Quantitative investing

# LASSO regression

## Where

λ is amount of shrinkage or penalty
λ = 0 implies all features are considered as no parameters are eliminated
λ = ∞ implies no feature is considered

LASSO is an acronym that stands for ‘least absolute shrinkage and selection operator’. It is associated with a machine learning technique – LASSO regression – that performs both shrinkage and variable selection to simplify linear regression models and prevent overfitting.

A linear regression allows you to determine if there is a relationship between variables. For example, it can quantify the relationship between a dependent variable (crop yields) and explanatory variables (soil fertility,temperature, water quality, etc.). But in cases where there are many candidate variables to explain crop yields, the statistical model can become complex and difficult to process.

The LASSO regression is helpful in such instances as it can select variables based on their importance. This is achieved through a process called shrinkage, a method which imposes a penalty to reduce the absolute size of the regression coefficients. Although reduced in magnitude, the most important variables will continue to reflect material coefficients, while the less-contributing variables will exhibit values close to zero or even zero.

Through this process, it identifies which variables to keep and which ones to exclude, based on the size of their coefficients. Using our example, the technique would gradually select the variables which best predict crop yields, beginning with the most important one before working its way through the list. At some point, adding more variables would no longer improve the prediction accuracy of the model sufficiently, but instead it would add substantial complexity.

Therefore, the technique allows you to simplify a model by reducing the number of parameters in a regression and precluding potential data noise. It also enables you to guard against overfitting by eliminating variables with little explanatory power, potentially making the model more robust across different datasets. Additionally, it can help optimize models with high multicollinearity as it can choose between correlated explanatory variables.

In general, the LASSO regression is a basic machine learning (ML) technique that can be used for many applications. It is essentially a standard linear regression with a slight twist. Contrary to more sophisticated ML techniques, however, it is not able to pick up non-linear relationships between variables.

For our quant investing platform, it has the potential to help fine-tune models by assisting us with variable selection. For instance, we have used it to select company characteristics that have linear predictive value for risk and returns. We have also used it to identify which industries lead or lag others in terms of returns.

As technology advances, so do the opportunities for quantitative investors. By incorporating more data and leveraging advanced modelling techniques, we can develop deeper insights and enhance decision-making.

## Let's keep the conversation going

Keep track of fast-moving events in sustainable and quantitative investing, trends and credits with our newsletters.

Robeco aims to enable its clients to achieve their financial and sustainability goals by providing superior investment returns and solutions.

Important information This disclaimer applies to any documents and the verbal or written comments of any person in presentations or webinars on this website and taken together is referred to herein as the “Information”. The services to which the Information relate are NOT FOR RETAIL CLIENTS - The information contained in the Website is solely intended for professional investors, defined as investors which (1) qualify as professional clients within the meaning of the Markets in Financial Instruments Directive (MiFID), (2) have requested to be treated as professional clients within the meaning of the MiFID or (3) are authorized to receive such information under any other applicable laws and must not be relied or acted upon by any other persons. This Information does not constitute an offer to sell, or a solicitation of an offer to buy, any financial product, and may not be relied upon in connection with the purchase or sale of any financial product. You are cautioned against using this Information as the basis for making a decision to purchase any financial product. To the extent that you rely on the Information in connection with any investment decision, you do so at your own risk. The Information does not purport to be complete on any topic addressed. The Information may contain data or analysis prepared by third parties and no representation or warranty about the accuracy of such data or analysis is provided.

In all cases where historical performance is presented, please note that past performance is not a reliable indicator of future results and should not be relied upon as the basis for making an investment decision. Investors may not get back the amount originally invested. Neither Robeco Institutional Asset Management B.V. nor any of its affiliates guarantees the performance or the future returns of any investments. If the currency in which the past performance is displayed differs from the currency of the country in which you reside, then you should be aware that due to exchange rate fluctuations the performance shown may increase or decrease if converted into your local currency. Robeco Institutional Asset Management B.V. (“Robeco”) expressly prohibits any redistribution of the Information without the prior written consent of Robeco. The Information is not intended for distribution to, or use by, any person or entity in any jurisdiction or country where such distribution or use is contrary to law, rule or regulation. Certain information contained in the Information includes calculations or figures that have been prepared internally and have not been audited or verified by a third party. Use of different methods for preparing, calculating or presenting information may lead to different results. Robeco Institutional Asset Management B.V. is authorised as a manager of UCITS and AIFs by the Netherlands Authority for the Financial Markets and subject to limited regulation in the UK by the Financial Conduct Authority. Details about the extent of our regulation by the Financial Conduct Authority are available from us on request.