Questions & explanations
1. What is multi-omics integration? Give an example of why it is useful.
Multi-omics integration combines data from different omics types, like genomics (DNA) and proteomics (proteins), to get a fuller picture of a biological system. For example, by integrating gene expression and protein data, you can see if changes in RNA lead to changes in proteins. This helps find key drivers of diseases that might be missed by looking at one omics alone. Methods like CCA (canonical correlation analysis) find patterns shared between two datasets. NMF (non-negative matrix factorization) breaks down data into parts that represent biological processes. MOFA (multi-omics factor analysis) identifies hidden factors that explain variation across multiple omics. SNF (similarity network fusion) combines patient similarity networks from each omics into one network for clustering.
2. Give an example of a distance matrix that is additive but not ultrametric.
Consider three species with distances: d(A,B)=2, d(A,C)=4, d(B,C)=4. The largest two distances (4 and 4) are equal, so this triple is actually ultrametric. For a non-ultrametric additive example, use four species: d(A,B)=2, d(A,C)=6, d(A,D)=6, d(B,C)=6, d(B,D)=6, d(C,D)=4. This matrix is additive (fits a tree) but not ultrametric because for A,B,C the two largest distances (6 and 6) are equal, but for A,C,D the largest two (6 and 6) are equal? Actually check: A,C=6, A,D=6, C,D=4 → equal. So need a better example: d(A,B)=3, d(A,C)=5, d(B,C)=4 → largest two 5 and 4 not equal, so not ultrametric. But is it additive? For three species, any distances satisfying triangle inequality are additive. So yes, it is additive.
3. Compare the use of global vs. local explanations in genomic medicine.
Global explanations describe how the model behaves overall, like which genes are most important across all patients. For example, a global explanation might show that age and BRCA mutations are top predictors for breast cancer. Local explanations focus on a single patient, explaining why that specific person got a particular prediction. For instance, for one patient, local explanation might highlight a rare mutation that increased their risk. Global explanations help researchers understand general trends, while local explanations help doctors make individual treatment decisions. Both are useful, but local explanations are more actionable in clinical settings.
4. How can posterior decoding using the Forward-Backward algorithm improve alignment accuracy compared to Viterbi?
Posterior decoding computes the probability that each position in the sequence aligns to each match state, given the entire sequence. It then chooses the alignment that maximizes the expected accuracy, often by selecting the state with the highest posterior probability at each position. This can be more accurate than Viterbi because it considers all possible paths, not just the single best one. For example, if there are two nearly equally likely alignments, Viterbi picks one, while posterior decoding can produce a consensus that is more reliable. However, posterior decoding may not yield a valid global alignment (e.g., it might have inconsistent insertions).
5. In a PPI network, why might the Louvain algorithm be preferred over Girvan-Newman?
Louvain is much faster and can handle large PPI networks with thousands of proteins, while Girvan-Newman is computationally expensive and may be impractical for large networks. PPI networks often have tens of thousands of interactions, so speed matters. Louvain also produces a hierarchical view of communities, which can reveal modules at different resolutions. Girvan-Newman gives a dendrogram but requires choosing where to cut. Additionally, Louvain's modularity optimization often yields communities that correspond well to known biological complexes. However, Louvain can sometimes merge small communities, so validation with known annotations is important.
6. How can ubiquitinomics help identify new drug targets in cancer?
Cancer cells often have faulty protein degradation, leading to accumulation of oncogenes. Ubiquitinomics can reveal which proteins are not being properly ubiquitinated and degraded. For example, if a tumor suppressor is not ubiquitinated, it stays active? Actually, lack of ubiquitination might cause it to accumulate? Wait: tumor suppressors often need to be degraded? Let me correct: In cancer, some proteins that promote growth are overactive because they are not ubiquitinated and degraded. By finding which ubiquitin ligases are missing or which substrates are not tagged, researchers can target those pathways with drugs that restore proper ubiquitination.
7. Why is it challenging to apply XAI methods to deep learning models in genomics?
Deep learning models have many layers and millions of parameters, making them very complex. XAI methods like SHAP or LIME can be computationally expensive for such models, especially with high-dimensional genomic data (e.g., thousands of genes). Also, explanations may be unstable, meaning small changes in input lead to different explanations. In genomics, features are often correlated (e.g., genes in the same pathway), which can confuse explanation methods. Additionally, deep learning models may learn non-linear interactions that are hard to summarize simply. Despite these challenges, XAI is still valuable for gaining insights from deep genomic models.
8. How does maximum likelihood estimation for network parameters differ from Bayesian estimation?
MLE provides a single point estimate of parameters that maximizes the likelihood of the observed data. Bayesian estimation, in contrast, combines the likelihood with a prior distribution to obtain a posterior distribution over parameters. MLE does not incorporate prior information, while Bayesian methods can include prior beliefs. MLE yields a point estimate and standard errors based on asymptotic theory, whereas Bayesian inference provides full posterior intervals. MLE is often computationally simpler, but Bayesian methods can better handle small samples and complex models. The choice depends on the research goals and available prior knowledge.
9. What is a common challenge in maximum likelihood estimation for ERGMs, and how is it overcome?
The main challenge is the intractable normalizing constant, which depends on the parameters and requires summing over an enormous number of networks. This makes direct maximization impossible. A common solution is to use Markov chain Monte Carlo (MCMC) MLE, where the constant is estimated by simulating networks from the model. The algorithm iteratively updates parameters to match the observed statistics to the simulated ones. Another approach is maximum pseudo-likelihood estimation (MPLE), which approximates the likelihood by assuming edge independence. MPLE is faster but less accurate. MCMC MLE is the standard method for ERGM estimation.
10. How does the EM algorithm differ from Gibbs sampling for network inference?
EM is a deterministic optimization algorithm that finds point estimates of parameters, while Gibbs sampling is a stochastic MCMC method that generates samples from the posterior distribution. EM iteratively maximizes the expected log-likelihood, providing a single best-fit model. Gibbs sampling, on the other hand, explores the entire posterior and can quantify uncertainty. EM is typically faster and simpler for parameter estimation, but it does not provide uncertainty intervals. Gibbs sampling is more flexible for complex models but requires more computation. The choice depends on whether point estimates or full distributions are needed.
11. What is maximum likelihood estimation (MLE) for network models?
MLE is a method to find the parameter values that make the observed network most probable under a given model. For a network model like the exponential random graph model (ERGM), the likelihood is a function of the network's sufficient statistics, such as the number of edges or triangles. MLE finds the parameter vector that maximizes this likelihood. However, for many network models, the likelihood is intractable because it involves a normalizing constant that sums over all possible networks. Therefore, MLE often requires approximation techniques like MCMC or pseudo-likelihood. MLE provides consistent estimates under certain conditions.
12. What is Gibbs sampling and how is it used for network inference?
Gibbs sampling is a Markov chain Monte Carlo method that samples from a joint distribution by iteratively sampling each variable conditioned on the current values of all others. In network inference, it is used to learn the structure of a Bayesian network from data. For each node, the algorithm samples a new parent set given the data and the current parent sets of other nodes. Over many iterations, the samples converge to the posterior distribution over network structures. This allows estimation of edge probabilities and model averaging. Gibbs sampling is especially useful when direct sampling from the joint distribution is difficult.