Outline the key differences between machine learning algorithms and conventional statistical models in the context of quantitative trading, and provide an example of when to use one over the other.

Machine learning algorithms and conventional statistical models are both used in quantitative trading, but they have different strengths, weaknesses, and are suitable for different types of tasks. The key differences lie in their approach to learning from data, their flexibility, and their interpretability. Conventional statistical models, like linear regression, ARIMA models, and logistic regression, are built on established statistical theories and assumptions. These models typically involve a well-defined mathematical structure based on the relationships between variables, and their parameters are estimated by optimizing certain criteria based on statistical properties. For example, linear regression, as discussed earlier, models a linear relationship between independent and dependent variables. ARIMA models capture the serial autocorrelation in time series data, using past values to forecast future ones. These models make strong assumptions about the underlying data distribution and the relationships between variables. For example, linear regression assumes a linear relationship, ARIMA models assume stationarity of time series data, and logistic regression assumes a sigmoid relationship between the outcome and the features. Conventional statistical models are typically easier to interpret. The parameters of these models have clear statistical meanings that can help in understanding how a model works. However, their limited flexibility can be a drawback when dealing with complex, non-linear relationships in financial data, and also the models can become fragile if the underlying statistical assumptions are not met. In contrast, machine learning algorithms are more data-driven and less constrained by theoretical assumptions. These algorithms are designed to learn patterns from the data with minimal human intervention, and the algorithm structure is determined by the learning process. Machine learning models can be broadly divided into supervised learning (predicting a target based on the fea....