Applicable on regression and classification. Multi-class classification is more tricky because there may be different effects for each class, so that visualization would need another dimension.