Applications of Gaussian Processes in Finance
Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM model.
 Summary The paper uses standard GPLVMs to model the covariance structure and a latent space representation of financial time series. On daily close prices of S&P500 data, the authors demonstrate that the approach is a useful covariance model. Quality Although the application is clear and the methodology is well established, the quality of the submission can be improved by a better connection to prior work in the finance domain. Being not an expert here, it seems that there should be more advanced methods one might want to compare to. In particular missing standard deviations in the figures make it hard to judge the relevance of the empirical evaluation. Clarity The manuscript is well written and the technical content and the experimental results are well accessible to the reader. A little bit more attention needs to be paid to properly defining all quantities. See "Details". Originality The application to financial time series is straight forward but I have not seen it before. The manuscript does not modify the standard GPLVM methodology. Significance As the application is obvious and as the evaluation of the methodology does only include very little comparison to existing algorithms, the significance of the presented work is limited. Reproducibility The data can be obtained from Yahoo finance, the implementation is based on scikit-learn. Although the authors do not provide code and data, the work should be reproducible with reasonable effort. Missing details of the GPLVM optimization and the unknown random split might prevent the exact replication of the results. Pros and Cons 1-) Non-stationarity is not dealt with. 2-) Figure 1: standard deviations should be added. 3+) The model is simple and well established. 4-) Proper optimization can be cumbersome and is inherently plagued by local minima. Details a) Title: The paper is about GPLVMs rather than GPs b) Abstract: betas is an undefined term here c) Intro: w, r, K are not properly defined d) Intro: Gaussian Process -> Gaussian process e) Intro: In Bayesian framework -> In a Bayesian framework f) Sec 2.1: -> g) Eq. 5/6: this is only correct for m(x)=0 and no noise h) Sec 3.1: missing reference for CAPM i) Sec 4.1: please also mention N and D j) References: Neil Lawrence, ... Gaussian process latent ... k) References: Bayesian Gaussian
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Applications of Gaussian Processes in Finance
Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM model.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 Summary The paper uses standard GPLVMs to model the covariance structure and a latent space representation of financial time series. On daily close prices of S&P500 data, the authors demonstrate that the approach is a useful covariance model. Quality Although the application is clear and the methodology is well established, the quality of the submission can be improved by a better connection to prior work in the finance domain. Being not an expert here, it seems that there should be more advanced methods one might want to compare to. In particular missing standard deviations in the figures make it hard to judge the relevance of the empirical evaluation. Clarity The manuscript is well written and the technical content and the experimental results are well accessible to the reader. A little bit more attention needs to be paid to properly defining all quantities. See "Details". Originality The application to financial time series is straight forward but I have not seen it before. The manuscript does not modify the standard GPLVM methodology. Significance As the application is obvious and as the evaluation of the methodology does only include very little comparison to existing algorithms, the significance of the presented work is limited. Reproducibility The data can be obtained from Yahoo finance, the implementation is based on scikit-learn. Although the authors do not provide code and data, the work should be reproducible with reasonable effort. Missing details of the GPLVM optimization and the unknown random split might prevent the exact replication of the results. Pros and Cons 1-) Non-stationarity is not dealt with. 2-) Figure 1: standard deviations should be added. 3+) The model is simple and well established. 4-) Proper optimization can be cumbersome and is inherently plagued by local minima. Details a) Title: The paper is about GPLVMs rather than GPs b) Abstract: betas is an undefined term here c) Intro: w, r, K are not properly defined d) Intro: Gaussian Process -> Gaussian process e) Intro: In Bayesian framework -> In a Bayesian framework f) Sec 2.1: -> g) Eq. 5/6: this is only correct for m(x)=0 and no noise h) Sec 3.1: missing reference for CAPM i) Sec 4.1: please also mention N and D j) References: Neil Lawrence, ... Gaussian process latent ... k) References: Bayesian Gaussian
assistant
 Summary The paper uses standard GPLVMs to model the covariance structure and a latent space representation of financial time series. On daily close prices of S&P500 data, the authors demonstrate that the approach is a useful covariance model. Quality Although the application is clear and the methodology is well established, the quality of the submission can be improved by a better connection to prior work in the finance domain. Being not an expert here, it seems that there should be more advanced methods one might want to compare to. In particular missing standard deviations in the figures make it hard to judge the relevance of the empirical evaluation. Clarity The manuscript is well written and the technical content and the experimental results are well accessible to the reader. A little bit more attention needs to be paid to properly defining all quantities. See "Details". Originality The application to financial time series is straight forward but I have not seen it before. The manuscript does not modify the standard GPLVM methodology. Significance As the application is obvious and as the evaluation of the methodology does only include very little comparison to existing algorithms, the significance of the presented work is limited. Reproducibility The data can be obtained from Yahoo finance, the implementation is based on scikit-learn. Although the authors do not provide code and data, the work should be reproducible with reasonable effort. Missing details of the GPLVM optimization and the unknown random split might prevent the exact replication of the results. Pros and Cons 1-) Non-stationarity is not dealt with. 2-) Figure 1: standard deviations should be added. 3+) The model is simple and well established. 4-) Proper optimization can be cumbersome and is inherently plagued by local minima. Details a) Title: The paper is about GPLVMs rather than GPs b) Abstract: betas is an undefined term here c) Intro: w, r, K are not properly defined d) Intro: Gaussian Process -> Gaussian process e) Intro: In Bayesian framework -> In a Bayesian framework f) Sec 2.1: -> g) Eq. 5/6: this is only correct for m(x)=0 and no noise h) Sec 3.1: missing reference for CAPM i) Sec 4.1: please also mention N and D j) References: Neil Lawrence, ... Gaussian process latent ... k) References: Bayesian Gaussian