MashR: Guidance On Cov_pca, EM & Troubleshooting Cov_flash

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mashR: Guidance on cov_pca, EM & Troubleshooting cov_flash

Hey everyone! I'm thrilled to delve into the fascinating world of mashR and address some common questions and a peculiar issue encountered while using the package. Let's break down the guidance on cov_pca and EM usage, along with troubleshooting the cov_flash error.

1. Choosing the Number of PCs in cov_pca

When working with cov_pca, one of the first questions that pops up is: how many principal components (PCs) should I use? This is crucial for capturing the underlying structure of your data without overfitting.

Here's the deal: There isn't a one-size-fits-all answer, but let's explore some guidelines. Generally, the number of conditions (columns) in your bhat / shat matrices can influence your decision. In the original simulations, the number of PCs was equal to the number of conditions (5 conditions, 5 PCs). However, that doesn't necessarily mean n_conditions = n_PCs in every scenario.

Think of PCs as capturing the major axes of variation in your data. If your conditions are highly correlated, a smaller number of PCs might suffice to explain most of the variance. On the other hand, if your conditions are quite different, you might need more PCs to capture the nuances. When your conditions are not independent, using Principal Component Analysis (PCA) via cov_pca becomes essential. PCA helps in identifying the major axes of variation in your data, which can then be used to model the correlation structure.

Here’s a more structured approach to deciding the number of PCs:

  1. Variance Explained: A common method is to look at the variance explained by each PC. You can calculate the percentage of variance explained by each PC and plot it. A scree plot can help you visualize this. Look for an "elbow" in the plot, where the explained variance starts to level off. The number of PCs before the elbow can be a good starting point.
  2. Cross-Validation: Another approach is to use cross-validation. You can try different numbers of PCs and see which one gives the best predictive performance. This can be computationally intensive but can give you a more objective answer.
  3. Prior Knowledge: Consider whether you have any prior knowledge about the structure of your data. For instance, if you know that a few key factors drive the correlation between your conditions, you might only need a few PCs.
  4. Experimentation: Don't be afraid to experiment with different numbers of PCs and see how it affects your results. You can monitor the performance of your mashR analysis with different numbers of PCs and choose the one that gives the best results. It's also worth noting that using too many PCs can lead to overfitting, where you're capturing noise in your data rather than the true underlying signal. Overfitting can decrease the generalizability of your results, making them less reliable for new data or conditions.

In summary, start by examining the variance explained by each PC, consider cross-validation if feasible, incorporate any prior knowledge you have, and experiment with different numbers of PCs. Keep an eye out for overfitting and select the number of PCs that best captures the true underlying signal in your data.

2. EM Method for Correlated Measurements

Moving on to the EM method, let's tackle the question of what type of matrices to include when running mash_estimate_corr_em. Should you include canonical matrices, data-driven matrices, or both? Here's the scoop: It's generally a good idea to include both canonical and data-driven matrices.

Why? Canonical matrices provide a set of simple, interpretable covariance structures (e.g., identity, exchangeable, AR1). These can capture broad patterns of correlation that might be present in your data. On the other hand, data-driven matrices (like those from cov_pca or cov_flash) can capture more specific and complex correlation structures that are unique to your data.

By including both types of matrices, you allow mashR to learn from both general patterns and data-specific patterns. The EM algorithm can then weight these matrices appropriately to find the best fit to your data.

Here's a more detailed breakdown:

  1. Canonical Matrices: These are pre-defined matrices that represent common correlation structures. Examples include the identity matrix (no correlation), the exchangeable matrix (constant correlation between all pairs of conditions), and the AR1 matrix (correlation that decays with distance). Including these matrices allows mashR to capture simple, interpretable correlation patterns.
  2. Data-Driven Matrices: These are matrices estimated directly from your data. cov_pca and cov_flash are two functions that can be used to estimate data-driven covariance matrices. These matrices can capture more complex and data-specific correlation patterns.
  3. Combining Both: By including both canonical and data-driven matrices, you give mashR the flexibility to learn from both general patterns and data-specific patterns. The EM algorithm can then weight these matrices appropriately to find the best fit to your data. If the true correlation structure is well-represented by one of the canonical matrices, mashR will learn to weight that matrix heavily. If the true correlation structure is more complex and data-specific, mashR will learn to weight the data-driven matrices heavily. Including both types of matrices ensures that mashR has the flexibility to capture a wide range of correlation patterns.

In conclusion, when using mash_estimate_corr_em, it's best to incorporate both canonical and data-driven matrices to leverage the strengths of both approaches. This ensures that mashR can capture a wide range of correlation patterns, leading to more accurate and reliable results.

3. Error When Running cov_flash

Now, let's address the error encountered while running cov_flash. The error message Error in if (any(s == 0)) { : missing value where TRUE/FALSE needed suggests that there might be an issue with the standard errors (s) used internally by cov_flash. Even though you've confirmed that your bhat and shat matrices have no missing values and shat contains no negative entries, the error might still arise due to numerical instability or other internal computations within cov_flash.

Here's a breakdown of potential causes and solutions:

  1. Near-Zero Standard Errors: Even if your shat matrix doesn't contain negative entries, it might contain very small positive values that are effectively zero for computational purposes. These near-zero values can cause issues in the internal calculations of cov_flash. To address this, you can try adding a small positive constant to your shat matrix before running cov_flash. For example:

    shat <- shat + 1e-6  # Add a small constant

  2. Convergence Issues: The warning message Convergence not achieved by 100 iterations suggests that the algorithm used by cov_flash might not be converging properly. This can happen if the data is particularly challenging or if the algorithm's parameters are not well-suited to the data. You can try increasing the maximum number of iterations allowed by cov_flash or adjusting other parameters.

    flash_fit <- flash(data, var_type = 2, maxiter = 1000)

    Adjusting var_type could also help; experiment with options 1 or 2.

  3. Underlying Data Issues: There might be subtle issues with your data that are not immediately apparent. For example, there might be collinearity between some of your conditions, which can cause numerical instability. You can try removing highly correlated conditions or adding a small amount of regularization to your data.

  4. Version Compatibility: Although you're using relatively recent versions of mashr and flashier, it's still worth checking if there are any known compatibility issues between these versions. You can consult the package documentation or online forums to see if other users have encountered similar issues.

Here’s a step-by-step approach to troubleshooting:

  1. Update Packages: Ensure that all your packages, including mashr, flashier, and their dependencies, are up-to-date. Sometimes, updating packages can resolve issues related to version compatibility or bug fixes.
  2. Check for Non-Positive SEs: Even though you mentioned that your shat matrix contains no negative entries, double-check for any non-positive standard errors. Replace any such values with a small positive number.
```R
shat[shat <= 0] <- 1e-6
```
  1. Simplify the Data: Try running cov_flash on a smaller subset of your data to see if the error persists. This can help you isolate the issue and determine if it's related to the size or complexity of your data.
  2. Contact Package Maintainers: If none of the above solutions work, consider reaching out to the package maintainers or posting on online forums. They might be able to provide more specific guidance or identify a bug in the code.

In summary, the error you're encountering with cov_flash is likely due to numerical instability or convergence issues. By adding a small constant to your shat matrix, increasing the maximum number of iterations, simplifying your data, and consulting package documentation, you should be able to troubleshoot and resolve the issue. If all else fails, don't hesitate to reach out to the package maintainers for further assistance.

I hope this comprehensive guide helps you navigate the intricacies of mashR and overcome the challenges you're facing. Happy analyzing, and may your data always reveal its secrets!